Conversation with Merlin [email protected] · Sat Nov 25 2023

Hey, My teacher gave me some case studies for the subject Decision Making Under Uncertainty. I wanted to discuss it with you.

Of course, I'd be happy to help. Please go ahead and provide the details of the case studies you'd like to discuss, including any specific questions or areas you need assistance with.

The automotive industry is undergoing a transformative shift towards sustainability with electric vehicles gaining prominence. Examine in this scenario how the decision making is influencing the adoption and market dynamics of electric vehicles. Please give a detailed answer.

The transition from conventional vehicles (CVs) to electric vehicles (EVs) represents a significant shift in the automotive industry, influenced by various factors related to decision making. A study focused on understanding the factors driving the decision to purchase an EV among potential Chinese vehicle buyers provided valuable insights into the influence of decision making on the adoption and market dynamics of electric vehicles.

The study highlighted several key findings regarding the factors influencing the intention to purchase EVs. It revealed that males and individuals with higher household incomes showed a greater inclination towards purchasing EVs, both plug-in and battery electric vehicles. This suggests that demographic and socioeconomic factors play a significant role in the decision-making process concerning EV adoption.

Moreover, the study identified that a previous inclination to choose conventional vehicles had a negative impact on the willingness to purchase EVs. This highlights the influence of prior preferences and experiences on decision making in the context of transitioning to electric vehicles.

Furthermore, the type of EV also influenced purchase decisions. For instance, with Plug-in Hybrid EVs (PHEVs), the study found that the intention to obtain a driver's license within three years and the duration of owning a motorized vehicle negatively associated with PHEV purchase likelihood. On the other hand, the presence of electric bicycles in the household was positively linked to PHEV purchase intention. These findings illustrate how individual circumstances and lifestyle choices can influence the decision to adopt specific types of electric vehicles.

In the case of Battery EVs (BEVs), respondents with previous experience with EVs, either as a driver or passenger, were more likely to consider purchasing a BEV. Conversely, existing ownership of a driver's license and a higher purchase budget were associated with a reduced likelihood of purchasing a BEV. These findings underscore the impact of personal experiences, financial considerations, and familiarity with EV technology on the decision-making process related to electric vehicle adoption.

These insights shed light on the complex interplay of various factors in the decision-making process for adopting electric vehicles, including individual preferences, socioeconomic status, prior vehicle preferences, lifestyle choices, and personal experiences with EVs. Understanding these influences is crucial for stakeholders in the automotive industry to develop targeted strategies to encourage greater EV adoption and effectively navigate the evolving market dynamics.

In summary, decision making significantly influences the adoption and market dynamics of electric vehicles in the automotive industry, with individual preferences, socioeconomic factors, and prior experiences playing crucial roles in shaping consumer attitudes and behaviors towards EV adoption. Recognizing and addressing these factors is essential for shaping effective policies and strategies aimed at accelerating the transition to sustainable electric mobility.

Author / Affiliation / Email Article Menu Font Type: Arial Georgia Verdana Open AccessEditors ChoiceArticle 1 Virginia Department of Transportation, Richmond, VA 23219, USA 2 Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996, USA * Author to whom correspondence should be addressed. Received: 15 September 2021 / Revised: 11 October 2021 / Accepted: 16 October 2021 / Published: 23 October 2021 Abstract: The transition from conventional vehicles (CVs) to electric vehicles (EVs) could be promising in tackling environmental challenges in China. Using a sample of 1216 respondents in Beijing, China, our study intends to understand the underlying factors that drive the decision to purchase an EV among potential Chinese vehicle purchasers. We built two choice models to estimate vehicle purchase behavior and fuel choice. We found that males and having higher household income are associated with greater intention to purchase EVs (both plug-in and battery electric vehicles). However, a previous inclination to choose CV negatively impacted willingness to buy EVs. Between specific EV types, we found that Plug-in Hybrid EV (PHEV) purchase was negatively associated with plans to obtain a drivers license within three years and longer durations of having owned a motorized vehicle first. Yet, the number of electric bicycles in the household was positively associated with PHEV-purchase likelihood. For Battery EVs (BEV), we found that respondents who had previous experience with an EV (either as a driver or passenger) were more likely to purchase a BEV while existing ownership of a drivers license and a higher purchase budget reduced such possibility. Based on our findings, we recommend authorities continue to, or increasingly, provide direct monetary incentives to purchase EVs, and to provide EV driving and riding experience to customers, especially who are in the middle- and low-income vehicle purchasing groups, to improve the Chinese EV market relative to CVs. 1. IntroductionSince 2003, more than 250 million passenger cars have been sold in Chinas domestic market [1,2,3,4,5,6]. By 2050, the total vehicle stock could be as large as 530 to 623 million vehicles [7]. It is predicted that these vehicles will consume up to an equivalent of 564 million tons of oil and will emit up to 1636 metric tons of CO2 per year [8]. In 2012, China became the worlds largest emitter of greenhouse gases (GHG) [9]. In June 2015, China set a target to lower the carbon intensity of its GDP by 60-to-65% by 2030, from its 2005 values [10]. A strategy for solving a series of energy and environmental issues appears to be the adoption of electric vehicles (EVs) over conventional vehicles (CVs). The Chinese government aims to curb GHG emission in the road transportation sector by promoting new energy vehicles (NEVs) and regulating vehicle fuel economy [11,12].From 2010 to 2020, 4.92 million NEVs were sold in China, as shown in Figure 1 [1,6,13,14,15,16,17]. Although NEVs sales are increasing rapidly, the NEV market share was only 6.2% of the 20.18 million passenger cars sold in the domestic market in 2020. A large gap still exists between current NEV sales and stated goals [18]. Understanding potential consumers attitudes and perspective towards NEVs (mainly battery electric vehicles [BEVs] or plug-in hybrid electric vehicles [PHEVs]) is important, because it not only will support the decisions made by the government and private sectors, but also contributes to decision-makers overall understanding of market demand. A number of studies have pointed out how technological advancements and changes in policies may accelerate EV adoption in China [19,20]. Yet, as a country with a large percentage of e-bike users (over 250 million e-bikes have been sold since 1998 [3]), few studies have explored e-bike users experiences and their influence on the purchase of EVs, the purchasing of which is beset by similar characteristics and barriers

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1. IntroductionUsing statistical methods and data analysis based on grey systems theory, this research examines some factors affecting the adoption of electric vehicles (EVs), including vehicle characteristics, the level of sustainable development, and the impact of the COVID-19 pandemic on them. Today, most governments of developed countries promote using electric vehicles to reduce the concentration of pollutants, CO2, and other greenhouse gases [1]. They promote sustainable and efficient mobility, in particular through a variety of initiatives, mainly through tax subsidies, consumer shopping guides, or other specific measures, such as free public parking or free use of highways [2]. Since EVs are thought to reduce the problem of air pollution, consumers perception of this benefit could lead to greater adoption of EVs. Governments in auto-producing countries are eager to make their local manufacturers more competitive, as the auto industry has a major impact on employment and exports in these countries [3]. On the other hand, humanity is currently facing the challenge of a major transition from the current fossil fuel-based economy to a sustainable society within planetary boundaries [4].One of the most important aspects of this development is the reduction of CO2 emissions to reduce climate change, which requires major changes in many areas. One of the important contributions to these goals is undoubtedly the change from combustion engine vehicles to alternative fuel vehicles, including electric vehicles. Sustainability is a very urgent and global concern, and in this electric way, they believe electric vehicles can be a suitable option to solve this concern [5]. However, governments need a systematic view and a thorough understanding of the interrelationships between EVs adoptions and other aspects of sustainable development, including the economy, culture, environment, and public health, to formulate effective EVs policies [6]. As a result, discovering and understanding the factors affecting the demand for EVs and their interrelationships with different aspects of sustainable development is one of the first steps and the basic policy principles in this field. Through cross-national and systematic studies, we may be able to uncover certain generalizable principles as well as country-specific findings, which may then lead to different managerial and policy implications [7].Many researchers have shown that the adoption of electric vehicles and the development of such vehicles can have positive effects on various aspects of sustainable development, especially in the field of the environment [8]. However, there are many differences in this area, and many researchers believe that using electric vehicles will not help much in sustainable development [9]. On the other hand, Electric vehicle development is crucial for achieving sustainable development objectives, but the COVID-19 outbreak has impacted the market and posed hurdles for the entire sector. Quarantined laborers, extensive firm closures, disturbed global supply routes, and declining demand have all harmed the automotive industrys viability [10]. Hence, it is critical to understand the factors driving the demand for electric vehicles, which is the primary driver of this sector. The impact of the pandemic on this demand, in particular, can aid in better understanding future patterns [1].According to the description, many questions are raised about the different dimensions of EVs usage. The most important and main one is the relationship between sustainable development and EVs adoption rate. This research aims to investigate the interaction of electric vehicle adoption and sustainable development by considering its various aspects as a system and with a holistic view using grey econometric approaches. Therefore, the basic questions are what is the impact of sustainable development in different sectors on the adoption of electric vehicles? Will development, especially sust

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Battery electric vehicles (BEVs) have received increasing attention in recent years as BEV technical capabilities have rapidly developed. While many studies have attempted to investigate the societal impacts of BEV adoption, there is still a limited understanding of the extent to which widespread adoption of BEVs may affect both environmental and economic variables simultaneously. This study intends to address this research gap by conducting a comprehensive impact assessment of BEV adoption. Using demand estimates derived from a discrete choice experiment, the impact of various scenarios is evaluated using a computable general equilibrium model. Three drivers of BEV total cost of ownership are considered, namely, subsidy levels, cash incentives by manufacturers, and fuel costs. Furthermore, in light of current trends, improvements in BEV battery manufacturing productivity are considered. This research shows that changes in fuel price and incentives by manufacturers have relatively low impacts on GDP growth, but that the effect of subsidies on GDP and on BEV adoption is considerable, due to a stimulus effect on both household expenditures and on vehicle-manufacturing-related sectors. Productivity shocks moderately impact GDP but only affect BEV adoption in competitive markets. Conversely, the environmental impact is more nuanced. Although BEV adoption leads to decreases in tailpipe emissions, increased manufacturing activity as a result of productivity increases or subsidies can lead to growth in non-tailpipe emissions that cancels out some or all of the tailpipe emissions savings. This demonstrates that in order to achieve desired emissions reductions, policies to promote BEV adoption with subsidies should be accompanied by green manufacturing and green power generation initiatives.Transportation has overtaken power generation as the largest single source of greenhouse gas emissions in the United States. A key to reducing the carbon footprint of this sector is the widespread adoption of battery electric vehicles (BEVs), which, unlike hybrid-electric vehicles (HEVs) or plug-in HEVs (PHEVs), do not have an onboard combustion engine. Despite the increasing maturity of BEV technology, the share of BEVs in the US private fleet remains very low. One reason for this may be the fact that, on average, BEVs continue to be more expensive to purchase than conventional or hybrid vehicles of comparable size and type, although this is partially offset by the lower operating costs of BEVs (Breetz and Salon 2018). Since 2007, in an effort to boost BEV adoption, US federal and state governments have created tax incentives and fee rebate mechanisms in order to reduce the purchase price that end consumers pay for a BEV.There are currently several developments that could increase BEV adoption in the near future. First, there is a push by US policymakers to renew federal subsidies for BEVs since the previous federal tax credit, which offered purchasers of a new BEV up to $7500, is being phased out. The Clean Cars for America proposal would invest $454 billion into electrifying the US automobile fleet. Subsidies would start at $3000 per new vehicle purchase and could reach $5000$8000 according to some estimates. Second, an increasing number of automotive manufacturers is launching new BEV models with purchase prices that are comparable to upper-class conventional vehicles. As the number of BEVs on the market grows, manufacturers may offer cash incentives to potential buyers (Bjerkan et al 2016). Third, there are continued productivity improvements in battery manufacturing, with corresponding reductions in the cost of BEV batteries (Hensley et al 2012). Reductions of BEV purchase prices as a result of these factors would directly affect adoption rates, but they are overlaid with another relatively unpredictable factor, namely, the development of fuel prices. A lower fuel price may negatively affect BEV adoption by eroding the operating cost advantage

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A manager wants to boost the sales of a new iPhone. It will be launched next month. What strategies must be followed by him to achieve the objective? Explain this with the help of a decision tree and give a detailed answer

To create a decision tree to outline the strategies for boosting the sales of the new iPhone, we can consider several key factors and potential actions that the manager could take. Let's start by visualizing the decision-making process in the form of a decision tree:

  1. Root Node: Objective

    • Boost iPhone Sales
  2. Branches: Strategies

    • Online Marketing
    • In-Store Promotions
    • Partnerships with Telecom Companies
  3. Leaf Nodes: Potential Outcomes

    • Increased Brand Awareness
    • Higher Footfall in Stores
    • Enhanced Product Visibility
    • Expanded Customer Base
    • Boosted Sales Revenue

Now, let's delve into the specific strategies and potential outcomes for each branch:

Online Marketing

  • Branch: Social Media Campaign
    • Outcome: Increased Brand Awareness
  • Branch: Influencer Partnerships
    • Outcome: Expanded Customer Base
  • Branch: Targeted Ad Campaigns
    • Outcome: Enhanced Product Visibility
  • Branch: Promotional Offers on E-commerce Platforms
    • Outcome: Boosted Sales Revenue

In-Store Promotions

  • Branch: Product Demos and Test Units
    • Outcome: Higherfall in Stores
  • Branch: Limited-Time Offers
    • Outcome: Enhanced Product Visibility
  • Branch: Cross-Promotion with Accessories
    • Outcome: Increased Customer Spending

Partnerships with Telecom Companies

  • Branch: Exclusivity Deals
    • Outcome: Expanded Customer Base
  • **Branch: Bundled Data and Calling Plans - Outcome: Boosted Sales Revenue
  • Branch: Joint Marketing Campaigns
    • Outcome: Increased Brand Awareness

By using this decision tree, the manager can weigh the potential outcomes of each strategy and make informed decisions on where to allocate resources and focus efforts. For instance, if the goal is to increase brand awareness and expand the customer base, the manager might prioritize social media campaigns, influencer partnerships, and exclusivity deals with telecom companies.

The decision tree provides a structured framework for evaluating potential strategies and their associated outcomes, empowering the manager to make data-driven decisions aimed at effectively boosting the sales of the new iPhone.

In summary, to meet the objective of boosting the sales of the new iPhone, the manager should consider leveraging online marketing, in-store promotions, and partnerships with telecom companies, with each strategy leading to specific potential outcomes that contribute to achieving the overall sales objective.

