Results for 'imprecise probabilities'

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  1.  7
    Imprecise Probabilities.Seamus Bradley - 2019 - In Claus Beisbart & Nicole J. Saam (eds.), Computer Simulation Validation - Fundamental Concepts, Methodological Frameworks, and Philosophical Perspectives. Springer. pp. 525-540.
    This chapter explores the topic of imprecise probabilities as it relates to model validation. IP is a family of formal methods that aim to provide a better representationRepresentation of severe uncertainty than is possible with standard probabilistic methods. Among the methods discussed here are using sets of probabilities to represent uncertainty, and using functions that do not satisfy the additvity property. We discuss the basics of IP, some examples of IP in computer simulation contexts, possible interpretations of (...)
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  2.  54
    Can Imprecise Probabilities Be Practically Motivated? A Challenge to the Desirability of Ambiguity Aversion.Miriam Schoenfield - 2020 - Philosophers Imprint 20 (30):1-21.
    The usage of imprecise probabilities has been advocated in many domains: A number of philosophers have argued that our belief states should be “imprecise” in response to certain sorts of evidence, and imprecise probabilities have been thought to play an important role in disciplines such as artificial intelligence, climate science, and engineering. In this paper I’m interested in the question of whether the usage of imprecise probabilities can be given a practical motivation (a (...)
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  3. Imprecise Probabilities and Unstable Betting Behaviour.Anna Mahtani - 2018 - Noûs 52 (1):69-87.
    Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.
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  4. Imprecise Probability and Higher Order Vagueness.Susanna Rinard - 2017 - Res Philosophica 94 (2):257-273.
    There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...)
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  5.  52
    Imprecise Probabilities.Seamus Bradley - 2019 - Stanford Encyclopedia of Philosophy.
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  6. Imprecise Probabilities.Anna Mahtani - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 107-130.
  7.  59
    Imprecise Probability and Chance.Anthony F. Peressini - 2016 - Erkenntnis 81 (3):561-586.
    Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, (...)
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  8. Probabilistic Opinion Pooling with Imprecise Probabilities.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Journal of Philosophical Logic 47 (1):17-45.
    The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...)
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  9. Imprecise Probability and the Measurement of Keynes's "Weight of Arguments".William Peden - 2018 - IfCoLog Journal of Logics and Their Applications 5 (4):677-708.
    Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the usefulness (...)
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  10. Resolving Peer Disagreements Through Imprecise Probabilities.Lee Elkin & Gregory Wheeler - 2018 - Noûs 52 (2):260-278.
    Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...)
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  11.  29
    Using imprecise probabilities to address the questions of inference and decision in randomized clinical trials.Lyle C. Gurrin, Peter D. Sly & Paul R. Burton - 2002 - Journal of Evaluation in Clinical Practice 8 (2):255-268.
    Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...)
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  12. Imprecise Probabilities in Quantum Mechanics.Stephan Hartmann - 2015 - In Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.), Foundations and Methods from Mathematics to Neuroscience. Stanford: CSLI Publications. pp. 77-82.
    In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for example, the paper collected (...)
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  13. Statistical Reasoning with Imprecise Probabilities.Peter Walley - 1991 - Chapman & Hall.
    An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.
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  14.  19
    Imprecise Probability: Theories and Applications.Fabio Cozman, Sebastien Destercke & Teddy Seidenfeld - unknown
    This special issue of the International Journal of Approximate Reasoning grew out of the 8th International Symposium on Imprecise Probability: Theories and Applications. The symposium was organized by the Society for Imprecise Probability: Theories and Applications at the Université de Technologie de Compiègne in July 2013. The biennial ISIPTA meetings are well established among international conferences on generalized methods for uncertainty quantification. The first ISIPTA took place in Gent in 1999, followed by meetings in Cornell, Lugano, Carnegie Mellon, (...)
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  15.  2
    Imprecise probability trees: Bridging two theories of imprecise probability.Gert de Cooman & Filip Hermans - 2008 - Artificial Intelligence 172 (11):1400-1427.
  16.  1
    Propagating imprecise probabilities in Bayesian networks.Gernot D. Kleiter - 1996 - Artificial Intelligence 88 (1-2):143-161.
  17. A Decision Theory for Imprecise Probabilities.Susanna Rinard - 2015 - Philosophers' Imprint 15.
    Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness (...)
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  18. A Gentle Approach to Imprecise Probabilities.Gregory Wheeler - forthcoming - In Thomas Augustin, Fabio Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld. Springer.
    The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can (...)
     
