Bayesian Conditionalization Research Articles

The Supremacy of IBE over Bayesian Conditionalization

Van Fraassenas savąją pragmatinę mokslinio aiškinimo teoriją paremia Bayeso sąlyginės tikimybės matu ir kartu, priešingai nei teigia Prasetya, jos patvirtinimui panaudoja geriausio paaiškinimo išvedimą (GPI). Priešingai nei mano van Fraassenas, Bayeso sąlyginės tikimybės skaičiavimas negali būti atliktas pirmiausia nepritaikius GPI. Argumentas, apeliuojantis į blogų aibę, kurį naudoja van Fraassenas kritikuodamas GPI, grįžta bumerangu į pragmatinę teoriją ir Bayeso sąlyginę tikimybę, taigi tampa argumentu prieš van Fraasseną ir Prasetyą.

On the Ecological and Internal Rationality of Bayesian Conditionalization and Other Belief Updating Strategies

Previous articleNext article No AccessOn the Ecological and Internal Rationality of Bayesian Conditionalization and Other Belief Updating StrategiesOlav Benjamin VassendOlav Benjamin Vassend Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The British Journal for the Philosophy of Science Just Accepted Society: The British Society for the Philosophy of Science Article DOIhttps://doi.org/10.1086/724447 HistoryAccepted December 11, 2022 © 2023 The British Society for the Philosophy of Science. All Rights reserved.PDF download Crossref reports no articles citing this article.

Preference Change and Utility Conditionalization

Olav Vassend has recently (2021) presented a decision-theoretic argument for updating utility functions by what he calls “utility conditionalization.” Vassend’s argument is meant to mirror closely the well-known argument for Bayesian conditionalization due to Hilary Greaves and David Wallace (2006). I show that Vassend’s argument is inconsistent with ZF set theory and argue that it therefore does not provide support for utility conditionalization.

Conciliatory Views on Peer Disagreement and the Order of Evidence Acquisition

Abstract The evidence that we get from peer disagreement is especially problematic from a Bayesian point of view since the belief revision caused by a piece of such evidence cannot be modelled along the lines of Bayesian conditionalisation. This paper explains how exactly this problem arises, what features of peer disagreements are responsible for it, and what lessons should be drawn for both the analysis of peer disagreements and Bayesian conditionalisation as a model of evidence acquisition. In particular, it is pointed out that the same characteristic of evidence from disagreement that explains the problems with Bayesian conditionalisation also suggests an interpretation of suspension of belief in terms of imprecise probabilities.

Bayesian Updating When What You Learn Might Be False (Forthcoming in Erkenntnis)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle.

The logic of partial supposition

AbstractAccording to orthodoxy, there are two basic moods of supposition: indicative and subjunctive. The most popular formalizations of the corresponding norms of suppositional judgement are given by Bayesian conditionalization and Lewisian imaging, respectively. It is well known that Bayesian conditionalization can be generalized (via Jeffrey conditionalization) to provide a model for the norms of partial indicative supposition. This raises the question of whether imaging can likewise be generalized to model the norms of ‘partial subjunctive supposition’. The present article casts doubt on whether the most natural generalizations of imaging are able to provide a plausible account of the norms of partial subjunctive supposition .

Not So Phenomenal!

The main aims in this article are to discuss and criticize the core thesis of a position that has become known as phenomenal conservatism. According to this thesis, its seeming to one that p provides enough justification for a belief in p to be prima facie justified (a thesis the article labels Standard Phenomenal Conservatism). This thesis captures the special kind of epistemic import that seemings are claimed to have. To get clearer on this thesis, the article embeds it, first, in a probabilistic framework in which updating on new evidence happens by Bayesian conditionalization, and second, a framework in which updating happens by Jeffrey conditionalization. The article spells out problems for both views, and then generalizes some of these to nonprobabilistic frameworks. The main theme of the discussion is that the epistemic import of a seeming (or experience) should depend on its content in a plethora of ways that phenomenal conservatism is insensitive to.

