Search results for 'imprecise probabilities' (try it on Scholar)

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  1.  11
    Lyle C. Gurrin, Peter D. Sly & Paul R. Burton (2002). Using Imprecise Probabilities to Address the Questions of Inference and Decision in Randomized Clinical Trials. 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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  2.  39
    Niki Pfeifer & G. D. Kleiter (2007). Human Reasoning with Imprecise Probabilities: Modus Ponens and Denying the Antecedent. In Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications. 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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  3.  63
    Brian Weatherson, Decision Making with Imprecise Probabilities.
    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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  4.  4
    Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo (2015). Transitive Reasoning with Imprecise Probabilities. In S. Destercke & T. Denoeux (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015). Springer LNAI 9161 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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  5.  12
    Lee Elkin & Gregory Wheeler (2016). Resolving Peer Disagreements Through Imprecise Probabilities. Noûs 50 (4).
    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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  6. Seamus Bradley (2012). Dutch Book Arguments and Imprecise Probabilities. In Dennis Dieks, Stephan Hartmann, Michael Stoeltzner & Marcel Weber (eds.), Probabilities, Laws and Structures. Springer
  7.  58
    Peter Walley (1991). Statistical Reasoning with Imprecise Probabilities. Chapman & Hall.
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  8.  37
    Anna Mahtani (2016). Imprecise Probabilities and Unstable Betting Behaviour. Noûs 50 (4).
    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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  9.  5
    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 (...)
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  10.  6
    Gregory Wheeler & Lee Elkin (2016). Resolving Peer Disagreements Through Imprecise Probabilities. Noûs 50 (3).
    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.  36
    Steffen Andersen, John Fountain, Glenn W. Harrison, Arne Risa Hole & E. Elisabet Rutström (2012). Inferring Beliefs as Subjectively Imprecise Probabilities. 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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  12.  34
    Susanna Rinard (2015). A Decision Theory for Imprecise Probabilities. Philosophers' Imprint 15 (7).
    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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  13.  58
    Stephan Hartmann (forthcoming). Imprecise Probabilities in Quantum Mechanics. In Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.), Foundations and Methods from Mathematics to Neuroscience. CSLI Publications
  14. Conor Mayo‐Wilson & Gregory Wheeler (2016). Scoring Imprecise Credences: A Mildly Immodest Proposal. 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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  15. Horacio Arló-Costa & Jeffrey Helzner (2010). Ambiguity Aversion: The Explanatory Power of Indeterminate Probabilities. Synthese 172 (1):37 - 55.
    Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...)
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  16.  29
    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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  17. Jake Chandler (2014). Subjective Probabilities Need Not Be Sharp. 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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  18. Arthur Paul Pedersen & Gregory Wheeler (2014). Demystifying Dilation. Erkenntnis 79 (6):1305-1342.
    Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is (...)
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  19.  60
    Paul D. Thorn (forthcoming). On the Preference for More Specific Reference Classes. Synthese:1-27.
    In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency (...)
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  20. Jonathan Weisberg (forthcoming). You’Ve Come a Long Way, Bayesians. Journal of Philosophical Logic:1-18.
    Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in (...)
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  21. Brad Armendt (2014). Pragmatic Interests and Imprecise Belief. Philosophy of Science 80 (5):758-768.
    Does the strength of a particular belief depend upon the significance we attach to it? Do we move from one context to another, remaining in the same doxastic state concerning p yet holding a stronger belief that p in one context than in the other? For that to be so, a doxastic state must have a certain sort of context-sensitive complexity. So the question is about the nature of belief states, as we understand them, or as we think a theory (...)
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  22. Yann Benétreau-Dupin (2015). Blurring Out Cosmic Puzzles. Philosophy of Science 82 (5):879–891.
    The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation (...)
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  23.  55
    Nils‐Eric Sahlin & Paul Weirich (2014). Unsharp Sharpness. Theoria 80 (1):100-103.
