About

Teddy Seidenfeld holds the title of Herbert A. Simon University Professor of Philosophy and Statistics at Carnegie Mellon University. His research focuses on the foundational, conceptual, and methodological questions of broad importance within philosophy and statistics. As a distinguished faculty member, he contributes to the interdisciplinary environment of the Department of Philosophy, integrating insights from philosophy, logic, and statistical sciences to address complex issues in rationality, decision theory, and related fields.

Research topics

• Artificial Intelligence
• Computer Science
• Mathematics
• Machine Learning
• Mathematical economics
• Statistics
• Philosophy
• Econometrics
• Economics
• Epistemology

Selected publications

• Posterior Invariance of Multiplicative Contrasts under Margin Constraints in Contingency Tables

  ArXiv.org · 2026-04-27

  articleOpen accessSenior author

  Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that certain odds ratios are unaffected by constraining the margins, it is less clear when this invariance holds more generally. This paper studies posterior inference for a broad class of multiplicative contrasts of multinomial cell probabilities, which we refer to as generalized odds ratios, and addresses exactly when fixing a margin alters inference about them. We consider Bayesian inference under multinomial sampling and under models in which partition sums of the table are fixed in advance, and assume that the marginal and conditional parameters are independent a priori. Under additional mild assumptions, we show that the posterior distribution of a generalized odds ratio is invariant to fixing a margin if and only if the coefficients defining the contrast sum to zero within the margin.

  PublisherOA PDF

• Posterior Invariance of Multiplicative Contrasts under Margin Constraints in Contingency Tables

  arXiv (Cornell University) · 2026-04-27

  preprintOpen accessSenior author

  Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that certain odds ratios are unaffected by constraining the margins, it is less clear when this invariance holds more generally. This paper studies posterior inference for a broad class of multiplicative contrasts of multinomial cell probabilities, which we refer to as generalized odds ratios, and addresses exactly when fixing a margin alters inference about them. We consider Bayesian inference under multinomial sampling and under models in which partition sums of the table are fixed in advance, and assume that the marginal and conditional parameters are independent a priori. Under additional mild assumptions, we show that the posterior distribution of a generalized odds ratio is invariant to fixing a margin if and only if the coefficients defining the contrast sum to zero within the margin.

  PublisherDOI

• Information lost by conditioning on the random margins in a two-by-two table

  Biometrika · 2025-01-01

  articleOpen access

  Abstract We study the amount of Fisher information about the odds ratio parameter that one loses by conditioning on the random margin totals of a $ 2\times 2 $ table for the cases in which the data arise either as a multinomial sample or as two independent binomial samples. When there is a nuisance parameter, as in this problem, many authors have proposed the concept of partial information to quantify the amount of Fisher information about the parameter of interest. We show that, as the sample size of the table becomes infinite (in such a way that all margin totals also become infinite), the fraction of partial information that one loses by conditioning on both margins goes to 0.

  PublisherOA PDFDOI

• Finite Additivity, Complete Additivity, and the Comparative Principle

  Erkenntnis · 2024-02-29

  articleOpen access1st authorCorresponding

  Abstract In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) Existence : Settings where no countably additive probability exists though finitely additive probabilities do. (2) Complete Additivity : Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has probability 0, regardless the cardinality of that union. Then probability distributions are discrete, not continuous. We use Easwaran’s (Easwaran, Thought 2:53–61, 2013) advocacy of the Comparative principle to illustrate these two concerns. Easwaran supports countable additivity, both for numerical probabilities and for finer, qualitative probabilities, by defending a condition he calls the Comparative principle [ $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> ]. For numerical probabilities, principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> contrasts pairs, P 1 and P 2 , defined over a common partition $$\prod$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∏</mml:mo> </mml:math> = {a i : i ∈ I} of measurable events. $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> requires that no P 1 may be pointwise dominated, i.e., no (finitely additive) probability P 2 exists such that for each i ∈ I, P 2 (a i ) &gt; P 1 (a i ). By design, the cardinality of $$\prod$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∏</mml:mo> </mml:math> is not limited in $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> , which Easwaran asserts is important when arguing that the principle does not require more, or less, than that probability is countably additive. We agree that a numerical probability P satisfies principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> in all partitions just in case P is countably additive. However, we show that for numerical probabilities, by considering the size of the algebra of events to which probability is applied, principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> is subject to each of the above concerns, (1) and (2). Also, Easwaran considers principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> with non-numerical, qualitative probabilities, where a qualitative probability may be finer than an almost agreeing numerical probability P. A qualitative probability is regular if possible events are strictly more likely than impossible events. Easwaran motivates and illustrates regular qualitative probabilities using a continuous, almost agreeing quantitative probability that is uniform on the unit interval. We make explicit the conditions for applying principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> with qualitative probabilities and show that $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> restricts regular qualitative probabilities to those whose almost agreeing quantitative probabilities are completely additive. For instance, Easwaran’s motivating example of a regular qualitative probability is precluded by principle $${\mathcal{C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> .

  PublisherOA PDFDOI

• WHEN NO PRICE IS RIGHT

  The Review of Symbolic Logic · 2024

  • Economics

  Abstract In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by a nonstandard utility function. Non-Archimedean preferences arise when some random quantities have no fair price. Two common situations give rise to non-Archimedean preferences: random quantities whose values must be greater than every real number, and strict preferences between random quantities that are deemed closer in value than every positive real number. We also show how to extend a non-Archimedean preference to a larger set of random quantities. The random quantities that we consider include real-valued random variables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions made by the existing theories and give conditions under which the utility that represents preference is the expected value of a state-dependent utility with respect to a probability over states.

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• More on the Logic(s) of Evaluation in Basic and Clinical Science

  2023-04-28

  book-chapter1st authorCorresponding
  PublisherDOI

• Constriction for sets of probabilities

  arXiv (Cornell University) · 2023-01-13

  preprintOpen accessSenior author

  Given a set of probability measures $\mathcal{P}$ representing an agent's knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A procedure generating a new assessment of beliefs is said to constrict $A$ if the bounds on the probability of $A$ after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes' updating does not allow for constriction, for all $A\in\mathcal{F}$. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.

  PublisherOA PDFDOI

• Learning and total evidence with imprecise probabilities

  International Journal of Approximate Reasoning · 2022 · 2 citations

  • Computer Science
  • Artificial Intelligence
  • Machine Learning
  PublisherDOI

• The Value Provided by a Scientific Explanation

  Theory and decision library. Series A, Philosophy and methodology of the social sciences · 2022-01-01

  book-chapterCorresponding
  PublisherDOI

• Exposing some points of interest about non-exposed points of desirability

  International Journal of Approximate Reasoning · 2022-02-24 · 2 citations

  articleOpen accessSenior author
  PublisherOA PDFDOI

Frequent coauthors

• Joseph B. Kadane

  Carnegie Mellon University

  70 shared

• Mark J. Schervish

  Carnegie Mellon University

  67 shared

• Rafael B. Stern

  10 shared

• Ruobin Gong

  Rutgers Sexual and Reproductive Health and Rights

  7 shared

• Henry E. Kyburg

  3 shared

• Sébastien Destercke

  Heuristics and Diagnostics for Complex Systems

  3 shared

• Hailin Liu

  Fuzhou University

  3 shared

• Larry Wasserman

  3 shared