Jeffrey Meets Kolmogorov

Jeffrey conditionalization is a rule for updating degrees of belief in light of uncertain evidence. It is usually assumed that the partitions involved in Jeffrey conditionalization are finite and only contain positive-credence elements. But there are interesting examples, involving continuous quantities, in which this is not the case. Q1 Can Jeffrey conditionalization be generalized to accommodate continuous cases? Meanwhile, several authors, such as Kenny Easwaran and Michael Rescorla, have been interested in Kolmogorov’s theory of regular conditional distributions (rcds) as a possible framework for conditional probability which handles probability-zero events. However the theory faces a major shortcoming: it seems messy and ad hoc. Q2 Is there some axiomatic theory which would justify and constrain the use of rcds, thus serving as a possible foundation for conditional probability? These two questions appear unrelated, but they are not, and this paper answers both. We show that when one appropriately generalizes Jeffrey conditionalization as in Q1, one obtains a framework which necessitates the use of rcds. It is then a short step to develop a general theory which addresses Q2, which we call the theory of extensions. The theory is a formal model of conditioning which recovers Bayesian conditionalization, Jeffrey conditionalization, and conditionalization via rcds as special cases.

Commutativity, Normativity, and Holism: Lange Revisited

AbstractLange (2000) famously argues that although Jeffrey Conditionalization is non-commutative over evidence, it’s not defective in virtue of this feature. Since reversing the order of the evidence in a sequence of updates that don’t commute does not reverse the order of the experiences that underwrite these revisions, the conditions required to generate commutativity failure at the level of experience will fail to hold in cases where we get commutativity failure at the level of evidence. If our interest in commutativity is, fundamentally, an interest in the order-invariance of information, an updating sequence that does not violate such a principle at the more fundamental level of experiential information should not be deemed defective. This paper claims that Lange’s argument fails as a general defense of the Jeffrey framework. Lange’s argument entails that the inputs to the Jeffrey framework differ from those of classical Bayesian Conditionalization in a way that makes them defective. Therefore, either the Jeffrey framework is defective in virtue of not commuting its inputs, or else it is defective in virtue of commuting the wrong kinds of ones.

Truth and Conformity on Networks

Typically, public discussions of questions of social import exhibit two important properties: (1) they are influenced by conformity bias, and (2) the influence of conformity is expressed via social networks. We examine how social learning on networks proceeds under the influence of conformity bias. In our model, heterogeneous agents express public opinions where those expressions are driven by the competing priorities of accuracy and of conformity to one’s peers. Agents learn, by Bayesian conditionalization, from private evidence from nature, and from the public declarations of other agents. Our key findings are that networks that produce configurations of social relationships that sustain a diversity of opinions empower honest communication and reliable acquisition of true beliefs, and that the networks that do this best turn out to be those which are both less centralized and less connected.

Probability, coherent belief and coherent belief changes

This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent’s credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing one’s belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change.

Bayesian argumentation and the value of logical validity.

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, in which the fundamental norms are traditionally assumed to be logical. Here, we present a major generalization of extant Bayesian approaches to argumentation that (a) utilizes a new class of Bayesian learning methods that are better suited to modeling dynamic and conditional inferences than standard Bayesian conditionalization, (b) is able to characterize the special value of logically valid argument schemes in uncertain reasoning contexts, (c) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (d) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

A PUZZLE ABOUT EXPERTS, EVIDENTIAL SCREENING-OFF AND CONDITIONALIZATION

ABSTRACTI present a puzzle about the epistemic role beliefs about experts' beliefs play in a rational agent's system of beliefs. It is shown that accepting the claim that an expert's degree of belief in a proposition, A, screens off the evidential support another proposition, B, gives to A in case the expert knows and is certain about whether B is true, leads in some cases to highly unintuitive conclusions. I suggest a solution to the puzzle according to which evidential screening off is rejected, but show that the price of this solution is either giving up on the mere idea of deferring to expert's opinion or giving up on Bayesian conditionalization.

Inference to the Best Explanation in Uncertain Evidential Situations

Abstract It has recently been argued that a non-Bayesian probabilistic version of inference to the best explanation (IBE*) has a number of advantages over Bayesian conditionalization (Douven [2013]; Douven and Wenmackers [2017]). We investigate how IBE* could be generalized to uncertain evidential situations and formulate a novel updating rule IBE**. We then inspect how it performs in comparison to its Bayesian counterpart, Jeffrey conditionalization (JC), in a number of simulations where two agents, each updating by IBE** and JC, respectively, try to detect the bias of a coin while they are only partially certain what side the coin landed on. We show that IBE** more often prescribes high probability to the actual bias than JC. We also show that this happens considerably faster, that IBE** passes higher thresholds for high probability, and that it in general leads to more accurate probability distributions than JC. 1Introduction2Generalizing Inference to the Best Explanation to Uncertain Evidential Situations3Detecting the Bias of a Coin4Overall Performance of IBE** versus Jeffrey Conditionalization5Speed of Convergence6The Threshold for High Subjective Probability7Epistemic Inaccuracy8Conclusions