    In a recent, thought-provoking paper Adam Elga argues against unsharp – e.g., indeterminate, fuzzy and unreliable – probabilities. Rationality demands sharpness, he contends, and this means that decision theories like Levi's, Gärdenfors and Sahlin's, and Kyburg's, though they employ different decision rules, face a common, and serious, problem. This article defends the rule to maximize minimum expected utility against Elga's objection.
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  24.  28
    Miriam Schoenfield (2014). Decision Making in the Face of Parity. Philosophical Perspectives 28 (1):263-277.
    Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases in (...)
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  25.  36
    Arthur Paul Pedersen & Gregory Wheeler (2015). Dilation, Disintegrations, and Delayed Decisions. In Thomas Augistin, Serena Dora, Enrique Miranda & Erik Quaeghebeur (eds.), Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015). Aracne Editrice 227–236.
    Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although (...)
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  26. Paul Weirich (1996). Mark Kaplan, Decision Theory as Philosophy. [REVIEW] Philosophy in Review 16 (3):179-180.
    Mark Kaplan proposes amending decision theory to accommodate better cases in which an agent's probability assignment is imprecise. The review describes and evaluates his proposals.
     
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  27.  33
    Barry Lam (2013). Vagueness and Ambivalence. Acta Analytica 28 (3):359-379.
    What is the proper attitude toward what is expressed by a vague sentence in the face of borderline evidence? Some call this attitude “ambivalence” and distinguish it from uncertainty. It has been argued that Classical Epistemicism conjoined with classical probability theory fails to characterize this attitude, and that we must therefore abandon classical logic or classical probabilities in the presence of vagueness. In this paper, I give a characterization of ambivalence assuming a supervaluationist semantics for vague terms that does (...)
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  28.  5
    Paolo Vicig (2016). A Note on the Equivalence of Coherence and Constrained Coherence. Minds and Machines 26 (3):303-305.
    Constrained coherence is compared to coherence and its role in the behavioural interpretation of coherence is discussed. The equivalence of these two notions is proven for coherent conditional previsions, showing that the same course of reasoning applies to several similar concepts developed in the realm of imprecise probability theory.
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  29. Seamus Bradley & Katie Steele (2014). Should Subjective Probabilities Be Sharp? Episteme 11 (3):277-289.
    There has been much recent interest in imprecise probabilities, models of belief that allow unsharp or fuzzy credence. There have also been some influential criticisms of this position. Here we argue, chiefly against Elga , that subjective probabilities need not be sharp. The key question is whether the imprecise probabilist can make reasonable sequences of decisions. We argue that she can. We outline Elga's argument and clarify the assumptions he makes and the principles of rationality he (...)
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  30.  11
    Marshall Abrams, Imprecise Probability and Biological Fitness.
    I argue that biological fitness sometimes depends on imprecise probabilities. I give a new argument that some outcomes are without objective probability, and argue that organisms encountering environments might sometimes be outcomes of this kind. I argue that since fitness depends on relationships between traits and environments, this means that fitness can depend on imprecise probabilities, and can be defined by an interval between maximum and minimum precise fitnesses. One trait is fitter than another when its (...)
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  31. Adam Elga (2010). Subjective Probabilities Should Be Sharp. Philosophers' Imprint 10 (05).
    Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.
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  32.  27
    F. P. A. Coolen (2006). On Nonparametric Predictive Inference and Objective Bayesianism. Journal of Logic, Language and Information 15 (1-2):21-47.
    This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes (...)
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  33. Moisés Goldszmidt & Judea Pearl (1996). Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling. Artificial Intelligence 84:57-112.
    This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering (...)
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  34.  23
    Anthony F. Peressini (2016). Imprecise Probability and Chance. 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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  35.  36
    Aidan Lyon (forthcoming). Vague Credence. Synthese:1-24.
    It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a (...)
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  36.  13
    Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo (2016). Transitivity in Coherence-Based Probability Logic. Journal of Applied Logic 14:46-64.
    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. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to (...)
