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Results for 'Sets of probability distributions'
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- Sets of probability distributions, independence, and convexity.Fabio G. Cozman - 2012 - Synthese 186 (2):577-600.This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg (...)
- The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference.Timothy Herron, Teddy Seidenfeld & Larry Wasserman - 1994 - 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 (...)
- Uniform Probability Distribution Over All Density Matrices.Eddy Keming Chen & Roderich Tumulka - 2022 - Quantum Studies: Mathematics and Foundations.Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to (...)No categories
- Simultaneous measurement and joint probability distributions in quantum mechanics.Willem M. de Muynck, Peter A. E. M. Janssen & Alexander Santman - 1979 - Foundations of Physics 9 (1-2):71-122.The problem of simultaneous measurement of incompatible observables in quantum mechanics is studied on the one hand from the viewpoint of an axiomatic treatment of quantum mechanics and on the other hand starting from a theory of measurement. It is argued that it is precisely such a theory of measurement that should provide a meaning to the axiomatically introduced concepts, especially to the concept of observable. Defining an observable as a class of measurement procedures yielding a certain prescribed result for (...)
- Ergodic theory, interpretations of probability and the foundations of statistical mechanics.Janneke van Lith - 2001 - Studies in History and Philosophy of Modern Physics 32 (4):581--94.The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these (...)
- The foundations of probability and quantum mechanics.Peter Milne - 1993 - Journal of Philosophical Logic 22 (2):129 - 168.Taking as starting point two familiar interpretations of probability, we develop these in a perhaps unfamiliar way to arrive ultimately at an improbable claim concerning the proper axiomatization of probability theory: the domain of definition of a point-valued probability distribution is an orthomodular partially ordered set. Similar claims have been made in the light of quantum mechanics but here the motivation is intrinsically probabilistic. This being so the main task is to investigate what light, if any, this (...)
- Two Theories of Probability.Glenn Shafer - 1978 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978 (2):440-465.In a recent monograph, I advocated a new theory—the theory of belief functions—as an alternative to the Bayesian theory of epistemic probability. In this paper I compare the two theories in the context of a simple but authentic example of assessing evidence.The Bayesian theory is ostensibly the theory that assessment of evidence should proceed by conditioning additive probability distributions; this theory dates from the work of Bayes and Laplace in the second half of the eighteenth century. It (...)No categories
- Weighted sets of probabilities and minimax weighted expected regret: a new approach for representing uncertainty and making decisions.Joseph Y. Halpern & Samantha Leung - 2015 - Theory and Decision 79 (3):415-450.We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and (...)
- Validation of a bayesian belief network representation for posterior probability calculations on national crime victimization survey.Michael Riesen & Gursel Serpen - 2008 - Artificial Intelligence and Law 16 (3):245-276.This paper presents an effort to induce a Bayesian belief network (BBN) from crime data, namely the national crime victimization survey (NCVS). This BBN defines a joint probability distribution over a set of variables that were employed to record a set of crime incidents, with particular focus on characteristics of the victim. The goals are to generate a BBN to capture how characteristics of crime incidents are related to one another, and to make this information available to domain specialists. (...)
- How probable is an infinite sequence of heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so (...)
- How probable is an infinite sequence of heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so (...)
- The probability of inconsistencies in complex collective decisions.Christian List - 2005 - Social Choice and Welfare 24 (1):3-32.Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the
- Moving Beyond Sets of Probabilities.Gregory Wheeler - 2021 - Statistical Science 36 (2):201--204.The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demoting sets of probabilities from fundamental building blocks to (...)
- On the appropriate and inappropriate uses of probability distributions in climate projections and some alternatives.Joel Katzav, Erica L. Thompson, James Risbey, David A. Stainforth, Seamus Bradley & Mathias Frisch - 2021 - Climatic Change 169 (15).When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. (...)
- Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM.José Ignacio Rosado - 2011 - Foundations of Physics 41 (7):1200-1213.The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d 2−1)-dimensional simplex, we will call this set of vectors $\mathcal{Q}$ . Other way of represent a d-dimensional system is by the corresponding Bloch vector also in $\mathbb {R}^{d^{2}-1}$ , we will call this (...)
- Convergence of posterior probabilities in the Bayesian inference strategy.Marie Gaudard - 1985 - Foundations of Physics 15 (1):49-62.The formalism of operational statistics, a generalized approach to probability and statistics, provides a setting within which inference strategies can be studied with great clarity. This paper is concerned with the asymptotic behavior of the Bayesian inference strategy in this setting. We consider a sequence of posterior distributions, obtained from a prior as a result of successive conditionings by the events of an admissible sequence. We identify certain statistical hypotheses whose limiting posterior probabilities converge to one. We describe (...)
- Distention for Sets of Probabilities.Rush T. Stewart & Michael Nielsen - 2022 - Philosophy of Science 89 (3):604-620.Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...)
- Symmetry arguments against regular probability: A reply to recent objections.Matthew W. Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson (...)
- Skewness and asymmetry of distributions.Edmond A. Murphy - 1982 - Theoretical Medicine and Bioethics 3 (1):87-99.The skewness of a distribution, a poorly-defined term, is conventionally deemed to be invariant under linear transformations. A comparison is made of three criteria of it: the sign of odd central moments; the several relationships of the mean, the median and the mode; and asymmetry proper which is the set of ratios of the probability densities of all pairs of points equidistant above and below some arbitrary point, usually the principal mode. Some useful general relationships are discussed. The skeness (...)
- Believing Probabilistic Contents: On the Expressive Power and Coherence of Sets of Sets of Probabilities.Catrin Campbell-Moore & Jason Konek - 2019 - Analysis Reviews:anz076.Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic (...)
- Symmetry arguments against regular probability: A reply to recent objections.Matthew W. Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson (...)
- The Optimality of the Expert and Majority Rules Under Exponentially Distributed Competence.Luba Sapir - 1998 - Theory and Decision 45 (1):19-36.We study the uncertain dichotomous choice model. In this model a set of decision makers is required to select one of two alternatives, say âsupportâ or ârejectâ a certain proposal. Applications of this model are relevant to many areas, such as political science, economics, business and management. The purpose of this paper is to estimate and compare the probabilities that different decision rules may be optimal. We consider the expert rule, the majority rule and a few in-between rules. The information (...)
- Popper Functions, Uniform Distributions and Infinite Sequences of Heads.Alexander R. Pruss - 2015 - Journal of Philosophical Logic 44 (3):259-271.Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require (...)
- A set of independent axioms for probability.Karl R. Popper - 1938 - Mind 47 (186):275-277.
- On Statistical Properties of a New Bivariate Modified Lindley Distribution with an Application to Financial Data.Ahmed Elhassanein - 2022 - Complexity 2022:1-19.There is an increasing interest in expanding the one-parameter Lindley distribution to two-parameter, three-parameter, and five-parameter. The univariate one-parameter Lindley distribution is still one of the most applicable distributions in data analysis especially in lifetime data. Modeling dependent random quantities required bivariate parametric probability distributions. This study presents a new bivariate three-parameter probability distribution called bivariate modified Lindley distribution. The one-parameter modified Lindley distribution is used as a base line to construct the new model. Its statistical (...)
- A contrast between two decision rules for use with (convex) sets of probabilities: Γ-maximin versus e-admissibilty.T. Seidenfeld - 2004 - Synthese 140 (1-2):69 - 88.
- Putting probabilities first. How Hilbert space generates and constrains them.Michael Janas, Michael Cuffaro & Michel Janssen - manuscriptWe use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...)
- Entailment with near surety of scaled assertions of high conditional probability.Donald Bamber - 2000 - Journal of Philosophical Logic 29 (1):1-74.An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. (...)
- Mereological sets of distributive classes.Andrzej Pietruszczak - 1996 - Logic and Logical Philosophy 4:105-122.We will present an elementary theory in which we can speak of mereological sets composed of distributive classes. Besides the concept of a distributive class and the membership relation , it will possess the notion of a mereological set and the relation of being a mereological part. In this theory we will interpret Morse’s elementary set theory (cf. Morse [11]). We will show that our theory has a model, if only Morse’s theory has one.
- Coherence, Probability and Explanation.William Roche & Michael Schippers - 2014 - Erkenntnis 79 (4):821-828.Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution (...)
- Getting fancy with probability.Henry E. Kyburg - 1992 - Synthese 90 (2):189-203.There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should (...)
- Logic, probability, and quantum theory.Arthur I. Fine - 1968 - Philosophy of Science 35 (2):101-111.The aim of this paper is to present and discuss a probabilistic framework that is adequate for the formulation of quantum theory and faithful to its applications. Contrary to claims, which are examined and rebutted, that quantum theory employs a nonclassical probability theory based on a nonclassical "logic," the probabilistic framework set out here is entirely classical and the "logic" used is Boolean. The framework consists of a set of states and a set of quantities that are interrelated in (...)
- Probabilities on Sentences in an Expressive Logic.Marcus Hutter, John W. Lloyd, Kee Siong Ng & William T. B. Uther - 2013 - Journal of Applied Logic 11 (4):386-420.Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability (...)
- Getting Fancy with Probability.Henry E. Kyburg Jr - 1992 - Synthese 90 (2):189 - 203.There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should (...)
