# Teddy Seidenfeld

## Herbert A. Simon University Professor of Philosophy and Statistics

**Office:**Baker Hall 135J

**Phone:**412.268.2209

**Email:**teddy@stat.cmu.edu

## Bio

Teddy Seidenfeld (H.A. Simon University Professor of Philosophy and Statistics) works on foundations at the interface between philosophy and statistics, often being concerned with problems that involve multiple decision makers. For example, in collaboration with M.J. Schervish and J.B. Kadane (Statistics, CMU), they relax the norms of Bayesian theory to permit a unified standard, both for individuals acting as separate decision makers and collectively, in forming a cooperative group agent. By contrast, this is an impossibility for strict Bayesian theory. For a second example, in collaboration with Larry Wasserman (Statistics, CMU), they examine the short-run consequences of using Bayes rule for updating a set of expert Bayesian opinions with shared information. They focus on anomalous cases (they call dilation), where an experiment is certain to result in new evidence that increases the experts: uncertainty about an event of common interest where uncertainty is reflected in the extent of probabilistic disagreements among the experts.His current collaborations with Kadane and Schervish incude a theory for indexing the degree of incoherence in non-Bayesian statistical decisions, work on the representation of coherent choice-functions using sets of probabilitis, and investigations involving scoring rules for probabilistic forecasts. The three also work together on the development of finitely additive expectations for unbounded random variables.

A selection of Seidenfeld’s papers and some recent presentations are found below, clustered by topic area.

## Selection of research papers

*Relating to Coherence and Decision Theory*

- Decision Theory without "Independence" or without "Ordering" (1988)
- Decisions without Ordering (1990)
- State-dependent Utilities (1990)
- When Fair Odds are not Degrees of Belief (1990)
- When Normal and Extensive Form Decisions Differ (1994)
- A Representation of Partially Ordered Preferences (1995)
- A Rate of Incoherence Applied to Fixed-Level Testing (2000)
- Measures of Incoherence: How not to gamble if you must (2002)
- Extensions of Expected Utility Theory and Some Limitations of Pairwise Comparisons (2003)
- A Rubinesque Theory of Decision (2004)
- Coherent Choice Functions under Uncertainty (2007)
- The Fundamental Theorems of Prevision and Asset Pricing (2008)
- Preference for equivalent random variables: a price for unbounded utilities (2009)
- De Finetti and Imprecise Probabilities (2012)
- Uncertainty about logic and mathematics (2012)
- Sleeping Beauty (2015)

*Relating to Consensus*

- On the Shared Preferences of Two Bayesian Decision Makers (1989)
- An approach to consensus and certainty with increasing evidence (1990)
- Shared Preferences and State-dependent utilities (1991)
- When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion (1996)

*Relating to Dilation of Sets of Probabilities*

- Dilation for Sets of Probabilities (1993)
- Dilation in Robust Bayesian Inference (1994)
- The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference (1994)
- Divisive Conditioning: Further Results on Dilation (1997)

*Relating to Finite Additivity*

- A Conflict between Finite Additivity and Avoiding Dutch Book (1983)
- The Extent of non-Conglomerability of Finitely Additive Probabilities (1984)
- Statistical implications of Finitely Additive Probability (1986)
- A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Stratergies (1996)
- Non-conglomerability for Finitely valued, Finitely Additive Probability (1998)
- Remarks on the Theory of Conditional Probability (2001)
- Disintegration and Conglomerability for Unbounded Variables (2013)
- Infinite Previsions and Finitely Additive Expectations (2014)

*Relating to R.A.Fisher*

- Direct Inference and Inverse Inference (1978)
- Fisher's Fiducial Argument and Bayes Theorem (1992)
- R.A. Fisher on the Design of Experiments and Statistical Estimation (1992)
- Jeffreys, Fisher, and Keynes: predicting the third observation (1995)
- Probability and Inference : Essays in honor of Henry E. Kyburg, Jr. (2007)
- P’s in a Pod: some recipes for cooking Mendel’s data (2008)

*Relating to the Value of Information*

- Equilibirum, Common Knowledge, and Optimal Sequential Decisions (1992)
- Reasoning to a Foregone Conclusion (1996)
- A contrast between two decision rules for use with (convex) sets of probabilities:

Γ-Maximin versus E-admissibilty (2002) - Is Ignorance Bliss? (2008)

*Relating to other issues in Probability and Statistical Theory*

- Statistical Evidence and Belief Functions (1978)
- Why I am not a objective Bayesian; some refelctions propmpted by Rosenkrantz (1979)
- After-trial properties of best Neyman-Pearson Confidence Intervals (1981)
- Comments on Causal Decision Theory (1981)
- Remarks on Sequential Designs in Risk Assessment (1981)
- Entropy and Uncertainty (revised) (1987)
- Randomization in a Bayesian Perspective (1990)
- Remarks on the 'Bayesian' method of moments (1999)
- Improper Regular Conditional Distributions (2001)
- Stopping to Reflect: Comments and Criticism (2004)
- Independence for Full Conditional Measures, Graphoids and Bayesian Networks (2007)
- Non-conglomerability for countably additive probabilities (2015)

*Relating to Scoring Rules*

- Calibration, Coherence, and Scoring Rules (1985)
- Proper Scoring Rules, Dominated Forecasts, and Coherence (2009)
- Forecasting with Imprecise Probabilities (2011)
- Scoring Rules for Quantiles (2012)
- Exchange Rates (2013)
- Dominating Countably Many Forecasts (2014)

## Some recent presentations

- On the value of information in Games
- Bayesian Consensus
- Extending Bayesian Theory to Cooperative Groups
- Getting to know your probabilities
- Coherence with proper scoring rules
- How I Learned to Reduce My Incoherence
- Three contrasts between two senses of
*coherence* - ISIPTA-11
*Proceedings* - Three degrees of Imprecise Probability [IP] Theory (CLMPS-2015)