Statistical Decisions under Ambiguity: An Axiomatic Analysis

Consider a decision maker who faces a number of possible models of the world. Every model generates objective probabilities, but no probabilities of models are given. Applications of this framework include statistical decision making with model uncertainty, e.g. due to concerns for

[1]  Ramon Casadesus-Masanell,et al.  Maxmin Expected Utility over Savage Acts with a Set of Priors , 2000, J. Econ. Theory.

[2]  Peter C. Fishburn,et al.  Reconsiderations in the Foundations of Decision under Uncertainty , 1987 .

[3]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[4]  James O. Berger,et al.  Statistical Decision Theory and Bayesian Analysis, Second Edition , 1985 .

[5]  X. Sala-i-Martin,et al.  Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach , 2000 .

[6]  P. Fishburn.  Dominance in SSB utility theory , 1984 .

[7]  Christos H. Papadimitriou,et al.  Games against nature , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[8]  R. Sugden,et al.  Some implications of a more general form of regret theory , 1987 .

[9]  Thibault Gajdos,et al.  Decision making with imprecise probabilistic information , 2004 .

[10]  C. Manski.  Statistical treatment rules for heterogeneous populations , 2003 .

[11]  W. J. Studden,et al.  Robust Bayesian Experimental Designs in Normal Linear Models , 1991 .

[12]  Alfonso Suárez-Llorens,et al.  Bayesian Robustness with Quantile Loss Functions , 2003, ISIPTA.

[13]  H. Chernoff.  Rational Selection of Decision Functions , 1954 .

[14]  T. Schwartz.  Rationality and the Myth of the Maximum , 1972 .

[15]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[16]  Joel L. Horowitz,et al.  Computation of Bounds on Population Parameters When the Data Are Incomplete , 2003, Reliab. Comput..

[17]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[18]  William A Brock,et al.  Policy Evaluation in Uncertain Economic Environments , 2003 .

[19]  Kenneth J. Arrow,et al.  Studies in Resource Allocation Processes: Appendix: An optimality criterion for decision-making under ignorance , 1977 .

[20]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[21]  A. Dasgupta,et al.  ESTIMATING A BINOMIAL PARAMETER: IS ROBUST BAYES REAL BAYES? , 1993 .

[22]  David S. Ahn.  Ambiguity without a state space , 2004 .

[23]  Amit Kanudia,et al.  Minimax regret strategies for greenhouse gas abatement: methodology and application , 1997, Oper. Res. Lett..

[24]  Peter C. Fisi-Iburn.  Nontransitive preferences in decision theory , 1991 .

[25]  Gary Chamberlain,et al.  Econometrics and decision theory , 2000 .

[26]  Lars Peter Hansen,et al.  Robustness and Uncertainty Aversion , 2002 .

[27]  David M. Kreps.  Notes On The Theory Of Choice , 1988 .

[28]  Robert Sugden,et al.  Why be Consistent? A Critical Analysis of Consistency Requirements in Choice Theory , 1985 .

[29]  Bernd Droge,et al.  Minimax regret analysis of orthogonal series regression estimation : Selection versus shrinkage , 1998 .

[30]  Wojciech Olszewski,et al.  Preferences over Sets of Lotteries , 2006 .

[31]  Charles F. Manski,et al.  Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice , 2000 .

[32]  Amartya Sen,et al.  INTERNAL CONSISTENCY OF CHOICE , 1993 .

[33]  Robert Sugden,et al.  An Axiomatic Foundation for Regret Theory , 1993 .

[34]  J. Rawls.  A Theory of Justice , 1999 .

[35]  Charles F. Manski,et al.  Treatment Choice Under Ambiguity Induced by Inferential Problems , 2002, ISIPTA.

[36]  R. Sugden,et al.  Regret Theory: An alternative theory of rational choice under uncertainty Review of Economic Studies , 1982 .

[37]  Peter C. Fishburn,et al.  Context-Dependent Choice with Nonlinear and Nontransitive Preferences , 1988 .

[38]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[39]  Peter Klibanoff,et al.  Characterizing uncertainty aversion through preference for mixtures , 2001, Soc. Choice Welf..

[40]  K. Arrow.  Alternative Approaches to the Theory of Choice in Risk-Taking Situations , 1951 .

[41]  C. Manski.  Partial Identification of Probability Distributions , 2003 .

[42]  Leonard J. Savage,et al.  The Theory of Statistical Decision , 1951 .

[43]  Wojciech Olszewski,et al.  Preferences Over Sets of Lotteries -super-1 , 2007 .

[44]  Charles F. Manski,et al.  Search Profiling with Partial Knowledge of Deterrence , 2005 .

[45]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[46]  Charles F. Manski,et al.  Social Learning from Private Experiences: The Dynamics of the Selection Problem , 2004 .

[47]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[48]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .