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Bayesian epistemic values: focus on surprise, measure probability!

J. M. Stern, C. A. De Braganca Pereira
2013 Logic Journal of the IGPL  
The e-value or epistemic value, ev(H ), measures the statistical significance of H , a hypothesis about the parameter θ of a Bayesian model.  ...  In particular, we show how and why the e-value focus on or conforms with s(θ ) = p(θ )/r(θ ), the model's surprise function relative to the reference density r(θ ), while it keeps itself consistent with  ...  , Brazil; COBAL-2011, the III Latin American Meeting on Bayesian Statistics, held on October 23-27 at UFRO-Universidad de La Frontera, Pucón, Araucanía, Chile; MBR-2012, Model-Based Reasoning in Science  ... 
doi:10.1093/jigpal/jzt023 fatcat:x5c5dg6uujh45mdwcgspjnwpmu

Plausibility and probability in deductive reasoning [article]

Andrew MacFie
2019 arXiv   pre-print
Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws from both probability and the theory of algorithms.  ...  We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others.  ...  Probability spaces consist of a measurable space and a probability measure. In Bayesianism, the measurable space may be substituted by a "sentence space" which is closed under logical operations.  ... 
arXiv:1708.09032v6 fatcat:u4xliqk6zzavvf3jpkf47xkj3y

Graphical models for imprecise probabilities

Fabio Gagliardi Cozman
2005 International Journal of Approximate Reasoning  
This paper presents an overview of graphical models that can handle imprecision in probability values. The paper first reviews basic concepts and presents a brief historical account of the field.  ...  One of the recurring problems in probability theory is how to handle a collection of assessments that can be satisfied by more than one probability measure.  ...  In this paper we focus on graphical models that have nodes/edges associated with statistical objects.  ... 
doi:10.1016/j.ijar.2004.10.003 fatcat:icz32fuck5a65a26ndt5y4ooly

Shapley and Banzhaf Values as Probability Transformations

Enrique Miranda, Ignacio Montes
2018 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
We study a number of particular models of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distortion models.  ...  We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations.  ...  In this paper, we focus on games taking values on [0, 1] and that are normalized and monotone; in other words, in those that can be regarded as lower probabilities.  ... 
doi:10.1142/s0218488518500411 fatcat:lh5i4ajz7fcy3goofaq2bvsoqa

Confidence is epistemic probability for empirical science

Tore Schweder
2018 Journal of Statistical Planning and Inference  
Condence and (serious) p-values are interpreted as epistemic probabilities, which do not fully follow ordinary probability calculus.  ...  Condence distributions, which are posterior distributions not based on any Bayesian priors, are discussed in nontechnical terms, with emphasis on the condence curve.  ...  It is surprising that the optimality is with probability one, and not only that the risk is uniformly optimal.  ... 
doi:10.1016/j.jspi.2017.09.016 fatcat:5gfvils54ngvde3tjkrqfdyvui

Verified Computation with Probabilities [chapter]

Scott Ferson, Jack Siegrist
2012 IFIP Advances in Information and Communication Technology  
Probability bounds analysis computes bounds guaranteed to enclose probabilities and probability distributions even when these assumptions are relaxed or removed.  ...  This paper presents an overview of probability bounds analysis as a computationally practical implementation of the theory of imprecise probabilities that represents verified computation of probabilities  ...  Bayesian statistics quantifies epistemic uncertainty with subjective probabilities.  ... 
doi:10.1007/978-3-642-32677-6_7 fatcat:lmnzlik2djbsdmlhrfzbqg7wgm

Uncertainty about the value of quantum probability for cognitive modeling

Christina Behme
2013 Behavioral and Brain Sciences  
from classical probability theory (CPT).  ...  AbstractI argue that the overly simplistic scenarios discussed by Pothos & Busemeyer (P&B) establish at best that quantum probability theory (QPT) is a logical possibility allowing distinct predictions  ...  One feature of assigning probabilities is that uncertainty can be aleatory or epistemic.  ... 
doi:10.1017/s0140525x12002889 pmid:23673026 fatcat:wowhoqf2ivemvn2k2wo57ic26a

Combining Probability and Logic

Fabio Cozman, Rolf Haenni, Jan-Willem Romeijn, Federica Russo, Gregory Wheeler, Jon Williamson
2009 Journal of Applied Logic  
The papers in this volume concern either the special focus on the connection between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic  ...  Note that, depending on the semantics in question, the X 1 , . . . , X n , Y might be probabilities or sets of probabilities.  ...  Second, the research often focuses on learning logical and probabilistic sentences from data.  ... 
doi:10.1016/j.jal.2007.12.001 fatcat:uosf3cmdlbbk5b3gxc4uqbxq7m