Ever wondered how to break down and examine your decisions so well that you can determine potential outcomes, assess various risks and ultimately predict your chances for success? Thats where a decision tree comes in its a handy diagram to improve your decision-making abilities and help prevent undesirable outcomes. In this step-by-step guide, well explain what a decision tree is, how you can visualize your decision-making process effectively using one and how you can make a decision tree easily using Venngage. Click to jump ahead: What is a decision tree? Why should you make a decision tree? How to make a decision tree Decision tree examples 3 Decision tree best practices What is a decision tree? A decision tree is a specific type of flowchart (or flow chart) used to visualize the decision-making process by mapping out different courses of action, as well as their potential outcomes. Take a look at this decision tree example. There are a few key sections that help the reader get to the final decision. Decision trees typically consist of three different elements: Root Node: Thetop-level node represents the ultimate objective or big decision youre trying to make. Branches: Branches, which stem from the root, represent different options or courses of action that are available when making a particular decision. They are most commonly indicated with an arrow line and often include associated costs, as well as the likelihood to occur. Leaf Node: The leaf nodes which are attached at the end of the branches represent possible outcomes for each action. There are typically two types of leaf nodes: square leaf nodes, which indicate another decision to be made, and circle leaf nodes, which indicate a chance event or unknown outcome. When formed together, these elements loosely resemble a tree, which is where the diagram gets its name. This gradient decision tree diagram example shows you how it works. Although you can certainly make a case for Grandmother Willows age-old advice to let your spirits guide you, sometimes a more formalized and calculated approach is necessary. This is why decision trees are so effective. Just so you know, some of our templates are free to use and some require a small monthly fee. Sign up is always free, as is access to Venngages online drag-and-drop editor. With Venngages decision tree maker, you can use multiple colors to represent different types of decisions and possible outcomes. Why should you make a decision tree? Now that you know exactly what a decision tree is, its time to consider why this type of flowchart is so effective for decision making. Decision trees, like problem-solving flowcharts, have several advantages due to their structured visual approach. Here are some of the perks: 1. Decision trees are flexible Decision trees are non-linear, which means theres a lot more flexibility to explore, plan and predict several possible outcomes to your decisions, regardless of when they actually occur. For example, if youre an HR professional, you can choose decision trees to help employees determine their ideal growth path based on skills, interests and traits, rather than timeline. On the other hand, if youre a product manager and are considering launching a new product line, you can use a decision tree flow chart to determine the best course of action. Using a tool like Venngages drag-and-drop decision tree maker makes it easy to go back and edit your decision tree as new possibilities are explored. 2. Decision trees effectively communicate complex processes Decision tree diagrams visually demonstrate cause-and-effect relationships, providing a simplified view of a potentially complicated process. Decision trees are also straightforward and easy to understand, even if youve never created one before. The decision tree diagram template below is a good example of a complex process thats easy to understand as its broken down and visualized in simpler steps: Design tip: If youd like to present your d

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Decision trees are the predictive models or visual/analytical Decision Support Tools that utilize a tree-like model of decisions in which predictions are made on the ground of a series of decisions. It is a method of displaying an algorithm that just comprises conditional control statements. A decision tree identifies your big decision as to the root, associated courses of action as the branches, and the possible outcomes as the leaves to let you have a birds-eye view of your decision-making procedure. The most common use of decision trees occurs in operation research or decision analysis for identifying a strategy that can lead to the goal of accomplishment. Decision trees are made through a flow-chart like structure whose- Internal node symbolizes a test on an attribute Each branch symbolizes the outcome of the test Each leaf node symbolizes a class label The paths from the root to leaf symbolizes classification rules This post will take you deep into the world of decision trees and help you understand how they can alleviate your tasks of decisions making most conveniently and effectively possible. So, without any further ado, let us start with the introduction of this flow-chart like structures- Table of Contents IntroductionWhat Are Decision Trees?Why use Decision Trees? Their AdvantagesFeatures of a Good Decision TreeTypes of Nodes How to Draw a Decision Tree?Step 1: Start with the primary decisionStep 2: Add chance nodes and decisions nodesStep 3: Go on expanding this tree until you reach an endpointRole of Decision Trees in Data Mining and Machine Learning Introduction Decision-making is one of the toughest tasks in life. We encounter robust points where we need to choose from the various options available. We need to make decisions for the betterment of us and the people around us. In personal as well as in professional lives, we need to make such decisions. We need to choose the path we want to take and justify the same. In our personal lives, we can make decisions based on emotions and states of mind. However, this cannot be done in the professional sphere. Here, the decisions need to be made based on a thorough knowledge of the topic and proper brainstorming with the rest of the colleagues. The process of decision-making can be made easier using decision trees. For the professionals working in business management, public health, and health economics, concepts associated with decision trees, utility functions, influence diagrams, and other decision analysis tools are of great significance. Due to their graphical structure, decision-trees are considered easy to understand and explain different business decisions, analytics, and operations. From predictive modeling to data exploration stages to understanding variable interactions, decision trees are of great use. Let us dig deeper and define this tree structure of decision making more lucidly- What Are Decision Trees? Trees are symbolic of life. They have many implications and variations of meanings. Even in decision analysis, the tree has an analogy. Reaching conclusions and making decisions can be achieved by representing situations in the format of a tree. A decision tree is the diagrammatic representation of a decision-making process. It maps out all the possible outcomes of a decision and then helps you choose the best path. A decision tree generally starts with a single node. This node then splits into different branches, which represent various options available along with their consequences. The consequences are weighed primarily based on probabilities, costs, and benefits. Why use Decision Trees? Their Advantages Decision trees make the process of making decisions pretty simple. It gives you the liberty of weighing different pros and cons and zeroing down on the best possible decision. 1. Flexibility It is one of the essential qualities of a decision tree. You can consider various decisions and weigh the positive and negative points of each of these probable d

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Decision trees have become one of the most popular tools in business analytics. They are a graphical representation of a decision-making process and help businesses make more informed decisions. Decision tree diagrams allow for faster and more accurate data analysis by visualizing all the available options. This article will discuss decision trees and how they can be used in business analytics. What is a Decision Tree in Business Analytics? A decision tree is a powerful tool used in business analytics to help in a robust decision-making process. Graphical representations of potential outcomes based on a series of decisions and decision trees can be used to identify the best course of action for any situation. Moreover, decision trees provide an efficient and practical approach to complex data sets. By leveraging decision tree algorithms, organizations can gain valuable insights into their data and make informed decisions that lead to better outcomes. They help businesses assess risks, understand the impact of their choices, and optimize their operations. By understanding the different factors that could influence an outcome, decision tree models can provide valuable insights into how organizations should act and how they will benefit from each decision. The Decision Tree and How it Works Decision trees are made up of nodes and branches that represent different stages in the decision-making process. Thus, it can identify which choices will lead to successful outcomes, allowing organizations to make data-based decisions. Decision trees are built through several steps: By gathering data related to the decision By using algorithms such as Classification and Regression Trees (CART) or Random Forest (RF) By analyzing the data By creating a decision tree model The decision tree model allows for easy visualization of potential outcomes based on different decisions taken. Benefits of Using a Decision Tree Decision trees can be useful in a variety of ways. Decision trees are used to predict the outcomes of different scenarios. By weighing the available data, Decision trees can provide insights into which decisions will lead to successful outcomes and which may result in undesirable results They can also be used for decision optimization. Decision trees allow organizations to identify the best course of action when faced with multiple options Decision trees are also helpful in assessing risks and understanding potential impacts on an organizations operations They help companies make informed decisions based on data analysis rather than intuition or guesswork alone How to Make a Decision Tree Start your tree with the main idea or the big decision you must make. This is called the root node From there, create branches of all possible outcomes based on the decision made Keep expanding each branch till you reach an end point beyond which no more decisions are possible. Evaluate each of the outcomes The key to making good use of decision trees is to ensure that all potential impacts are included in the analysis. That means considering the immediate costs or benefits of taking a certain course of action and its long-term effects on your business goals. Once you set up your decision tree, its time to analyze each branch. Ask yourself: If I take this route, what are the pros and cons? Are there any risks that I need to consider? What is the expected outcome of taking this path? You can determine which option provides the greatest benefit or least risk by weighing these factors. The Best Tools to Make a Decision Tree There are several tools available to help you make better decisions. Each tool offers unique advantages, so finding one that best fits your needs is important. Here are a few of the most popular decision tree tools: Microsoft Visio This program is designed specifically for creating visual representations of data. It allows you to create complex decision trees easily and provides helpful features like drag-and-drop nodes and automate

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What is meant by probabilistic models in decision making under uncertainty ?

Probabilistic models in decision making under uncertainty refer to mathematical frameworks and computational approaches used to make decisions when facing situations with incomplete or uncertain information. These models incorporate the concept of probability to quantify and manage uncertainty, allowing decision-makers to assess the likelihood of different outcomes and make informed choices based on these probabilities.

In the context of neuroscience and artificial intelligence, probabilistic models are utilized to understand how the human brain or artificial systems navigate decision-making processes when faced with uncertain or ambiguous information. For example, partially observable Markov decision processes (POMDPs) are a common type of probabilistic model used to analyze decision-making under uncertainty, particularly in settings where the decision-maker has limited information about the environment or the outcomes of their actions.

By integrating probabilistic models into decision-making processes, individuals or intelligent systems can account for uncertainty and make more rational and informed choices, considering the likelihood of various outcomes and potential risks associated with different actions. These models are essential for addressing real-world scenarios where uncertainty is prevalent, enabling more robust and adaptive decision-making in complex dynamic environments.

Loading metrics Open Access Peer-reviewed Research Article Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty Rajesh P. N. Rao Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty Yanping Huang, Rajesh P. N. Rao Published: January 22, 2013 https://doi.org/10.1371/journal.pone.0053344 Figures AbstractA key problem in neuroscience is understanding how the brain makes decisions under uncertainty. Important insights have been gained using tasks such as the random dots motion discrimination task in which the subject makes decisions based on noisy stimuli. A descriptive model known as the drift diffusion model has previously been used to explain psychometric and reaction time data from such tasks but to fully explain the data, one is forced to make ad-hoc assumptions such as a time-dependent collapsing decision boundary. We show that such assumptions are unnecessary when decision making is viewed within the framework of partially observable Markov decision processes (POMDPs). We propose an alternative model for decision making based on POMDPs. We show that the motion discrimination task reduces to the problems of (1) computing beliefs (posterior distributions) over the unknown direction and motion strength from noisy observations in a Bayesian manner, and (2) selecting actions based on these beliefs to maximize the expected sum of future rewards. The resulting optimal policy (belief-to-action mapping) is shown to be equivalent to a collapsing decision threshold that governs the switch from evidence accumulation to a discrimination decision. We show that the model accounts for both accuracy and reaction time as a function of stimulus strength as well as different speed-accuracy conditions in the random dots task. Citation: Huang Y, Rao RPN (2013) Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty. PLoS ONE 8(1): e53344. https://doi.org/10.1371/journal.pone.0053344Editor: Floris P. de Lange, Radboud University Nijmegen, the Netherlands Received: October 12, 2012; Accepted: November 27, 2012; Published: January 22, 2013Copyright: 2013 Rao, Huang. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Funding: This project was supported by the National Science Foundation (NSF) Center for Sensorimotor Neural Engineering (EEC-1028725), NSF grant 0930908, Army Research Office (ARO) award W911NF-11-1-0307, and Office of Naval Research (ONR) grant N000140910097. YH is a Howard Hughes Medical Institute International Student Research fellow. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Competing interests: The authors have declared that no competing interests exist. IntroductionAnimals are constantly confronted with the problem of making decisions given noisy sensory measurements and incomplete knowledge of their environment. Making decisions under such circumstances is difficult because it requires (1) inferring hidden states in the environment that are generating the noisy sensory observations, and (2) determining if one decision (or action) is better than another based on uncertain and delayed reinforcement. Experimental and theoretical studies [1][6] have suggested that the brain may implement an approximate form of Bayesian inference for solving the hidden state problem. However, these studies typically do not address the question of how probabilistic representations of hidden state are employed in action selection based on reinforcement. Daw, Dayan and their colleagues [7], [8] explored the suitability of decision theoretic and reinforcement learning models in understanding several well-known neurobiological experiments. Bogacz and col

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Probabilistic Decision MakingArtificial Intelligence: UncertaintyK.B. Laskey, T.S. Levitt, in International Encyclopedia of the Social & Behavioral Sciences, 20012 Graphical Networks of AlternativesSeveral related trends coalesced into a shift in AI community consensus in the 1980s. One trend was the resurgence of interest in connectionist models (e.g., Rumelhart and McClelland 1985). The connectionist movement, which includes the development of neural networks (see Neural Networks and Related Statistical Latent Variable Models; Neural Networks: Biological Models and Applications), lent strong support to the thesis that fundamentally numerical approaches could give rise to computational systems that exhibited intelligent behavior. Connectionism also sparked interest in symbol-level representations that integrated smoothly with numerical sub-symbolic representations, especially for reasoning from perceptual signals to higher level abstractions.The development of this research direction culminated in a series of breakthroughs in automated inference and the development of graphical models and associated algorithms for automated probabilistic decision making (Pearl 1988, D'Ambrosio 1999 and Bayesian Graphical Models and Networks and Latent Structure and Casual Variables). Graphical models combine qualitative rule-like and object-like knowledge structures with quantitative measures of the uncertainty associated with inferences. Alternative inferences are represented in all the possible chains of reasoning implicit in the graphical structure, and need not be explicitly enumerated. The loosely coupled, modular architecture of graphical models enables the creation of knowledge representations and tractable algorithms for inference, planning, and learning for realistically complex problems. Directed graphical probability models are called Bayesian networks and undirected graphical probability models are called Markov graphs (Pearl 1988, Jensen 1996). Shafer and Shenoy combined Dempster-Shafer calculus and Bayesian network concepts to build even more general knowledge structures out of graphs encoding dependencies among variables, and proved the existence of a universal representation for automating inductive inference (Shafer and Shenoy 1990). Graphical models became increasingly popular as a common framework, independent of uncertainty calculus, for representing the loosely coupled dependency relationships that give rise to the modular representations that are basic to AI. Graphical models are also useful for expressing the causal relationships that underlie the ability to predict the effects of manipulations and form effective plans (Pearl 2000, Spirtes et al. 2000).Many uncertain attributes of knowledge, including belief, credibility and completeness, can be expressed using graphical models and their related computational calculus. The most prominent issue in the field of uncertainty in AI has been the representation and reasoning about belief in alternatives given uncertain evidence. More recently there has been increased focus on planning and action, as well as approaches integrating perception to symbolic-level reasoning, planning, and action.Read full chapterURL:https://www.sciencedirect.com/science/article/pii/B0080430767003958The Present, Past, and Future of Research on Aging and Decision MakingJoNell Strough, ... Thomas M. Hess, in Aging and Decision Making, 2015Neurobiological MechanismsThe chapters in this section provide an overview of current knowledge about the neurobiological mechanisms behind age-related shifts in decision making and highlight emerging research methods and directions in this rapidly developing field. Beas, Setlow, Samanez-Larkin, and Bizon argue that animal models provide unique advantages for studying the influence of brain aging on decision processes since they offer high levels of experimenter control over contextual variables and prior experiencefactors that are often difficult to account for in hu

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Search modesAbout 12,50,00,000 results (0.41 seconds) Search Resultsby I Kramosil2001 Therefore we begin our explanation using informal terms charged by some extra-mathematical semantics, but our intention will be to get back to a formalized...Graphical models combine qualitative rule-like and object-like knowledge structures with quantitative measures of the uncertainty associated with inferences.by MJ Kochenderfer2015 This chapter focuses on the representation of uncertainty as a probability distribution. Real-world problems require reasoning about distributions over many...by T Badings2023Cited by 5 Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation.by RD Shachter2013Cited by 220 Many important problems can be addressed using decision analysis, a probabilistic approach to making decisions under uncertainty. The long established method...by MJ Kochenderfer2015Cited by 710 The aim of the first part of the book is to familiarize the reader with the foundations of probabilistic models and decision theory. The second part of...349 pagesMany important problems involve decision making under uncertaintythat is, choosing actions based on often imperfect observations, with unknown outcomes.by M Pergler2008Cited by 33 Putting probabilistic modeling into action As we have stated, probabilistic modeling is a mechanism for harnessing information about uncertainties to enable...21 pagesby Y Huang2013Cited by 43 We make two main assumptions in the POMDP model. First, the animal uses Bayes rule to update its belief about the hidden state after each new...by T Badings2023Cited by 5 The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior.Page Navigation

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What is meant by probabilistic models in decision making under uncertainty ?