Learning from others: conditioning versus averaging

How should we revise our beliefs in response to the expressed probabilistic opinions of experts on some proposition when these experts are in disagreement? In this paper I examine the suggestion that in such circumstances we should adopt a linear average of the experts’ opinions and consider whether such a belief revision policy is compatible with Bayesian conditionalisation. By looking at situations in which full or partial deference to the expressed opinions of others is required by Bayesianism I show that only in trivial circumstances are the requirements imposed by linear averaging compatible with it.

Learning and Pooling, Pooling and Learning

We explore which types of probabilistic updating commute with convex IP pooling (Stewart and Ojea Quintana 2017). Positive results are stated for Bayesian conditionalization (and a mild generalization of it), imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of (precise) externally Bayesian pooling operators due to Wagner (Log J IGPL 18(2):336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

A Novel Solution to the Problem of Old Evidence

One of the most troubling and persistent challenges for Bayesian Confirmation Theory is the Problem of Old Evidence (POE). The problem arises for anyone who models scientific reasoning by means of Bayesian Conditionalization. This article addresses the problem as follows: First, I clarify the nature and varieties of the POE and analyze various solution proposals in the literature. Second, I present a novel solution that combines previous attempts while making weaker and more plausible assumptions. Third and last, I summarize my findings and put them into the context of the general debate about POE and Bayesian reasoning.

Indeterminate versus Imprecise Interval Probabilities: The Keynes-Knight and the De Finetti-Savage Approaches

The operational definitions of uncertainty used by John M. Keynes and Frank H. Knight are based on missing information that will not be available to the decision maker at any time. The founder of this approach is George Boole. This leads to indeterminate interval probabilities. The definition of uncertainty proposed by Bruno de Finetti and Leonard J. Savage is significantly different from the one advanced by Keynes and Knight. Uncertainty, for de Finetti and Savage, can only exist in the initial conditions of an experiment or study due to measurement error or a lack of data available at the beginning of a study. Imprecise interval probabilities will always eventually result in precise probabilities due to Bayesian conditionalization. Recent studies, such as the papers by Feduzi, Runde and Zappia (2012, 2014), seem to have overlooked this particular aspect of de Finetti and Savage’s 1962 paper ‘Sul Modo di Scegliere le Probabilita Iniziali’. This particular work is cited by the said scholars as supporting their claim that there are similarities between the de Finetti-Savage conception of uncertainty and the Keynes-Knight approach. This claim, however, loses much of its appeal once it is realized that the discussion of de Finetti and Savage involves only the initial probabilities.

Reflecting on finite additivity

An infinite lottery experiment seems to indicate that Bayesian conditionalization may be inconsistent when the prior credence function is finitely additive because, in that experiment, it conflicts with the principle of reflection. I will show that any other form of updating credences would produce the same conflict, and, furthermore, that the conflict is not between conditionalization and reflection but, instead, between finite additivity and reflection. A correct treatment of the infinite lottery experiment requires a careful treatment of finite additivity. I will show that the results of the experiment, paradoxical though they may be, are not inconsistent, but that they conflict with one particular version of reflection (special reflection). I will reject that version and I will propose a slight modification of a different version of reflection (general reflection) such that the modified version does maintain the mutual consistency of finite additivity, reflection and conditionalization. As a result, I will strengthen the case for finite additivity by showing that Bayesian conditionalization is fully consistent with it.

Many irrelevant evils: a response to the Bayesian problem of evil

Robert Bass argues that the evidential problem of evil can be strengthened by the application of a Bayesian conditionalization argument. I argue that, whatever the merits of Bayesian conditionalization arguments, they are unsuccessful in substantiating the evidential problem of evil because the problem of evil doesn’t meet the necessary conditions for applying the formula informatively. I offer two examples to show that a successful application of the Bayesian formula must pass two tests, the competency test and the connection test. I then show that the problem of evil passes neither, and is therefore not strengthened by the Bayesian analysis. I conclude that Bass’s reformulated argument poses no substantive threat to theism.