Subjective probability and quantum certainty

Carlton M. Caves, Christopher A. Fuchs, Rüdiger Schack
2007 Studies in history and philosophy of modern physics  
Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations  ...  In the Bayesian approach to quantum mechanics, probabilities-and thus quantum states-represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems.  ...  Mermin for many, many discussions over the years, for a careful reading of an earlier draft of this paper, and for his continued encouragement that our Bayesian points are worth trying to make.  ... 
doi:10.1016/j.shpsb.2006.10.007 fatcat:3fwm3prqz5cl5hkjbvr7j6vsam

Subjective probability and quantum certainty [article]

Carlton M. Caves, Christopher A. Fuchs, Ruediger Schack
2007 arXiv   pre-print
Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations  ...  In the Bayesian approach to quantum mechanics, probabilities--and thus quantum states--represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems.  ...  Mermin for many, many discussions over the years, for a careful reading of an earlier draft of this paper, and for his continued encouragement that our Bayesian points are worth trying to make.  ... 
arXiv:quant-ph/0608190v2 fatcat:iwq2syrbb5epxpl53ayoyjyuuq

Active inference and epistemic value

Karl Friston, Francesco Rigoli, Dimitri Ognibene, Christoph Mathys, Thomas Fitzgerald, Giovanni Pezzulo
2015 Cognitive Neuroscience  
This is formally consistent with the Infomax principle, generalizing formulations of active vision based upon salience (Bayesian surprise) and optimal decisions based on expected utility and risk-sensitive  ...  This article focuses on the basic theory, illustrating the ideas with simulations.  ...  Bayesian surprise: Epistemic value is also the Bayesian surprise expected under counterfactual outcomes.  ... 
doi:10.1080/17588928.2015.1020053 pmid:25689102 fatcat:xl333x6oi5d5xkumzen624splm

Objective probability and the assessment of evidence

M. Redmayne
2003 Law, Probability and Risk  
and wider theories of epistemic justification.  ...  The purpose of the survey is, in part, to shed light on an argument about the use of Bayes' rule in fact-finding recently made by Alvin Goldman.  ...  There is a fairly general phenomenon here, which is that it is easier to agree if debate is conducted at an abstract, rather than a very finely focused level. 69 his idea of a level of focus was one we  ... 
doi:10.1093/lpr/2.4.275 fatcat:swxotonwibc2rckheuud45vxja

Simplicity, Truth, and Probability [chapter]

Kevin T. Kelly
2011 Philosophy of Statistics  
The idea is that simplicity does not point at or reliably indicate the truth but, rather, keeps inquiry on the cognitively most direct path to the truth.  ...  This chapter examines some standard, statistical explanations of the role of simplicity in scientific method and argues that none of them explains, without circularity, how a reliance on simplicity could  ...  Acknowledgements The results on random strategies were obtained in close collaboration with Conor Mayo-Wilson, who also provided detailed comments on the draft.  ... 
doi:10.1016/b978-0-444-51862-0.50031-9 fatcat:b74gm6kfrfhqvjklwxws5nsdee

Belief and probability: A general theory of probability cores

Horacio Arló-Costa, Arthur Paul Pedersen
2012 International Journal of Approximate Reasoning  
We argue that core systems can also play a natural and important role in Bayesian epistemology and decision theory.  ...  What is true is that his ideas have lasting value and the paradoxes he addressed continue to inspire innovative work in formal epistemology.  ...  We had access to a paper he had been preparing on the reduction of belief to degrees of belief.  ... 
doi:10.1016/j.ijar.2012.01.002 fatcat:vkrpogi3jvhrjab5oef3rwcrn4

How Probabilities Reflect Evidence

James M. Joyce
2005 Philosophical Perspectives  
This focus on decision-making can obscure the fact that Bayesianism is also an epistemology.  ...  Epistemic Bayesianism, as understood here, is the view that evidential relationships are best represented probabilistically. It has three central components: Evidential Probability.  ...  Measuring Balances of Evidence. Let's begin by focusing on what it means to say that a body of data provides some evidence in favor of a hypothesis.  ... 
doi:10.1111/j.1520-8583.2005.00058.x fatcat:ko4tfb7jq5cdfj4aitwyttsvti
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