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  19.  89
    Quasi-Bayesian Analysis Using Imprecise Probability Assessments And The Generalized Bayes' Rule.Kathleen M. Whitcomb - 2005 - Theory and Decision 58 (2):209-238.
    The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of (...)
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  20. Decision making with imprecise probabilities.Brian Weatherson - 1998
    Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with such cases, and (...)
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  21.  19
    Transitive reasoning with imprecise probabilities.Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2015 - In S. Destercke & T. Denoeux (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015). Springer LNAI 9161. pp. 95-105.
    We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.
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  22.  31
    Forecasting with Imprecise Probabilities.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - unknown
    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 (...)
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  23. Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent.Niki Pfeifer & G. D. Kleiter - 2007 - In Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications. pp. 347--356.
    The modus ponens (A -> B, A :. B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A -> B, ¬A :. ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities. (...)
     
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  24. Dutch Book Arguments and Imprecise Probabilities.Seamus Bradley - 2012 - In Dennis Dieks, Stephan Hartmann, Michael Stoeltzner & Marcel Weber (eds.), Probabilities, Laws and Structures. Springer.
  25. Evidentialism, Inertia, and Imprecise Probability.William Peden - forthcoming - The British Journal for the Philosophy of Science:1-23.
    Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state (...)
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  26.  4
    Radical Pooling and Imprecise Probabilities.Ignacio Ojea Quintana - forthcoming - Erkenntnis:1-28.
    This paper focuses on radical pooling, or the question of how to aggregate credences when there is a fundamental disagreement about which is the relevant logical space for inquiry. The solution advanced is based on the notion of consensus as common ground, where agents can find it by suspending judgment on logical possibilities. This is exemplified with cases of scientific revolution. On a formal level, the proposal uses algebraic joins and imprecise probabilities; which is shown to be compatible (...)
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  27.  6
    Rational Choice Using Imprecise Probabilities and Utilities.Paul Weirich - 2021 - Cambridge: Cambridge University Press.
    An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation (...)
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  28.  97
    Pascal’s Wager and Decision-making with Imprecise Probabilities.André Neiva - forthcoming - Philosophia:1-30.
    Unlike other classical arguments for the existence of God, Pascal’s Wager provides a pragmatic rationale for theistic belief. Its most popular version says that it is rationally mandatory to choose a way of life that seeks to cultivate belief in God because this is the option of maximum expected utility. Despite its initial attractiveness, this long-standing argument has been subject to various criticisms by many philosophers. What is less discussed, however, is the rationality of this choice in situations where the (...)
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  29.  51
    Inferring beliefs as subjectively imprecise probabilities.Steffen Andersen, John Fountain, Glenn W. Harrison, Arne Risa Hole & E. Elisabet Rutström - 2012 - Theory and Decision 73 (1):161-184.
    We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in (...)
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  30. The Principle of Indifference and Imprecise Probability.Susanna Rinard - 2014 - Thought: A Journal of Philosophy 3 (2):110-114.
    Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.
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  31.  1
    Respecting evidence: belief functions not imprecise probabilities.Nicholas J. J. Smith - 2022 - Synthese 200 (6):1-30.
    AbstractThe received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer belief functions (...)
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  32. Extending Bayesian Theory to Cooperative Groups: an introduction to Indeterminate/Imprecise Probability Theories [IP] also see www.sipta.org.Teddy Seidenfeld & Mark Schervish - unknown
    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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  33. Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015).Thomas Augistin, Serena Dora, Enrique Miranda & Erik Quaeghebeur (eds.) - 2015 - Aracne Editrice.
     
