Faculty

Teddy Seidenfeld

H.A. Simon and University Professor
of Philosophy and Statistics

Philosophy and Statistics

Baker Hall 135J

412.268.2209

teddy@stat.cmu.edu

Research Interests

Working on the foundations of statistics, I enjoy problems that arise from trying to make precise the vague notion of "ignorance." The question was alive for Thomas Bayes in 1760. Bayes' work stimulated Simon Laplace a decade later to argue that equiprobability was the key. He thought that where you are ignorant between two events, assign them equal probability. However, using this equiprobability rule to depict "ignorance" leads to some unanticipated results when there are infinitely many possibilities, as is typical of statistical problems with an unknown parameter. For a simple example, think of choosing a number x "at random." Formally, a uniform distribution for x corresponds to a finitely (but not countably) additive probability. Mark Schervish, Jay Kadane (both from Statistics) and I have shown some very surprising consequences for statistical inference that attend the use of merely finitely additive probabilities. The surprises affect statistical decision theory too. A related line of research deals with the theory of conditional probability and limitations of the (received) theory of countably additive, regular conditional distributions.

Also, I am interested in the general question whether the norms of Bayesian statistics can be extended from individuals acting alone to cooperative groups. In terms of comparing opinions of different researchers, when will common evidence drive them to agree in their personal probabilities? In terms of decisions, when can two Bayesians acting in partnership make (coherent) decisions that preserve their common strict preferences? Kadane, Schervish and I have found that these two perspectives on groups – considering the agreements in probabilities versus the agreements in decisions – lead to very different results.

Some of our current work is aimed at providing a unified treatment of group probabilities and group decisions via a theory of coherence choice functions. The strategy we employ is to relax a central assumption of Bayesian, expected utility theory: the "ordering" postulate. Instead, in our theory we do not assume that you always can judge which of two events is more probable and we do not assume that you always can judge which of two options is more preferred. The upshot is a theory involving sets of probability/utility pairs, in place of a single such pair.

These two areas of interest intersect in some joint research with Larry Wasserman (of Statistics) and Timothy Herron (a former PAL graduate student) on what we call "Dilation" for sets of probabilities. This anomaly occurs when new evidence leads different Bayesian investigators into greater disagreement than they had prior to the new evidence.

Other of my standing interests include the theory of experimental design, especially issues about the status of randomization in experimental design, and appreciating the controversial work of R.A. Fisher. One example of the latter is a paper about Fisher’s infamous speculation about Gregor Mendel’s classic plant hybridization studies that “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations.”

A selection of my research papers

• Preference for equivalent random variables: a price for unbounded utilities (pdf)
• Calibration, Coherence, and Scoring Rules (pdf)
• Coherent Choice Functions under Uncertainty (pdf)
• Decision Theory without  "Independence" or without  "Ordering" (pdf)
• Decisions without Ordering (pdf)
• Extensions of Expected Utility Theory and Some Limitations of Pairwise Comparisons (pdf)
• The Fundamental Theorems of Prevision and Asset Pricing (pdf)
• Proper Scoring Rules, Dominated Forecasts, and Coherence (pdf)
• A Rate of Incoherence Applied to Fixed-Level Testing (pdf)
• A Representation of Partially Ordered Preferences (pdf)
• A Rubinesque Theory of Decision (pdf)
• State-dependent Utilities (pdf)
• When Fair Odds are not Degrees of Belief (pdf)
• When Normal and Extensive Form Decisions Differ (pdf)
• Measures of Incoherence: How not to gamble if you must (pdf)

• When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusionn (pdf)
• Shared Preferences and State-dependent utilities (pdf)
• On the Shared Preferences of Two Bayesian Decision Makers (pdf)
• An approach to consensus and certainty with increasing evidence (pdf)
  

• The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference (pdf)
• Divisive Conditioning: Further Results on Dilation (pdf)
• Dilation for Sets of Probabilities (pdf)

• Disintegration and Conglomerability for Unbounded Variables (pdf)
• A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Stratergies (pdf)
• A Conflict between Finite Additivity and Avoiding Dutch Book (pdf)
• The Extent of non-Conglomerability of Finitely Additive Probabilities (pdf)
• Non-conglomerability for Finitely valued, Finitely Additive Probability (pdf)
• Statistical implications of Finitely Additive Probability (pdf)
• Remarks on the Theory of Conditional Probability (pdf)

• Direct Inference and Inverse Inference (pdf)
• R.A.Fisher on the Design of Experiments and Statistical Estimation (pdf)
• Fisher's Fiducial Argument and Bayes Theorem (pdf)
• Probability and Inference : Essays in honor of Henry E. Kyburg, Jr.(pdf)
• Jeffreys, Fisher, and Keynes: predicting the third observation. (pdf)
• P’s in a Pod: some recipes for cooking Mendel’s data (pdf)

• Is Ignorance Bliss? (pdf)
• Equilibirum, Common Knowledge, and Optimal Sequential Decisions (pdf)
• Reasoning to a Foregone Conclusion (pdf)
• A contrast between two decision rules for use with (convex) sets of probabilities:
  Γ-Maximin versus E-admissibilty. (pdf)

• Improper Regular Conditional Distributions (pdf)
• Remarks on the 'Bayesian' method of moments (pdf)
• Randomization in a Bayesian Perspective (pdf)
• Statistical Evidence and Belief Functions (pdf)
• Stopping to Reflect: Comments and Criticism (pdf)
• After-trial properties of best Neyman-Pearson Confidence Intervals (pdf)
• Comments on Causal Decision Theory (pdf)
• Entropy and Uncertainty (revised) (pdf)
• Independence for Full Conditional Measures, Graphoids and Bayesian Networks (pdf)
• Why I am not a objective Bayesian ; some refelctions propmpted by Rosenkrantz (pdf)

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