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Mark J. Schervish [24]Mark Schervish [5]
  1.  32
    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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  2.  2
    Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Forecasting with Imprecise Probabilities.
    We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly (...)
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  3.  4
    Jessica Cisewski, Joseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld & Rafael Stern, Sleeping Beauty’s Credences.
    The Sleeping Beauty problem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about Sleeping Beauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...)
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  4.  7
    Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane, Infinite Previsions and Finitely Additive Expectations.
    We give an extension of de Finetti’s concept of coherence to unbounded random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of the Fundamental Theorem of Prevision to deal with conditional previsions and unbounded random variables.
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  5. Joseph B. Kadane, Mark J. Schervish & Teddy Seidenfeld (1999). Rethinking the Foundations of Statistics. Cambridge University Press.
    This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...)
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  6. 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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  7.  6
    Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane, Dominating Countably Many Forecasts.
    We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.
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  8.  26
    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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  9.  17
    Joseph B. Kadane, Mark Schervish & Teddy Seidenfield (2008). Is Ignorance Bliss? Journal of Philosophy 105 (1):5-36.
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  10.  9
    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.
  11.  6
    Joseph B. Kadane, Teddy Seidenfeld & Mark J. Schervish, A Rubinesque Theory of Decision.
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  12.  8
    Teddy Seidenfel, Mark J. Schervish & Joseph B. Kadane (2012). What Kind of Uncertainty is That? Using Personal Probability for Expressing One's Thinking About Logical and Mathematical Propositions. Journal of Philosophy 109 (8-9):516-533.
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  13. 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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  14.  37
    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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  15.  1
    Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Non-­Conglomerability for Countably Additive Measures That Are Not Κ-­Additive.
    Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...)
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  16.  20
    Jessi Cisewski, Joseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld & Rafael Stern, The Rest of Sleeping Beauty.
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  17.  19
    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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  18.  26
    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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  19.  26
    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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  20.  19
    Mark J. Schervish, Teddy Seidenfeld & Joseph B. Kadane (2013). The Effect of Exchange Rates on Statistical Decisions. Philosophy of Science 80 (4):504-532.
    Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. When multiple currencies are available for paying the loss, one must take explicit (...)
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  21.  15
    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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  22.  18
    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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  23.  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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  24.  1
    Mark J. Schervish, Joseph B. Kadane & Teddy Seidenfeld, Characterization of Proper and Strictly Proper Scoring Rules for Quantiles.
    We give necessary and sufficient conditions for a scoring rule to be proper for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.
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  25.  12
    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.
    It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...)
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  26.  11
    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.
    It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...)
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  27.  2
    Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Decisions Without Ordering.
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  28.  4
    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. Joseph B. Kadane, Mark J. Schervish & Teddy Seidenfeld (2012). Rethinking the Foundations of Statistics. Cambridge University Press.
    This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...)
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