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  37.  34
    Yann Benétreau-Dupin (2015). Probabilistic Reasoning in Cosmology. Dissertation, The University of Western Ontario
    Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., (...)
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  38.  25
    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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  39.  20
    Horacio Arlo-Costa & Jeffrey Helzner, Comparative Ignorance and the Ellsberg Phenomenon.
    The "Ellsberg phenomenon" has played a significant role in research on imprecise probabilities. Fox and Tversky [5] have attempted to explain this phenomenon in terms of their "comparative ignorance" hypothesis. We challenge that explanation and present empirical work suggesting an explanation that is much closer to Ellsberg's own diagnosis.
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  40.  2
    Paolo Vicig & Teddy Seidenfeld, Bruno de Finetti and Imprecision.
    We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.
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  41.  86
    Ruth Chang (2016). Parity, Imprecise Comparability, and the Repugnant Conclusion. Theoria 82 (2):183-215.
    This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of (...)
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  42.  50
    Dylan Dodd (2013). Roger White's Argument Against Imprecise Credences. British Journal for the Philosophy of Science 64 (1):69-77.
    According to the Imprecise Credence Framework (ICF), a rational believer's doxastic state should be modelled by a set of probability functions rather than a single probability function, namely, the set of probability functions allowed by the evidence ( Joyce [2005] ). Roger White ( [2010] ) has recently given an arresting argument against the ICF, which has garnered a number of responses. In this article, I attempt to cast doubt on his argument. First, I point out that it's not (...)
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  43. Alan Hájek & Michael Smithson (2012). Rationality and Indeterminate Probabilities. Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with (...)
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  44.  7
    Claus Beisbart (2016). A Humean Guide to Spielraum Probabilities. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (1):189-216.
    The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may (...)
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  45.  36
    Rohan Sud (2014). A Forward Looking Decision Rule for Imprecise Credences. Philosophical Studies 167 (1):119-139.
    Adam Elga (Philosophers’ Imprint, 10(5), 1–11, 2010) presents a diachronic puzzle to supporters of imprecise credences and argues that no acceptable decision rule for imprecise credences can deliver the intuitively correct result. Elga concludes that agents should not hold imprecise credences. In this paper, I argue for a two-part thesis. First, I show that Elga’s argument is incomplete: there is an acceptable decision rule that delivers the intuitive result. Next, I repair the argument by offering a more (...)
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  46.  92
    J. Franklin (2001). Resurrecting Logical Probability. Erkenntnis 55 (2):277-305.
    The logical interpretation of probability, or ``objective Bayesianism''''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason'''' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from (...)
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  47.  37
    Takashi Hayashi & Ryoko Wada (2010). Choice with Imprecise Information: An Experimental Approach. [REVIEW] Theory and Decision 69 (3):355-373.
    This article provides an experimental analysis of attitude toward imprecise and variable information. Imprecise information is provided in the form of a set of possible probability values, such that it is virtually impossible for the subjects to guess or estimate, which one in the set is true or more likely to be true. We investigate how geometric features of such information pieces affect choices. We find that the subjects care about more features than the pairs of best-case and (...)
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  48.  42
    Daniel Jeremy Singer (2014). Sleeping Beauty Should Be Imprecise. Synthese 191 (14):3159-3172.
    The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(H\!eads)=[0,1/2]\) . I show, perhaps surprisingly, that this solution can account for the many of the (...)
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  49.  87
    Andrei Khrennikov (2015). CHSH Inequality: Quantum Probabilities as Classical Conditional Probabilities. Foundations of Physics 45 (7):711-725.
    In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework covering all (...)
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  50. Jarosław Pykacz (2006). “Solution” of the EPR Paradox: Negative, or Rather Fuzzy Probabilities? [REVIEW] Foundations of Physics 36 (3):437-442.
    Negative probabilities were several times proposed in the literature as a way to reconcile violation of Bell-type inequalities with the premise of local realism. It is argued that instead of using negative probabilities that have no physical meaning one can use for this purpose fuzzy probabilities that have sound and unambiguous interpretation.
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