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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 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 beli ... 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 propert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by economi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Jimmie Savage
Leonard Jimmie Savage (born Leonard Ogashevitz; 20 November 1917 – 1 November 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 stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategic Dominance
In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play. Terminology When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of: * B is equivalent to A: choosing B always gives the same outcome as choosing A, no matter what the other players do. * 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 dependencies via a directed acyclic graph (DAG). 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 learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. Graphical m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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, but the statisticians Karl Pearson (in 1899) and Udny Yule (in 1903 ) had mentioned similar effects earlier. The name ''Simpson's paradox'' was introduced by Colin R. Blyth in 1972. It is al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agree To Disagree
To "agree to disagree" is to resolve a conflict (usually a debate or quarrel) in a manner whereby all parties tolerate but do not accept the opposing positions. It generally occurs when all sides recognize that further conflict would be unnecessary, ineffective or otherwise undesirable. They may also remain on amicable terms while continuing to disagree about the unresolved issues. Origin The phrase "agree to disagree" appeared in print in its modern meaning in 1770 when, at the death of George Whitefield, John Wesley wrote a memorial sermon which acknowledged but downplayed the two men's doctrinal differences: Wesley enclosed the phrase in quotation marks,The Phrase Finder''Agree to disagree''.Retrieved on 20 April 2009. and in a subsequent letter to his brother Charles, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Daniel Ellsberg popularized the paradox in his 1961 paper, “Risk, Ambiguity, and the Savage Axioms”. John Maynard Keynes published a version of the paradox in 1921. 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 they have les ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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 choice between 2A and 2B, most people would choose 2B. Allais further asserted that it was reasonable to choose 1A alone or 2B alone. However, that the same person (who chose 1A alone or 2B alone) would choose both 1A and 2B together is inconsistent with expected utility theory. According to expected utility theory, the person should choose e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by economi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
