A Bayesian Account of Independent Evidence with Applications

Philosophy of Science, 2007

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988

We describe a viewpoint on the DempsterlSbafer "theory of evidence," and provide an interpretation which regards the combination formulas as statistics of the opinions of "experts." This is done by introducing spaces with binary operations that are simpler to interpret or simpler to implement than the standard combination formula, and showing that these spaces can be mapped homomorphically onto the DempsterlShafer theory of evidence space. The experts in the space of "opinions of experts" combine information in a Bayesian fashion. We present alternative spaces for the combination of evidence suggested by this viewpoint.

The British Journal for the Philosophy of Science, 2008

Bayesian epistemology postulates a probabilistic analysis of many sorts of ordinary and scientific reasoning. Huber ([2005]) has provided a novel criticism of Bayesianism, whose core argument involves a challenging issue: confirmation by uncertain evidence. In this paper, we argue that under a properly defined Bayesian account of confirmation by uncertain evidence, Huber's criticism fails. By contrast, our discussion will highlight what we take as some new and appealing features of Bayesian confirmation theory.

Book review of Paul Horwich, Probability and Evidence (Cambridge Philosophy Classics edition), