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    Decision Theory: Fundamentals and Applications
    Decision Theory: Fundamentals and Applications
    Decision Theory: Fundamentals and Applications
    Ebook109 pages1 hour

    Decision Theory: Fundamentals and Applications

    By Fouad Sabry

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    About this ebook

    What Is Decision Theory


    The theory of making judgments based on assigning probabilities to various aspects and assigning numerical implications to the conclusion is the subject of decision theory, which is a part of applied probability theory and analytic philosophy. Decision theory is concerned with the theory of making decisions.


    How You Will Benefit


    (I) Insights, and validations about the following topics:


    Chapter 1: Decision theory


    Chapter 2: Bayesian probability


    Chapter 3: Utility


    Chapter 4: Rationality


    Chapter 5: Bounded rationality


    Chapter 6: Prospect theory


    Chapter 7: Expected utility hypothesis


    Chapter 8: Subjective expected utility


    Chapter 9: Decision analysis


    Chapter 10: Von Neumann-Morgenstern utility theorem


    (II) Answering the public top questions about decision theory.


    (III) Real world examples for the usage of decision theory in many fields.


    Who This Book Is For


    Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of decision theory.


    What is Artificial Intelligence Series


    The artificial intelligence book series provides comprehensive coverage in over 200 topics. Each ebook covers a specific Artificial Intelligence topic in depth, written by experts in the field. The series aims to give readers a thorough understanding of the concepts, techniques, history and applications of artificial intelligence. Topics covered include machine learning, deep learning, neural networks, computer vision, natural language processing, robotics, ethics and more. The ebooks are written for professionals, students, and anyone interested in learning about the latest developments in this rapidly advancing field.
    The artificial intelligence book series provides an in-depth yet accessible exploration, from the fundamental concepts to the state-of-the-art research. With over 200 volumes, readers gain a thorough grounding in all aspects of Artificial Intelligence. The ebooks are designed to build knowledge systematically, with later volumes building on the foundations laid by earlier ones. This comprehensive series is an indispensable resource for anyone seeking to develop expertise in artificial intelligence.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateJun 27, 2023
    Decision Theory: Fundamentals and Applications

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      Book preview

      Decision Theory - Fouad Sabry

      Chapter 1: Decision theory

      Decision theory, also known as the theory of choice but not to be confused with choice theory, is the study of decision-making by assigning probabilities to potential outcomes and quantifying the impact of those outcomes.

      Decision theory is divided into three subfields:

      Optimal decisions are the focus of normative decision theory, which typically employs a perfectly rational and accurate calculator to determine the best course of action.

      Assuming that decision-makers are following a set of rules, prescriptive decision theory aims to describe their actions using theoretical frameworks.

      Individual decision-making processes are dissected in descriptive decision theory.

      Management scientists, medical researchers, mathematicians, data scientists, psychologists, biologists, and computer scientists are just some of the many disciplines that study decision theory.

      Computer science statistics and discrete mathematics are commonly used to apply this theory to the real world.

      Optimal decisions are sought after in normative decision theory, and this is typically done by imagining a decision-maker who is both fully rational and capable of performing calculations with pinpoint accuracy. Decision analysis is the practical implementation of this prescriptive approach (how people should make decisions) with the goal of discovering tools, methodologies, and software (decision support systems) to aid in decision making.

      The core of decision theory is the study of decision-making in the face of uncertainty.

      Popular since the 17th century (when Blaise Pascal used it to justify his bet),, which is contained in his Pensées, to be released in 1670, expected value is based on the idea that, when given a choice between several responses, each of which may generate multiple outcomes with varying probabilities, Identifying potential outcomes is the logical next step, evaluate the potential benefits and drawbacks of each option and the likelihood that they will materialize, add up the two numbers to get the expected value, or the typical forecast for a result; The best course of action is the one that results in the greatest sum of expected benefits.

      In 1738, Exposition of a New Theory on the Measurement of Risk, written by Daniel Bernoulli, was a seminal publication in the field of probability theory, wherein he references Saint.

      Expected value theory is shown to be normatively incorrect by the St. Petersburg paradox.

      He uses the scenario of a Dutch merchant debating whether or not to insure wintertime cargo traveling from Amsterdam to St. Petersburg to illustrate his point.

      With his plan, Instead of calculating monetary value, he calculates expected utility.

      demonstrated that maximization of expected utility followed from axioms of rational behavior.

      Human behavior, as shown by the research of people like Maurice Allais and Daniel Ellsberg, frequently deviates systematically and significantly from expected-utility maximization (Allais paradox and Ellsberg paradox). Kahneman and Tversky discovered three consistent patterns: losses loom larger than gains in real-world human decision-making; individuals pay more attention to transitions between utility states than they do to utility levels; and the estimation of subjective probabilities is highly biased by anchoring.

      In the context of intertemporal choice, the outcomes of various actions are realized at varying points in time. Someone who unexpectedly came into several thousand dollars could either take a luxurious vacation and enjoy the money now, or they could put the money into a pension plan and enjoy the income in the future. I need to know what my best option is. The expected rates of interest and inflation, the person's life expectancy, and their trust in the pensions industry are all relevant considerations. Despite these considerations, human behavior still frequently deviates from the predictions of prescriptive decision theory. This discrepancy has prompted researchers to develop alternative models, such as those in which subjective discount rates are used instead of objective interest rates.

      There are times when decision-making is challenging because of the need to consider the reactions of others involved. Although decision theory typically employs mathematical methods, it is frequently used to analyze such social decisions. Distributed decision-making in human organizations is a major area of study in the burgeoning discipline of socio-cognitive engineering, both under normal conditions and during abnormal or crisis situations.

      The complexity of the decision itself, or the complexity of the organization making the decision, are also major topics of study in other branches of decision theory. Decision-makers are bounded rational because of their finite capacities (time and knowledge), so the problem isn't so much the gap between actual and ideal behavior as it is the difficulty of pinpointing the latter. The distinction bias refers to how framing choices together or separately influences decisions.

      The ability to make decisions using unjustified or habitual thinking is known as heuristics in the realm of decision-making. Heuristic thinking is faster than sequential processing, but it often leads to errors.

      It's a hotly debated topic, whether or not probability need be used in decision theory.

      Supporters of applying probability theory often:

      the foundational work of Richard Threlkeld Cox that underpins modern probability theory, the Dutch book paradoxes of Bruno de Finetti to show how breaking the probability axioms can cause theoretical problems, and

      the full set of class theorems proving that, given a utility function and a prior distribution, any admissible decision rule is equivalent to the Bayesian decision rule (or for the limit of a sequence of prior distributions). This means that every decision rule has an equivalent Bayesian procedure (or the limit of an equivalent sequence of procedures) or an alternative rule that is sometimes better and never worse.

      Proponents of non-standard alternatives argue that probabilistic decision theory is sensitive to assumptions about the probabilities of various events, whereas non-probabilistic rules, such as minimax, are robust in that they do not rely on probabilities. These alternatives include fuzzy logic, possibility theory, quantum cognition, Dempster-Shafer theory, and info-gap decision theory.

      One common criticism leveled at decision theory that assumes a fixed set of possibilities is that it fails to account for unknown unknowns, or the significant events that may lie outside model, because it only takes into account the known unknowns, or the expected variations. The ludic fallacy asserts that any attempt to model the world accurately will inevitably result in error and that blind faith in models will lead one to ignore their limitations.

      {End Chapter 7}

      {End Chapter 1}

      Chapter 2: Bayesian probability

      When applied to propositions whose truth or falsity is unknown, Bayesian probability reframes probability as a reasonable

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