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  34.  2
    Real-time dynamic programming for Markov decision processes with imprecise probabilities.Karina V. Delgado, Leliane N. de Barros, Daniel B. Dias & Scott Sanner - 2016 - Artificial Intelligence 230 (C):192-223.
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  35. Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications.Niki Pfeifer & G. D. Kleiter - 2007
     
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  36. The sensitivity of belief networks to imprecise probabilities: an experimental investigation.A. Pradhan, M. Henrion, G. Provan, B. del Favero & K. Huang - 1996 - Artificial Intelligence 84 (1-2):357.
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  37. The sensitivity of belief networks to imprecise probabilities: an experimental investigation.Malcolm Pradhan, Max Henrion, Gregory Provan, Brendan Del Favero & Kurt Huang - 1996 - Artificial Intelligence 85 (1-2):363-397.
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  38.  58
    Imprecision and indeterminacy in probability judgment.Isaac Levi - 1985 - Philosophy of Science 52 (3):390-409.
    Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.
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  39. Scoring Imprecise Credences: A Mildly Immodest Proposal.Conor Mayo-Wilson & Gregory Wheeler - 2016 - Philosophy and Phenomenological Research 92 (1):55-78.
    Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show (...)
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  40.  13
    Logics of Imprecise Comparative Probability.Yifeng Ding, Wesley H. Holliday & Thomas F. Icard - 2021 - International Journal of Approximate Reasoning 132:154-180.
    This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures.
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  41.  44
    Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events.Peter Milne - 2008 - Studia Logica 90 (3):425-453.
    Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an (...)
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  42.  25
    Imprecise Bayesian Networks as Causal Models.David Kinney - 2018 - Information 9 (9):211.
    This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when (...)
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  43.  8
    On the imprecision of full conditional probabilities.Gregory Wheeler & Fabio G. Cozman - 2021 - Synthese 199 (1-2):3761-3782.
    The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.
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  44. Forecasting with Imprecise/Indeterminate Probabilities [IP] – some preliminary findings.Teddy Seidenfeld, Mark Schervish & Jay Kadane - unknown
    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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  45.  71
    Ambiguity Aversion in the Field of Insurance: Insurers' Attitude to Imprecise and Conflicting Probability Estimates. [REVIEW]Laure Cabantous - 2007 - Theory and Decision 62 (3):219-240.
    This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability of the loss. Second, it (...)
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  46.  59
    Chancy accuracy and imprecise credence.Jennifer Carr - 2015 - Philosophical Perspectives 29 (1):67-81.
    Can we extend accuracy-based epistemic utility theory to imprecise credences? There's no obvious way of proceeding: some stipulations will be necessary for either (i) the notion of accuracy or (ii) the epistemic decision rule. With some prima facie plausible stipulations, imprecise credences are always required. With others, they’re always impermissible. Care is needed to reach the familiar evidential view of imprecise credence: that whether precise or imprecise credences are required depends on the character of one's evidence. (...)
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  47.  8
    On Imprecise Bayesianism in the Face of an Increasingly Larger Outcome Space.Marc Fischer - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):367-379.
    Wilcox proposed an argument against imprecise probabilities and for the principle of indifference based on a thought experiment where he argues that it is very intuitive to feel that one’s confidence in drawing a ball of a given colour out of an unknown urn should decrease while the number of potential colours in the urn increases. In my response to him, I argue that one’s intuitions may be unreliable because it is very hard to truly feel completely ignorant (...)
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  48.  72
    A Counterexample to Three Imprecise Decision Theories.Seamus Bradley - 2019 - Theoria 85 (1):18-30.
    There is currently much discussion about how decision making should proceed when an agent's degrees of belief are imprecise; represented by a set of probability functions. I show that decision rules recently discussed by Sarah Moss, Susanna Rinard and Rohan Sud all suffer from the same defect: they all struggle to rationalize diachronic ambiguity aversion. Since ambiguity aversion is among the motivations for imprecise credence, this suggests that the search for an adequate imprecise decision rule is not (...)
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  49. Subjective Probabilities Need Not be Sharp.Jake Chandler - 2014 - Erkenntnis 79 (6):1273-1286.
    It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be borne (...)
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  50. Against Radical Credal Imprecision.Susanna Rinard - 2013 - Thought: A Journal of Philosophy 2 (1):157-165.
    A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...)
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