Probabilistic models in decision making under uncertainty refer to mathematical frameworks and computational approaches that incorporate the concept of probability to quantify and manage uncertainty. These models are utilized in diverse fields such as machine learning, cognitive computing, automation, and artificial intelligence to address decision-making processes when faced with incomplete or ambiguous information.

In the context of machine learning, probabilistic models are based on statistical codes applied to data analysis, forming one of the fundamental approaches in this field. models utilize stochastic, or random, variables to represent unobserved elements, and capture the interdependence between variables through joint probability distributions By doing so, they provide a robust foundation for learning and embracing uncertainties inherent in the data.

The key characteristic of probabilistic models is their ability to offer a natural way to reason about inconsistencies present in the data, making it easier to handle uncertainties. Furthermore, these models can be constructedarchically to build complex structures from basic elements, highlighting their versatility and adaptability in addressing diverse decision-making scenarios.

Overall, probabilistic models contribute significantly to decision making under uncertainty by providing a structured approach to representing and managing uncertainties and offering a natural framework for making informed decisions based on probabilities and statistical analysis.

Probabilistic Decision MakingArtificial Intelligence: UncertaintyK.B. Laskey, T.S. Levitt, in International Encyclopedia of the Social & Behavioral Sciences, 20012 Graphical Networks of AlternativesSeveral related trends coalesced into a shift in AI community consensus in the 1980s. One trend was the resurgence of interest in connectionist models (e.g., Rumelhart and McClelland 1985). The connectionist movement, which includes the development of neural networks (see Neural Networks and Related Statistical Latent Variable Models; Neural Networks: Biological Models and Applications), lent strong support to the thesis that fundamentally numerical approaches could give rise to computational systems that exhibited intelligent behavior. Connectionism also sparked interest in symbol-level representations that integrated smoothly with numerical sub-symbolic representations, especially for reasoning from perceptual signals to higher level abstractions.The development of this research direction culminated in a series of breakthroughs in automated inference and the development of graphical models and associated algorithms for automated probabilistic decision making (Pearl 1988, D'Ambrosio 1999 and Bayesian Graphical Models and Networks and Latent Structure and Casual Variables). Graphical models combine qualitative rule-like and object-like knowledge structures with quantitative measures of the uncertainty associated with inferences. Alternative inferences are represented in all the possible chains of reasoning implicit in the graphical structure, and need not be explicitly enumerated. The loosely coupled, modular architecture of graphical models enables the creation of knowledge representations and tractable algorithms for inference, planning, and learning for realistically complex problems. Directed graphical probability models are called Bayesian networks and undirected graphical probability models are called Markov graphs (Pearl 1988, Jensen 1996). Shafer and Shenoy combined Dempster-Shafer calculus and Bayesian network concepts to build even more general knowledge structures out of graphs encoding dependencies among variables, and proved the existence of a universal representation for automating inductive inference (Shafer and Shenoy 1990). Graphical models became increasingly popular as a common framework, independent of uncertainty calculus, for representing the loosely coupled dependency relationships that give rise to the modular representations that are basic to AI. Graphical models are also useful for expressing the causal relationships that underlie the ability to predict the effects of manipulations and form effective plans (Pearl 2000, Spirtes et al. 2000).Many uncertain attributes of knowledge, including belief, credibility and completeness, can be expressed using graphical models and their related computational calculus. The most prominent issue in the field of uncertainty in AI has been the representation and reasoning about belief in alternatives given uncertain evidence. More recently there has been increased focus on planning and action, as well as approaches integrating perception to symbolic-level reasoning, planning, and action.Read full chapterURL:https://www.sciencedirect.com/science/article/pii/B0080430767003958The Present, Past, and Future of Research on Aging and Decision MakingJoNell Strough, ... Thomas M. Hess, in Aging and Decision Making, 2015Neurobiological MechanismsThe chapters in this section provide an overview of current knowledge about the neurobiological mechanisms behind age-related shifts in decision making and highlight emerging research methods and directions in this rapidly developing field. Beas, Setlow, Samanez-Larkin, and Bizon argue that animal models provide unique advantages for studying the influence of brain aging on decision processes since they offer high levels of experimenter control over contextual variables and prior experiencefactors that are often difficult to account for in hu

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Probabilistic Models are one of the most important segments in Machine Learning, which is based on the application of statistical codes to data analysis. This dates back to one of the first approaches of machine learning and continues to be widely used today. Unobserved variables are seen as stochastic in probabilistic models, and interdependence between variables is recorded in a joint probability distribution. It provides a foundation for embracing learning for what it is. The probabilistic framework outlines the approach for representing and deploying model reservations. In scientific data analysis, predictions play a dominating role. Their contribution is also critical in machine learning, cognitive computing, automation, and artificial intelligence. These probabilistic models have many admirable characteristics and are quite useful in statistical analysis. They make it quite simple to reason about the inconsistencies present across most data. In fact, they may be built hierarchically to create complicated models from basic elements. One of the main reasons why probabilistic modeling is so popular nowadays is that it provides natural protection against overfitting and allows for completely coherent inferences over complex forms from data. What Is Probabilistic Modeling? Probabilistic modeling is a statistical approach that uses the effect of random occurrences or actions to forecast the possibility of future results. It is a quantitative modeling method that projects several possible outcomes that might even go beyond what has happened recently. Probabilistic modeling considers new situations and a wide range of uncertainty while not underestimating dangers. The three primary building blocks of probabilistic modeling are adequate probability distributions, correct use of input information for these distribution functions, and proper accounting for the linkages and interactions between variables. The downside of the probabilistic modeling technique is that it needs meticulous development, a process that depends on several assumptions and large input data. Importance of Probabilistic ML Models One of the most significant advantages of the probabilistic modeling technique is that it provides a comprehensive understanding of the uncertainty associated with predictions. Using this method, we can quickly determine how confident any mobile learning model is and how accurate its prediction is. An example of a probabilistic classifier that assigns a probability of 0.9 to the 'Dog' class suggests the classifier is quite confident that the animal in the image is a dog. It is heavily dependent on the opposing concepts of uncertainty and confidence. In reality, it is extremely helpful when used to key machine learning applications such as illness detection and autonomous driving. Furthermore, probabilistic outcomes would be beneficial for many Machine Learning-related approaches, such as Active Learning. Examples of Probabilistic Models Generalised Linear Models One of the better applications of probabilistic modeling is generalised linear models. This vastly generalises linear regression using exponential families. The expected return of a specified unknown factor (the response variable, a random variable) is predicted by ordinary linear regression as a linear combination of a collection of observed values. This means that each change in a predictor causes a change in the response variable (i.e. a linear response model). This is useful when the response variable may fluctuate endlessly in either direction or when any number varies by a relatively modest amount compared to the variance in the predictive factors, such as human heights. These assumptions, however, are incorrect for several types of response variables. Straight Line Modeling A straight-line probabilistic model is sometimes known as a linear regression model or a best-fit straight line. It's a best-fit line since it tries to reduce the size of all the different error comp

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An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance.Many important problems involve decision making under uncertaintythat is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance.Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance.Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

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How probabilistic models help making in decision making under uncertainty? Give a very detailed answer.

Probabilistic models play a crucial role in decision making under uncertainty by providing a systematic framework to analyze and navigate ambiguous incomplete information. These models are particularly valuable in complex and dynamic environments where the outcome of a decision is uncertain, and the decision-maker needs to assess and manage the associated risks effectively. Here's a detailed explanation of how probabilistic models aid in decision making under uncertainty:

  1. Quantifying Uncertainty: Probabilistic models enable decision-makers to quantify the level of uncertainty associated with different variables or outcomes. By incorporating probabilities into the decision-making process, these models offer a clear understanding of the likelihood of various scenarios, allowing for more informed assessments and decisions.

  2. Risk Assessment and Management: Through probabilistic modeling, decision-makers can assess the potential risks and their associated probabilities. This empowers them to make risk-aware, considering both the potential gains and losses in uncertain situations. By evaluating the range of possible outcomes and their likelihood, decision-makers can implement strategies to mitigate risks effectively.

  3. Adaptive Decision-Making: In dynamic and uncertain environments, probabilistic models facilitate adaptive decision-making. These models allow decision-makers to update their assessments and strategies as new information becomes available, thereby enabling them to dynamically respond to changing conditions and evolving uncertainties.

  4. Optimal Resource Allocation: Probabilistic models aid in optimizing resource allocation by considering the probabilities of different outcomes. Decision can prioritize and allocate resources based on the likelihood of specific scenarios, maximizing the efficiency and effectiveness of their decisions in uncertain contexts.

  5. Scenario Analysis and Sensitivity Testing: Probabilistic models allow decision-makers to conduct scenario analysis and sensitivity testing. By simulating various scenarios and assessing their probabilities, decision-makers can evaluate the robustness of their decisions and strategies under different conditions, leading to more resilient and well-informed decision-making processes.

  6. Communicating Uncertainty: Probabilistic models provide a formalized way to communicate uncertainty effectively. Decision-makers can use probabilistic representations to convey the level of uncertainty associated with different aspects of a decision, enabling transparent and informative communication within organizations or with stakeholders.

In summary, probabilistic models contribute to decision making under uncertainty by quantifying and managing uncertainty, assessing and mitigating risks, enabling adaptive decision, optimizing resource allocation, facilitating scenario analysis, and enhancing communication of uncertainty. By leveraging probabilistic models, decision-makers can navigate uncertain situations with greater clarity and confidence, leading to more robust and effective decision-making processes.

Loading metrics Open Access Peer-reviewed Research Article Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty Rajesh P. N. Rao Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty Yanping Huang, Rajesh P. N. Rao Published: January 22, 2013 https://doi.org/10.1371/journal.pone.0053344 Figures AbstractA key problem in neuroscience is understanding how the brain makes decisions under uncertainty. Important insights have been gained using tasks such as the random dots motion discrimination task in which the subject makes decisions based on noisy stimuli. A descriptive model known as the drift diffusion model has previously been used to explain psychometric and reaction time data from such tasks but to fully explain the data, one is forced to make ad-hoc assumptions such as a time-dependent collapsing decision boundary. We show that such assumptions are unnecessary when decision making is viewed within the framework of partially observable Markov decision processes (POMDPs). We propose an alternative model for decision making based on POMDPs. We show that the motion discrimination task reduces to the problems of (1) computing beliefs (posterior distributions) over the unknown direction and motion strength from noisy observations in a Bayesian manner, and (2) selecting actions based on these beliefs to maximize the expected sum of future rewards. The resulting optimal policy (belief-to-action mapping) is shown to be equivalent to a collapsing decision threshold that governs the switch from evidence accumulation to a discrimination decision. We show that the model accounts for both accuracy and reaction time as a function of stimulus strength as well as different speed-accuracy conditions in the random dots task. Citation: Huang Y, Rao RPN (2013) Reward Optimization in the Primate Brain: A Probabilistic Model of Decision Making under Uncertainty. PLoS ONE 8(1): e53344. https://doi.org/10.1371/journal.pone.0053344Editor: Floris P. de Lange, Radboud University Nijmegen, the Netherlands Received: October 12, 2012; Accepted: November 27, 2012; Published: January 22, 2013Copyright: 2013 Rao, Huang. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Funding: This project was supported by the National Science Foundation (NSF) Center for Sensorimotor Neural Engineering (EEC-1028725), NSF grant 0930908, Army Research Office (ARO) award W911NF-11-1-0307, and Office of Naval Research (ONR) grant N000140910097. YH is a Howard Hughes Medical Institute International Student Research fellow. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Competing interests: The authors have declared that no competing interests exist. IntroductionAnimals are constantly confronted with the problem of making decisions given noisy sensory measurements and incomplete knowledge of their environment. Making decisions under such circumstances is difficult because it requires (1) inferring hidden states in the environment that are generating the noisy sensory observations, and (2) determining if one decision (or action) is better than another based on uncertain and delayed reinforcement. Experimental and theoretical studies [1][6] have suggested that the brain may implement an approximate form of Bayesian inference for solving the hidden state problem. However, these studies typically do not address the question of how probabilistic representations of hidden state are employed in action selection based on reinforcement. Daw, Dayan and their colleagues [7], [8] explored the suitability of decision theoretic and reinforcement learning models in understanding several well-known neurobiological experiments. Bogacz and col

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Probabilistic Decision MakingArtificial Intelligence: UncertaintyK.B. Laskey, T.S. Levitt, in International Encyclopedia of the Social & Behavioral Sciences, 20012 Graphical Networks of AlternativesSeveral related trends coalesced into a shift in AI community consensus in the 1980s. One trend was the resurgence of interest in connectionist models (e.g., Rumelhart and McClelland 1985). The connectionist movement, which includes the development of neural networks (see Neural Networks and Related Statistical Latent Variable Models; Neural Networks: Biological Models and Applications), lent strong support to the thesis that fundamentally numerical approaches could give rise to computational systems that exhibited intelligent behavior. Connectionism also sparked interest in symbol-level representations that integrated smoothly with numerical sub-symbolic representations, especially for reasoning from perceptual signals to higher level abstractions.The development of this research direction culminated in a series of breakthroughs in automated inference and the development of graphical models and associated algorithms for automated probabilistic decision making (Pearl 1988, D'Ambrosio 1999 and Bayesian Graphical Models and Networks and Latent Structure and Casual Variables). Graphical models combine qualitative rule-like and object-like knowledge structures with quantitative measures of the uncertainty associated with inferences. Alternative inferences are represented in all the possible chains of reasoning implicit in the graphical structure, and need not be explicitly enumerated. The loosely coupled, modular architecture of graphical models enables the creation of knowledge representations and tractable algorithms for inference, planning, and learning for realistically complex problems. Directed graphical probability models are called Bayesian networks and undirected graphical probability models are called Markov graphs (Pearl 1988, Jensen 1996). Shafer and Shenoy combined Dempster-Shafer calculus and Bayesian network concepts to build even more general knowledge structures out of graphs encoding dependencies among variables, and proved the existence of a universal representation for automating inductive inference (Shafer and Shenoy 1990). Graphical models became increasingly popular as a common framework, independent of uncertainty calculus, for representing the loosely coupled dependency relationships that give rise to the modular representations that are basic to AI. Graphical models are also useful for expressing the causal relationships that underlie the ability to predict the effects of manipulations and form effective plans (Pearl 2000, Spirtes et al. 2000).Many uncertain attributes of knowledge, including belief, credibility and completeness, can be expressed using graphical models and their related computational calculus. The most prominent issue in the field of uncertainty in AI has been the representation and reasoning about belief in alternatives given uncertain evidence. More recently there has been increased focus on planning and action, as well as approaches integrating perception to symbolic-level reasoning, planning, and action.Read full chapterURL:https://www.sciencedirect.com/science/article/pii/B0080430767003958The Present, Past, and Future of Research on Aging and Decision MakingJoNell Strough, ... Thomas M. Hess, in Aging and Decision Making, 2015Neurobiological MechanismsThe chapters in this section provide an overview of current knowledge about the neurobiological mechanisms behind age-related shifts in decision making and highlight emerging research methods and directions in this rapidly developing field. Beas, Setlow, Samanez-Larkin, and Bizon argue that animal models provide unique advantages for studying the influence of brain aging on decision processes since they offer high levels of experimenter control over contextual variables and prior experiencefactors that are often difficult to account for in hu

