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410
When did Bayesian inference become “Bayesian"?
 BAYESIAN ANALYSIS
, 2006
"... While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesi ..."
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Cited by 26 (1 self)
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While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian developments, beginning with Bayes’ posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when “Bayesian” emerged as the label of choice for those who advocated Bayesian methods.
A Unique Subjective State Space for Unforeseen Contingencies
, 1997
"... We axiomatically characterize a representation of preferences over opportunity sets which exhibit a preference for flexibility, interpreted as a model of unforeseen contingencies. In this representation, the agent acts as if she had a coherent prior over a set of possible future preferences, each of ..."
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Cited by 25 (1 self)
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We axiomatically characterize a representation of preferences over opportunity sets which exhibit a preference for flexibility, interpreted as a model of unforeseen contingencies. In this representation, the agent acts as if she had a coherent prior over a set of possible future preferences, each of which is an expectedutility preference. We show that the state space is essentially unique given the restriction that all future preferences are expectedutility preferences and is minimal even without this restriction. Finally, because the state space is identified, the additivity across states is meaningful in the sense that all representations are intrinsically additive.
Econometric Applications Of Maxmin Expected Utility
 Journal of Applied Econometrics
, 1999
"... Gilboa and Schmeidler (1989) provide axioms on preferences that imply a set of distributions and a preference ordering based on the minimum expected utility with respect to this set. We consider joint distributions for data and for the random variables that, together with the agent's choice, de ..."
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Cited by 25 (0 self)
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Gilboa and Schmeidler (1989) provide axioms on preferences that imply a set of distributions and a preference ordering based on the minimum expected utility with respect to this set. We consider joint distributions for data and for the random variables that, together with the agent's choice, determine utilityrelevant outcomes; for example, a joint distribution for data that will be available when a portfolio decision is made and for future returns that will determine the value of the portfolio. The set of distributions is generated by combining a parametric model with a set of prior distributions. We seek a decision rule (a function of the data) that maximizes the minimum expected utility (or, equivalently, minimizes maximum risk) over the set of prior distributions. An algorithm is provided for the case of a finite set of prior distributions. It is based on finding the Bayes rule for a given prior and then solving a concave program to find the leastfavorable prior distribution. The ...
Lexicographic probability, conditional probability, and nonstandard probability
 In Theoretical Aspects of Rationality and Knowledge: Proc. Eighth Conference (TARK 2001
, 2001
"... The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If coun ..."
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Cited by 24 (2 self)
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The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS’s are equivalent to NPS’s. However, if the state space is infinite, NPS’s are shown to be more general than LPS’s. JEL classification numbers: C70; D80; D81; 1
On the Axiomatization of Qualitative Decision Criteria
 Journal of the ACM
, 1997
"... Qualitative decision tools have been used in AI and CS in various contexts. However, their adequacy is unclear. Following Brafman and Tennenholtz, we use the axiomatic approach to investigate the adequacy and usefulness of various decision rules. We present constructive representation theorems for a ..."
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Cited by 23 (2 self)
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Qualitative decision tools have been used in AI and CS in various contexts. However, their adequacy is unclear. Following Brafman and Tennenholtz, we use the axiomatic approach to investigate the adequacy and usefulness of various decision rules. We present constructive representation theorems for a number of qualitative decision criteria, including minmax regret , competitive ratio, and maximax , and characterize conditions under which a maximin agent can be ascribed qualitative beliefs. Introduction Decision theory plays a central role in various disciplines, including mathematical economics, game theory, operations research, industrial engineering, and statistics. It is widely recognized by now that decision making is crucial to AI as well, since artificial agents are, in fact, automated decision makers (RN95). However, many decision making techniques found in the AI literature are quite different from those found in other fields. Work in other disciplines has mostly adopted the v...
Learning How to Invest when Returns are Uncertain
, 2003
"... Most asset returns are uncertain, not merely risky: investors do not know the probabilities of different possible future returns. A large body of evidence suggests that investors are averse to uncertainty, as well as to risk. This paper builds up an axiomatic foundation for the dynamic portfolio and ..."
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Cited by 21 (2 self)
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Most asset returns are uncertain, not merely risky: investors do not know the probabilities of different possible future returns. A large body of evidence suggests that investors are averse to uncertainty, as well as to risk. This paper builds up an axiomatic foundation for the dynamic portfolio and consumption choices of an uncertaintyaverse (as well as riskaverse) investor who tries to learn from historical data. The theory developed, modelbased multiplepriors, generalizes existing theories of dynamic choice under uncertainty aversion by relaxing the assumption of consequentialism. Examples are given to show that consequentialism, the property that counterfactuals are ignored, can be problematic when combined with uncertainty aversion. An analog of de Finetti’s statistical representation theorem is proven under modelbased multiplepriors, but consequentialism combines with multiple priors to rule out priorbyprior exchangeability. A simple dynamic portfolio choice problem illustrates the contrast between a modelbased multiplepriors investor and a consequentialist multiplepriors investor.
Regret Aversion and Opportunity Dependence
 Journal of Economic Theory
"... This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated expost regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multi ..."
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Cited by 21 (0 self)
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This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated expost regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage’s minimax regret, and a smooth model of regret aversion. 1
Social Decision Theory: Choosing within and between Groups.
 The Review of Economic Studies
, 2012
"... Abstract We introduce a theoretical framework to study interdependent preferences, where the outcome of others affects the welfare of the decision maker. The dependence may take place in two conceptually different ways, which depend on how the decision maker evaluates his and others' outcomes. ..."
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Abstract We introduce a theoretical framework to study interdependent preferences, where the outcome of others affects the welfare of the decision maker. The dependence may take place in two conceptually different ways, which depend on how the decision maker evaluates his and others' outcomes. In the first he values his outcomes and those of others on the basis of his own utility. In the second, he ranks outcomes according to a social value function. These two representations express two different views of the nature and functional role of interdependent preferences. The first is Festinger's view that the evaluation of peers' outcomes is useful to improve individual choices by learning from the comparison. The second is Veblen's view that interdependent preferences keep track of social status derived from a social value attributed to the goods one consumes. We give different axiomatic foundations to these two different, but complementary, views of the nature of the interdependence. On the basis of this axiomatic foundation we build a behavioral theory of comparative statics within subjects and across subjects. We characterize preferences according to the relative importance assigned to social gains and losses, that is, pride and envy. This parallels the standard analysis of private gains and losses (as well as that of regret and relief). We give an axiomatic foundation of inter personal comparison of preferences, ordering individuals according to their sensitivity to social ranking. These characterizations provide the behavioral foundation for applied analysis of market and game equilibria with interdependent preferences.
A tutorial introduction to decision theory
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... AbstractDecision theory provides a rational framework for choosing between alternative courses of action when the consequences resulting from this choice are imperfectly known. Two ..."
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AbstractDecision theory provides a rational framework for choosing between alternative courses of action when the consequences resulting from this choice are imperfectly known. Two