- Certain sets of postulates for distributive lattices with the constant elements.Bolesław Sobociński - 1972 - Notre Dame Journal of Formal Logic 13 (1):119-123.
- On the Joint Distribution of Observables.Beloslav Riečan - 2000 - Foundations of Physics 30 (10):1679-1686.A general algebraic system M is considered with two binary operations. The family of all measurable functions with values in the unit interval is a motivating example. A state is a morphism from M to the unit interval, an observable is a morphism from the family of Borel sets to M. A joint distribution of two observables is constructed. It is applied for the construction of the sum of observables and for a representation of conditional probability.
- Probability Dynamics.Amos Nathan - 2006 - Synthese 148 (1):229-256.‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of PD. PD (...)
- Quasi-probability distributions for arbitrary spin-j particles.G. Ramachandran, A. R. Usha Devi, P. Devi & Swarnamala Sirsi - 1996 - Foundations of Physics 26 (3):401-412.Quasi-probability distribution functions fj WW, fj MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fj sph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.
- Probabilities for Observing Mixed Quantum States given Limited Prior Information.Matthew J. Donald - unknownThe original development of the formalism of quantum mechanics involved the study of isolated quantum systems in pure states. Such systems fail to capture important aspects of the warm, wet, and noisy physical world which can better be modelled by quantum statistical mechanics and local quantum field theory using mixed states of continuous systems. In this context, we need to be able to compute quantum probabilities given only partial information. Specifically, suppose that B is a set of operators. This set (...)Export citation
Bookmark - Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications.Farwa Willayat, Naz Saud, Muhammad Ijaz, Anita Silvianita & Mahmoud El-Morshedy - 2022 - Complexity 2022:1-23.Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure (...)
- Negative and complex probability in quantum information.Vasil Penchev - 2012 - Philosophical Alternatives 21 (1):63-77.“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and (...)
- Compatibility of Subsystem States.Paul Butterley, Anthony Sudbery & Jason Szulc - 2006 - Foundations of Physics 36 (1):83-101.We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of (...)
- Boltzmann's probability distribution of 1877.Alexander Bach - 1990 - Archive for History of Exact Sciences 41 (1):1-40.No categories
- A Consistent Set of Infinite-Order Probabilities.David Atkinson & Jeanne Peijnenburg - 2013 - International Journal of Approximate Reasoning 54:1351-1360.Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a
- 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 (...)
- Quasi-probability distribution for spin-1/2 particles.C. Chandler, L. Cohen, C. Lee, M. Scully & K. Wódkiewicz - 1992 - Foundations of Physics 22 (7):867-878.Quantum distribution functions for spin-1/2 systems are derived for various characteristic functions corresponding to different operator orderings.
- WHAT IS. . . a Halting Probability?Cristian S. Calude - 2010 - Notices of the AMS 57:236-237.Turing’s famous 1936 paper “On computable numbers, with an application to the Entscheidungsproblem” defines a computable real number and uses Cantor’s diagonal argument to exhibit an uncomputable real. Roughly speaking, a computable real is one that one can calculate digit by digit, that there is an algorithm for approximating as closely as one may wish. All the reals one normally encounters in analysis are computable, like π, √2 and e. But they are much scarcer than the uncomputable reals because, as (...)Export citation Bookmark
- On subjective probability and related problems.Günter Menges - 1970 - Theory and Decision 1 (1):40-60.Of late, probability subjectivism was resuscitated by the development of statistical decision theory. In the decision model, which is briefly described in the paper, the knowledge of a probability distribution over the states of nature plays a decisive role. What sources of probability knowledge are legitimate, or at all possible, is the main point at issue. Different definitions, evaluations, and foundations of probability are narrated, discussed, and weighed against each other. The typical research strategy of the (...)
- Multisets and Distributions, in Drawing and Learning.Bart Jacobs - 2023 - In Alessandra Palmigiano & Mehrnoosh Sadrzadeh (eds.), Samson Abramsky on Logic and Structure in Computer Science and Beyond. Springer Verlag. pp. 1095-1146.Multisets are ‘sets’ in which elements may occur multiple times. Discrete probability distributions capture states in which elements may occur with probabilities that add up to one. This paper describes how the interaction between multisets and distributions lies at the heart of some basic constructions in probability theory, especially in distributions arising from drawing from an urn with multiple balls and in learning distributions from multiple occurrences of data. Drawing multiple balls from an (...)No categories
- Fair Infinite Lotteries, Qualitative Probability, and Regularity.Nicholas DiBella - 2022 - Philosophy of Science 89 (4):824-844.A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous (...)
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