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Sure-thing Principle
In decision theory, the sure-thing principle states that a decision maker who decided they would take a certain action in the case that event ''E'' has occurred, as well as in the case that the negation of ''E'' has occurred, should also take that same action if they know nothing about ''E''. The principle was coined by L.J. Savage:Savage, L. J. (1954), ''The foundations of statistics''. John Wiley & Sons Inc., New York. Savage formulated the principle as a dominance principle, but it can also be framed probabilistically. Richard Jeffrey and later Judea Pearl showed that Savage's principle is only valid when the probability of the event considered (e.g., the winner of the election) is unaffected by the action (buying the property). Under such conditions, the sure-thing principle is a theorem in the ''do''-calculus (see Bayes networks). Blyth constructed a counterexample to the sure-thing principle using sequential sampling in the context of Simpson's paradox, but this example v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Decision Theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, rationally under uncertainty. It differs from the Cognitive science, cognitive and Behavioural sciences, behavioral sciences in that it is mainly Prescriptive economics, prescriptive and concerned with identifying optimal decision, optimal decisions for a rational agent, rather than Descriptive economics, describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by Social science, social scientists, as it lays the foundations to Mathematical model, mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science. History The roots of decision theory lie in probability theory, developed by Blai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Leonard Jimmie Savage
Leonard Jimmie Savage (born Leonard Ogashevitz; 1917 – 1971) was an American mathematician and statistician. Economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." Education and career Savage was born and grew up in Detroit. He studied at Wayne State University in Detroit before transferring to University of Michigan, where he first majored in chemical engineering, then switched to mathematics, graduating in 1938 with a bachelor's degree. He continued at the University of Michigan with a PhD on differential geometry in 1941 under the supervision of Sumner Byron Myers. Savage subsequently worked at the Institute for Advanced Study in Princeton, New Jersey, the University of Chicago, the University of Michigan, Yale University, and the Statistical Research Group at Columbia University. Though his thesis advisor was Sumner Myers, he also credited Milton Friedman and W. Allen Wallis as statistical mentors. Durin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Strategic Dominance
In game theory, a strategy ''A'' dominates another strategy ''B'' if ''A'' will always produce a better result than ''B'', regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance. Terminology A player can compare two strategies, A and B, to determine which one is better. The result of the comparison is one of: * B strictly dominates (>) A: choosing B always gives a better outcome than choosing A, no matter what the other players do. * B weakly dominates (≥) A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, and there is at least one set of opponents' actions for which B gives a better outcome than A. (Notice that if B strictly dominates A, then B weakly dominates A. Therefore, we can say "B dominates A" to mean "B weakly dominates A".) * B is weakly dominated by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Richard Jeffrey
Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher, logician, and probability theorist. He is best known for developing and championing the philosophy of radical probabilism and the associated heuristic of probability kinematics, also known as Jeffrey conditioning. Life and career Born in Boston, Massachusetts, Jeffrey served in the U.S. Navy during World War II. As a graduate student he studied under Rudolf Carnap and Carl Hempel. He received his M.A. from the University of Chicago in 1952 and his Ph.D. from Princeton in 1957. After holding academic positions at MIT, City College of New York, Stanford University, and the University of Pennsylvania, he joined the faculty of Princeton in 1974 and became a professor emeritus there in 1999. He was also a visiting professor at the University of California, Irvine. Jeffrey, who died of lung cancer at the age of 76, was known for his sense of humor, which often came through in his breezy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Judea Pearl
Judea Pearl (; born September 4, 1936) is an Israeli-American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks (see the article on belief propagation). He is also credited for developing a theory of causal and counterfactual inference based on structural models (see article on causality). In 2011, the Association for Computing Machinery (ACM) awarded Pearl with the Turing Award, the highest distinction in computer science, "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning". He is the author of several books, including the technical '' Causality: Models, Reasoning and Inference'', and '' The Book of Why'', a book on causality aimed at the general public. Judea Pearl is the father of journalist Daniel Pearl, who was kidnapped and murdered by terrorists in Pakistan connected with Al-Qaeda a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bayes Networks
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their Conditional dependence, conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and machine learning, learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech recognition, speech signals or peptide sequence, protein sequences) ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Counterexample
A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are lazy." In mathematics In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers can then avoid going down blind alleys and learn to modify conjectures to produce provable theorems. It is sometimes said that mathematical development consists primarily in finding (and proving) theorems and counterexamples. Rectangle example Suppose that a mathematician is studying geometry and shapes, and she wishes to prove certain theorems about them. She conjectures that "All re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Simpson's Paradox
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). . The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling (e.g., through cluster analysis). Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. Edward H. Simpson first described this phenomenon in a technical paper in 1951; the statisticians Karl Pearson (in 1899) and Udny Yule (in 1903) had mentioned similar effects earlier. The name ''Simpson's paradox'' was introduced by Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Agree To Disagree
To "agree to disagree" is to resolve a conflict (usually a debate or quarrel) by having all parties tolerating but not accepting the opposing positions. It generally occurs when all sides recognize that further conflict would be unnecessary, ineffective or otherwise undesirable. Origin In 1770, the phrase "agree to disagree" appeared in print in its modern meaning when, at the death of George Whitefield, John Wesley wrote a memorial sermon which acknowledged but downplayed the two men's doctrinal differences: In a subsequent letter to his brother Charles, Wesley attributed it to Whitefield (presumably George Whitefield): "If you agree with me, well: if not, we can, as Mr. Whitefield used to say, agree to disagree." Whitefield had used it in a letter as early as June 29, 1750. Though Whitefield and Wesley appear to have popularized the expression in its usual meaning, it had appeared in print much earlier (1608) in a work by James Anderton, writing under the name of John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ellsberg Paradox
In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921. Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks. Ellsberg's findings indicate that choices with an underlying level of risk are favored in instances where the likelihood of risk is clear, rather than instances in which the likelihood of risk is unknown. A decision-maker will overwhelmingly favor a choice with a transparent likelihood of risk, even in instances where the unknown alternative will likely produce greater utility. When offered choices with varying risk, people prefer choices with calculable risk, even when those choices ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Allais Paradox
The Allais paradox is a choice problem designed by to show an inconsistency of actual observed choices with the predictions of expected utility theory. The Allais paradox demonstrates that individuals rarely make rational decisions consistently when required to do so immediately. The independence axiom of expected utility theory, which requires that the preferences of an individual should not change when altering two lotteries by equal proportions, was proven to be violated by the paradox. Statement of the problem The Allais paradox arises when comparing participants' choices in two different experiments, each of which consists of a choice between two gambles, A and B. The payoffs for each gamble in each experiment are as follows: Several studies involving hypothetical and small monetary payoffs, and recently involving health outcomes, have supported the assertion that when presented with a choice between 1A and 1B, most people would choose 1A. Likewise, when presented with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Decision Tree
A decision tree is a decision support system, decision support recursive partitioning structure that uses a Tree (graph theory), tree-like Causal model, model of decisions and their possible consequences, including probability, chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in Decision tree learning, machine learning. Overview A decision tree is a flowchart-like structure in which each internal node represents a test on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test, and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represent classification rules. In decision analysis, a de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