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References Achiam, J., Held, D., Tamar, A., Abbeel, P.: Constrained policy optimization. In: ICML. Proceedings of Machine Learning Research, vol.70, pp.2231. PMLR, mlr.press (2017) Google Scholar Alegre, L.N., Bazzan, A.L.C., da Silva, B.C.: Minimum-delay adaptation in non-stationary reinforcement learning via online high-confidence change-point detection. In: AAMAS, pp.97105. ACM, New York (2021) Google Scholar Alshiekh, M., Bloem, R., Ehlers, R., Knighofer, B., Niekum, S., Topcu, U.: Safe reinforcement learning via shielding. In: AAAI, pp.26692678. AAAI Press, Menlo Park (2018) Google Scholar Altman, E.: Constrained Markov Decision Processes: Stochastic Modeling. Routledge, London (1999) MATH Google Scholar Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proc. IEEE 88(7), 971984 (2000) Article Google Scholar Amato, C.: Decision-making under uncertainty in multi-agent and multi-robot systems: Planning and learning. In: IJCAI, pp.56625666 (2018). ijcai.org Google Scholar Amato, C., Bernstein, D.S., Zilberstein, S.: Optimizing fixed-size stochastic controllers for POMDPs and decentralized POMDPs. Auton. Agents Multi-Agent Syst. 21(3), 293320 (2010) Article Google Scholar Anderson, B.D., Moore, J.B.: Optimal control: linear quadratic methods. Courier Corporation, Mineola, New York (2007) Google Scholar Andrs, I., de Barros, L.N., Mau, D.D., Simo, T.D.: When a robot reaches out for human help. In: IBERAMIA. Lecture Notes in Computer Science, vol.11238, pp.277289. Springer, Berlin (2018) Google Scholar Antsaklis, P.J., Michel, A.N.: Linear Systems. Birkhuser, Basel (2006) MATH Google Scholar Argote, L.: Input uncertainty and organizational coordination in hospital emergency units. Administrative science quarterly, 420434 (1982) Arrowsmith, D.K., Place, C.M., Place, C., et al.: An introduction to dynamical systems. Cambridge University Press, Cambridge (1990) MATH Google Scholar As, Y., Usmanova, I., Curi, S., Krause, A.: Constrained policy optimization via bayesian world models. In: ICLR (2022). OpenReview.net Google Scholar Ashok, P., Kretnsk, J., Weininger, M.: PAC statistical model checking for markov decision processes and stochastic games. In: CAV (1). Lecture Notes in Computer Science, vol.11561, pp.497519. Springer, Berlin (2019). Google Scholar strm, K.J., Murray, R.M.: Feedback systems: an introduction for scientists and engineers. Princeton University Press, Princeton (2010) MATH Google Scholar Azizzadenesheli, K., Brunskill, E., Anandkumar, A.: Efficient exploration through bayesian deep Q-networks. In: ITA, pp.19. IEEE, ieee.org (2018) Google Scholar Badings, T., Cubuktepe, M., Jansen, N., Junges, S., Katoen, J.P., Topcu, U.: Scenario-based verification of uncertain parametric MDPs. International Journal on Software Tools for Technology Transfer, 117 (2022) Badings, T., Romao, L., Abate, A., Parker, D., Poonawala, H.A., Stoelinga, M., Jansen, N.: Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions. J. Artif. Intell. Res. 76, 341391 (2023) Article MathSciNet MATH Google Scholar Badings, T.S., Abate, A., Jansen, N., Parker, D., Poonawala, H.A., Stoelinga, M.: Sampling-based robust control of autonomous systems with non-gaussian noise. In: AAAI, pp.96699678. AAAI Press, Menlo Park (2022) Google Scholar Badings, T.S., Jansen, N., Junges, S., Stoelinga, M., Volk, M.: Sampling-Based Verification of CTMCs with Uncertain Rates. Preprint arXiv:2205.08300 (2022) Badings, T.S., Jansen, N., Poonawala, H.A., Stoelinga, M.: Filter-based abstractions with correctness guarantees for planning under uncertainty. Preprint arXiv:2103.02398 (2021) Badings, T.S., Romao, L., Abate, A., Jansen, N.: Probabilities are not enough: Formal controller synthesis for stochastic dynamical models with epistemic uncertainty. In: AAAI (2023) Google Scholar Baier, C., Katoen, J.: Principles of model checking. MIT Press, Cambridge (2008) MATH Google Scholar Bellman, R.: Dyn

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Explain Bayesian Approach in decision making considering factors such as Transparency Bias and Interpretability. Give a very detailed answer.

The Bayesian approach in decision making leverages probability theory to make informed decisions, considering uncertainties and available evidence. When considering factors such as Transparency Bias and Interpretability, the Bayesian approach offers unique advantages in addressing these challenges.

  1. Transparency Bias:

    • The Bayesian approach acknowledges that decision-making processes may be influenced by transparency bias, where individuals may rely on readily available or easily understandable information, rather than considering the full scope of available evidence. To mitigate transparency bias, Bayesian decision making employs a systematic evaluation of all available evidence, utilizing prior probabilities, likelihood probabilities, and new evidence to calculate posterior probabilities. By incorporating a comprehensive range of evidence into the decision-making process, the Bayesian approach helps counteract the potential impact of transparency bias.
  2. Interpretability:

    • Bayesian models often offer high interpretability, as they provide a clear framework for incorporating prior knowledge, new evidence, and the associated uncertainties into the decision-making process. This interpretability allows decision-makers to understand and communicate the rationale behind their decisions, as well as the uncertainties associated with each choice. Furthermore, Bayesian models facilitate the transparent assessment of trade-offs between different factors, enabling decision-makers to weigh the impact of uncertainties and make well-informed choices.
  3. Adaptive Decision-Making:

    • Bayesian decision making supports adaptive and iterative approaches, allowing decision-makers to update their beliefs and decisions as new evidence becomes available. This adaptability is particularly valuable in dynamic environments where decision contexts may change over time. By continually updating probabilities based on new information, the Bayesian approach promotes flexibility and responsiveness in decision making.
  4. Risk Assessment:

    • The Bayesian approach provides a robust framework for assessing and managing risks. By integrating prior probabilities and new evidence, decision-makers can systematically evaluate the likelihood of different outcomes and associated risks. This process enables the identification of potential risks and uncertainties, allowing decision-makers to make decisions that account for these factors.
  5. Communication of Uncertainty:

    • Bayesian decision making facilitates the communication of uncertainty, as it allows decision-makers to articulate the probabilities associated with different outcomes. This transparent communication enables stakeholders to understand the level of uncertainty in the decision-making process, fostering informed discussions and collaborations.

In summary, the Bayesian approach in decision making addresses challenges such as transparency bias and interpretability by providing a systematic framework for incorporating evidence, managing, supporting adaptive decision-making, and facilitating transparent communication of uncertainty. By leveraging probabilities and incorporating a wide range of evidence, Bayesian decision making promotes robust and informed decision-making in complex and uncertain environments.

