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  1. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane, Wahrscheinlichkeiistheorie.
    uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability..
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  2. Teddy Seidenfeld, Three Contrasts Between Two Senses of Coherence.
    = { 1, …, n} is a finite partition of the sure event: a set of states. Consider two acts A1, A2 defined by the their outcomes relative to.
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  3. Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Preference for Equivalent Random Variables: A Price for Unbounded Utilities.
    When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...)
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  4. Joseph B. Kadane, Mark J. Schervish & Teddy Seidenfeld, What Experiment Did We Just Do?
    Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from the (...)
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  5. Mark Schervish, Teddy Seidenfeld & Mark Schervish Joseph, Coherence with Proper Scoring Rules.
    • Coherence1 for previsions of random variables with generalized betting; • Coherence2 for probability forecasts of events with Brier score penalty; • Coherence3 probability forecasts of events with various proper scoring rules.
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  6. Teddy Seidenfeld, Extensions of Expected Utility Theory and Some Limitations of Pairwise Comparisons.
    We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set is (...)
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  7. Teddy Seidenfeld, Getting to Know Your Probabilities: Three Ways to Frame Personal Probabilities for Decision Making.
    Teddy Seidenfeld – CMU An old, wise, and widely held attitude in Statistics is that modest intervention in the design of an experiment followed by simple statistical analysis may yield much more of value than using very sophisticated statistical analysis on a poorly designed existing data set.
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  8. Teddy Seidenfeld, 1. Introduction.
    This paper offers a comparison between two decision rules for use when uncertainty is depicted by a non-trivial, convex2 set of probability functions Γ. This setting for uncertainty is different from the canonical Bayesian decision theory of expected utility, which uses a singleton set, just one probability function to represent a decision maker’s uncertainty. Justifications for using a non-trivial set of probabilities to depict uncertainty date back at least a half century (Good, 1952) and a foreshadowing of that idea can (...)
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  9. Teddy Seidenfeld, Independence for Full Conditional Measures, Graphoids and Bayesian Networks.
    This paper examines definitions of independence for events and variables in the context of full conditional measures; that is, when conditional probability is a primitive notion and conditioning is allowed on null events. Several independence concepts are evaluated with respect to graphoid properties; we show that properties of weak union, contraction and intersection may fail when null events are present. We propose a concept of “full” independence, characterize the form of a full conditional measure under full independence, and suggest how (...)
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  10. Teddy Seidenfeld, Mark Schervish.
    Consider two SEU Bayesian decision makers, Dick and Jane, who wish to form a cooperative partnership that will make decisions, constrained by the following two principles governing coherence and compromise.
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  11. Teddy Seidenfeld, On the Equivalence of Conglomerability and Disintegrability for Unbounded Random Variables.
    We extend a result of Dubins [3] from bounded to unbounded random variables. Dubins [3] showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a sufficient condition to extend this result to the collection Z of all random variables that have finite expected value and whose (...)
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  12. Teddy Seidenfeld, Proper Scoring Rules, Dominated Forecasts, and Coherence.
    De Finetti introduced the concept of coherent previsions and conditional previsions through a gambling argument and through a parallel argument based on a quadratic scoring rule. He shows that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules which might be used in place of the quadratic scoring rule. We give conditions under which a general strictly proper scoring rule can replace the quadratic scoring rule while (...)
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  13. Teddy Seidenfeld, The Fundamental Theorems of Prevision and Asset Pricing.
    DeFinetti took the concept of random variables as gambles very seriously, and used the concept to motivate the familiar concepts of probability and expectation. For each gamble X, he assumed that “You” would assign a value P (X), called the prevision of X so that you would be willing to accept the gamble β[X − P (X)] as fair for all positive and negative values β. The only constraint that deFinetti envisioned for you and your previsions is that you insisted (...)
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  14. Teddy Seidenfeld & Mark Schervish, Extending Bayesian Theory to Cooperative Groups: An Introduction to Indeterminate/Imprecise Probability Theories [IP] Also See Www.Sipta.Org.
    Pi(AS) = Pi(A)Pi(S) for i = 1, 2. But the Linear Pool created a group opinion P3 with positive dependence. P3(A|S) > P3(A).
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  15. Teddy Seidenfeld, Mark Schervish & Jay Kadane, Forecasting with Imprecise/Indeterminate Probabilities [IP] – Some Preliminary Findings.
    Part 1 Background on de Finetti’s twin criteria of coherence: Coherence1: 2-sided previsions free from dominance through a Book. Coherence2: Forecasts free from dominance under Brier (squared error) score. Part 2 IP theory based on a scoring rule.
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  16. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane (forthcoming). Stopping to Reflect. Journal of Philosophy.
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  17. Gordon Belot, Mark J. Schervish, Teddy Seidenfeld, Joseph B. Kadane, Miles MacLeod, Nancy J. Nersessian, Hylarie Kochiras, Bryan W. Roberts, Elay Shech & Richard Healey (2013). 1. Bayesian Orgulity Bayesian Orgulity (Pp. 483-503). Philosophy of Science 80 (4).
     
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  18. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane (2013). The Effect of Exchange Rates on Statistical Decisions. Philosophy of Science 80 (4):504-532.
  19. Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane (2010). Coherent Choice Functions Under Uncertainty. Synthese 172 (1):157 - 176.
    We discuss several features of coherent choice functions —where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of (...)
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  20. Teddy Seidenfeld, Mark Schervish & Joseph Kadane, When Coherent Preferences May Not Preserve Indifference Between Equivalent Random Variables: A Price for Unbounded Utilities.
    We extend de Finetti’s (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we demonstrate when the prevision of the difference between two such equivalent random variables must be positive. This result conflicts with the usual approach to theories of Subjective Expected Utility, where preference is defined over lotteries. In addition, we explore (...)
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  21. Joseph B. Kadane, Teddy Seidenfeld & Mark J. Schervish, A Rubinesque Theory of Decision.
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  22. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane (2002). A Rate of Incoherence Applied to Fixed-Level Testing. Proceedings of the Philosophy of Science Association 2002 (3):S248-S264.
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  23. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane (2002). A Rate of Incoherence Applied to Fixed‐Level Testing. Philosophy of Science 69 (S3):S248-S264.
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  24. Teddy Seidenfeld (2001). Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity. In Vincent F. Hendricks, Stig Andur Pederson & Klaus Frovin Jørgensen (eds.), Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, Kluwer.
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  25. Teddy Seidenfeld, Remarks on the Theory of Conditional Probability: Some Issues of Finite Versus Countable Additivity.
    This paper (based on joint work with M.J.Schervish and J.B.Kadane) discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P(a|a) = 0} = 1. This work builds upon the results of Blackwell and Dubins (1975).
     
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  26. Teddy Seidenfeld (2000). Substitution of Indifferent Options at Choice Nodes and Admissibility: A Reply to Rabinowicz. Theory and Decision 48 (4):305-310.
    Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery f, 0.5b> is strictly preferred to the compound lottery f, 0.5a>. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and b at (...)
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  27. Teddy Seidenfeld (2000). The Independence Postulate, Hypothetical and Called-Off Acts: A Further Reply to Rabinowicz. [REVIEW] Theory and Decision 48 (4):319-322.
    The Independence postulate links current preferences between called-off acts with current preferences between constant acts. Under the assumption that the chance-events used in compound von Neumann-Morgenstern lotteries are value-neutral, current preferences between these constant acts are linked to current preferences between hypothetical acts, conditioned by those chance events. Under an assumption of stability of preferences over time, current preferences between these hypothetical acts are linked to future preferences between what are then and there constant acts. Here, I show that a (...)
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  28. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane, Two Measures of Incoherence: How Not to Gamble If You Must.
    The degree of incoherence, when previsions are not made in accordance with a probability measure, is measured by either of two rates at which an incoherent bookie can be made a sure loser. Each bet is considered as an investment from the points of view of both the bookie and a gambler who takes the bet. From each viewpoint, we define an amount invested (or escrowed) for each bet, and the sure loss of incoherent previsions is divided by the escrow (...)
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  29. Teddy Seidenfeld, P's in a Pod: Some Recipes for Cooking Mendel's Data.
    In 1936 R.A.Fisher asked the pointed question, "Has Mendel's Work Been Rediscovered?" The query was intended to open for discussion whether someone altered the data in Gregor Mendel's classic 1866 research report on the garden pea, "Experiments in Plant-Hybridization." Fisher concluded, reluctantly, that the statistical counts in Mendel's paper were doctored in order to create a better intuitive fit between Mendelian expected values and observed frequencies. That verdict remains the received view among statisticians, so I believe. Fisher's analysis is a (...)
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  30. Timothy Herron, Teddy Seidenfeld & Larry Wasserman (1997). Divisive Conditioning: Further Results on Dilation. Philosophy of Science 64 (3):411-444.
    Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect "dilation". In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. In this paper we further investigate dilation on several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs.
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  31. Joseph B. Kadane, Mark J. Schervish & Teddy Seidenfeld (1996). When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion. Philosophy of Science 63 (3):289.
    When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model (...)
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  32. Stephen Menn, G. E. Reyes, Teddy Seidenfeld & Wilfrid Sieg (1996). Frege Versus Cantor and Dedekind: On the Concept of Number WW Tait. In Matthias Schirn (ed.), Frege: Importance and Legacy. Walter de Gruyter. 70.
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  33. Timothy Herron, Teddy Seidenfeld & Larry Wasserman (1994). The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:250 - 259.
    We report two issues concerning diverging sets of Bayesian (conditional) probabilities-divergence of "posteriors"-that can result with increasing evidence. Consider a set P of probabilities typically, but not always, based on a set of Bayesian "priors." Fix E, an event of interest, and X, a random variable to be observed. With respect to P, when the set of conditional probabilities for E, given X, strictly contains the set of unconditional probabilities for E, for each possible outcome X = x, call this (...)
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  34. Teddy Seidenfeld (1994). When Normal and Extensive Form Decisions Differ. In Dag Prawitz, Brian Skyrms & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. Elsevier. 451-463.
    The "traditional" view of normative decision theory, as reported (for example) in chapter 2 of Luce and RaiÃa's [1957] classic work, Games and Decisions, proposes a reduction of sequential decisions problems to non-sequential decisions: a reduction of extensive forms to normal forms. Nonetheless, this reduction is not without its critics, both from inside and outside expected utility theory, It islay purpose in this essay to join with those critics by advocating the following thesis.
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  35. Teddy Seidenfeld (1993). Outline of a Theory of Partially Ordered Preferences. Philosophical Topics 21 (1):173-189.
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  36. Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane, State-Dependent Utilities.
    Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several possible (...)
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  37. Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Decisions Without Ordering.
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  38. Teddy Seidenfeld, Joseph B. Kadane & Mark J. Schervish (1989). On the Shared Preferences of Two Bayesian Decision Makers. Journal of Philosophy 86 (5):225-244.
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  39. Teddy Seidenfeld (1988). Decision Theory Without “Independence” or Without “Ordering”. Economics and Philosophy 4 (02):267-.
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  40. Teddy Seidenfeld (1988). Rejoinder. Economics and Philosophy 4 (02):309-.
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  41. Teddy Seidenfeld (1986). Entropy and Uncertainty. Philosophy of Science 53 (4):467-491.
    This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity of (...)
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  42. Teddy Seidenfeld (1985). Calibration, Coherence, and Scoring Rules. Philosophy of Science 52 (2):274-294.
    Can there be good reasons for judging one set of probabilistic assertions more reliable than a second? There are many candidates for measuring "goodness" of probabilistic forecasts. Here, I focus on one such aspirant: calibration. Calibration requires an alignment of announced probabilities and observed relative frequency, e.g., 50 percent of forecasts made with the announced probability of.5 occur, 70 percent of forecasts made with probability.7 occur, etc. To summarize the conclusions: (i) Surveys designed to display calibration curves, from which a (...)
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  43. Teddy Seidenfeld (1984). Comments on Causal Decision Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:201 - 212.
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1984, Volume Two: Symposia and Invited Papers. (1984), pp. 201-212.
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  44. Teddy Seidenfeld (1983). Decisions with Indeterminate Probabilities. Behavioral and Brain Sciences 6 (2):259.
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  45. Teddy Seidenfeld & Mark J. Schervish (1983). A Conflict Between Finite Additivity and Avoiding Dutch Book. Philosophy of Science 50 (3):398-412.
    For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these (...)
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  46. Teddy Seidenfeld (1981). On After-Trial Properties of Best Neyman-Pearson Confidence Intervals. Philosophy of Science 48 (2):281-291.
    The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.
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  47. Teddy Seidenfeld (1979). Why I Am Not an Objective Bayesian; Some Reflections Prompted by Rosenkrantz. Theory and Decision 11 (4):413-440.
  48. Teddy Seidenfeld (1978). Direct Inference and Inverse Inference. Journal of Philosophy 75 (12):709-730.
    The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.
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  49. Teddy Seidenfeld (1978). Statistical Evidence and Belief Functions. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:478 - 489.
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1978, Volume Two: Symposia and Invited Papers. (1978), pp. 478-489.
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  50. Jessi Cisewski, Joseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld & Rafael Stern, The Rest of Sleeping Beauty.
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