Bayesian Decision Theory is the statistical approach to pattern classification. It leverages probability to make classifications, and measures the risk (i.e. cost) of assigning an input to a given class.In this article we'll start by taking a look at prior probability, and how it is not an efficient way of making predictions. Bayesian Decision Theory makes better predictions by using the prior probability, likelihood probability, and evidence to calculate the posterior probability. We'll discuss all of these concepts in detail. Finally, we'll map these concepts from Bayesian Decision Theory to their context in machine learning.The outline of this article is as follows:Prior ProbabilityLikelihood ProbabilityPrior and Likelihood ProbabilitiesBayesian Decision TheorySum of All Prior Probabilities Must be 1Sum of All Posterior Probabilities Must be 1EvidenceMachine Learning & Bayesian Decision TheoryConclusionAfter completing this article, stay tuned for Part 2 in which we'll apply Bayesian Decision Theory to both binary and multi-class classification problems. To assess the performance of the classifier, both the loss and the risk of making a prediction are discussed. If the classifier makes a weak prediction, a new class named "reject" is used to accept samples with a high uncertainty. Part 2 discusses when and why a sample is assigned to the reject class.Let's get started.Bring this project to lifePrior ProbabilityTo discuss probability, we should start with how to calculate the probability that an action occurs. The probability is calculated according to the past occurrences of the outcomes (i.e. events). This is called the prior probability ("prior" meaning "before"). In other words, the prior probability refers to the probability in the past.Assume that someone asks who will be the winner of a future match between two teams. Let $A$ and $B$ refer to the first or second team winning, respectively.In the last 10 cup matches, $A$ occurred 4 times and $B$ occurred the remaining 6 times. So, what is the probability that $A$ occurs in the next match? Based on the experience (i.e., the events that occurred in the past), the prior probability that the first team ($A$) wins in the next match is:$$ P(A)=\frac{4}{10}=0.4 $$But the past events may not always hold, because the situation or context may change. For example, team $A$ could have won only 4 matches because there were some injured players. When the next match comes, all of these injured players will have recovered. Based on the current situation, the first team may win the next match with a higher probability than the one calculated based on past events only.The prior probability measures the probability of the next action without taking into consideration a current observation (i.e. the current situation). It's like predicting that a patient has a given disease based only on past doctors visits.In other words, because the prior probability is solely calculated based on past events (without present information), this can degrade the prediction value quality. The past predictions of the two outcomes $A$ and $B$ may have occurred while some conditions were satisfied, but at the current moment, these conditions may not hold.This problem is solved using the likelihood.Likelihood ProbabilityThe likelihood helps to answer the question: given some conditions, what is the probability that an outcome occurs? It is denoted as follows:$$ P(X|C_i) $$Where $X$ refers to the conditions, and $C_i$ refers to the outcome. Because there may be multiple outcomes, the variable $C$ is given the subscript $i$.The likelihood is read as follows:Under a set of conditions $X$, what is the probability that the outcome is $C_i$?According to our example of predicting the winning team, the probability that the outcome $A$ occurs does not only depend on past events, but also on current conditions. The likelihood relates the occurrence of an outcome to the current conditions at the time of making a predicti

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Bayesian Decision TheoryPhoto by Clark Van on UnsplashOh! What are we if not patterns?Its amazing how we perform so many sophisticated tasks easily and yet yearn to teach machines how to do them. Telling the difference between apples and oranges is quite trivial for us but to teach this to someone who only understands 0 and 1 is troublesome. Now what would seem an strenous task can be made easy (or at least, feasible) using a very familiar mathematical formula. But the question is: Is the formula intuitive?Bayes Theorem is like E=mc of probability theory. Everyone has seen it but only few understands it. If I had to choose one adjective for it, itd be revolutionary! It changed the course of many applications we were fiddling with before. But before diving into the nitty dritty of the algorithm, we need to set our fundamentals straight.P.S.: To explain the concepts I have taken the example of binary classification for the sake of simplicity but without any loss of generality.Marginal, Conditional and Joint ProbabilitiesMarginal ProbabilityWhen we usually talk about probability of an event, it is the marginal probability we are concerned with. In other words, it is the probability of an event irrespective of any other factor/event/circumstance. Basically, you marginalize other events and hence the name. It is denoted by P(A) and read as probability of A.Conditional ProbabilityConditional probability is when the occurence of an event is wholly or partially affected by other event(s). Alternatively put, it is the probability of occurrence of an event A when an another event B has already taken place. It is denoted by P(A|B) and read as probability of A given B.Joint ProbabilityJoint probability is calculated when we are interested in the occurrence of two different events simultaneously. It is also often referenced as probability of intersection of two events. It is denoted by P(A, B) and read as probability of A and B.Probability and LikelihoodThere is a very subtle difference between likelihood and probability and perhaps this is the very reason why people often consider them similar, if not same.To understand the difference between them, we first need to understand what a model is, more specifically, statistical model.A model can be viewed as any one of the process, relationship, equation or an approximation to understand and describe the data.Consider the below graph:This could be a model as it gives us a description of how our data look like. We can see a relationship between the features (x and y) in the above graph i.e., the variation of the features w.r.t each other.Now, if I try to approximate it with a mathematical equation, I get:y = 1.3055 * x - 5.703which when plotted gives:This equation is also a model as it gives a more concrete description of the data (more specifically the relationship between the features).A lot of statistics is dedicated to determining if a model is a good or bad approximation of the data.Now that we have the intuition behind statistical model, we can address the difference between likelihood and probability.Whenever we calculate the probability of an event in a stochastic process, it depends on the parameters of the model we are using to describe our process. Say, O is an observed outcome of the process and be the parameter describing the underlying model. Then the probability we are interested in calculating is denoted by P(O|) i.e., the probability of a particular outcome given the parameter of the model used to describe the process.But seldom does it happens that we know the value of beforehand. We simply observe O and the goal then is to arrive at an estimate for that would be a plausible choice given the observed outcome O. Our best estimate for the parameter is the value which gives the maximum probability for the outcome O to occur. We can then define the likelihood function as L(|O) i.e., it is function of for the given set of outcomes, and then use it to find the optimal value of t

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This article was published as a part of theData Science Blogathon Bayesian decision theory refers to the statistical approach based on tradeoff quantification among various classification decisions based on the concept of Probability(Bayes Theorem) and the costs associated with the decision. It is basically a classification technique that involves the use of the Bayes Theorem which is used to find the conditional probabilities. In Statistical pattern Recognition, we will focus on the statistical properties of patterns that are generally expressed in probability densities (pdfs and pmfs), and this will command most of our attention in this article and try to develop the fundamentals of the Bayesian decision theory. Prerequisites Random Variable A random variable is a function that maps a possible set of outcomes to some values like while tossing a coin and getting head H as 1 and Tail T as 0 where 0 and 1 are random variables. Bayes Theorem The conditional probability of A given B, represented by P(A | B) is the chance of occurrence of A given that B has occurred. P(A | B) = P(A,B)/P(B) or By Using the Chain rule, this can also be written as: P(A,B) = P(A|B)P(B)=P(B|A)P(A) P(A | B) = P(B|A)P(A)/P(B) - (1) Where,P(B) = P(B,A) + P(B,A) = P(B|A)P(A) + P(B|A)P(A) Here, equation (1) is known as the Bayes Theorem of probability Our aim is to explore each of the components included in this theorem. Lets explore step by step: (a) Prior or State of Nature: Prior probabilities represent how likely is each Class is going to occur. Priors are known before the training process. The state of nature is a random variable P(wi). If there are only two classes, then the sum of the priors is P(w1) + P(w2)=1, if the classes are exhaustive. (b) Class Conditional Probabilities: It represents the probability of how likely a feature x occurs given that it belongs to the particular class. It is denoted by, P(X|A) where x is a particular feature It is the probability of how likely the feature x occurs given that it belongs to the class wi. Sometimes, it is also known as the Likelihood. It is the quantity that we have to evaluate while training the data. During the training process, we have input(features) X labeled to corresponding class w and we figure out the likelihood of occurrence of that set of features given the class label. (c) Evidence: It is the probability of occurrence of a particular feature i.e. P(X). It can be calculated using the chain rule as, P(X) = in P(X | wi) P(wi) As we need the likelihood of class conditional probability is also figure out evidence values during training. (d) Posterior Probabilities: It is the probability of occurrence of Class A when certain Features are given It is what we aim at computing in the test phase in which we have testing input or features (the given entity) and have to find how likely trained model can predict features belonging to the particular class wi. For a better understanding of the above theory, we consider an example Problem Description Suppose we have a classification problem statement where we have to classify among the object-1 and object-2 with the given set of features X = [x1, x2, , xn]T. Objective The main objective of designing a such classifier is to suggest actions when presented with unseen features, i.e, object not yet seen i.e, not in training data. In this example let w denotes the state of nature with w = w1 for object-1 and w = w2 for object-2. Here, we need to know that in reality, the state of nature is so unpredictable that we generally consider that was variable that is described probabilistically. Priors Generally, we assume that there is some prior value P(w1) that the next object is object-1 and P(w2) that the next object is object-2. If we have no other object as in this problem then the sum of their prior is 1 i.e. the priors are exhaustive. The prior probabilities reflect the prior knowledge of how likely we will get object-1 and object-2. It is domain-dependent as t

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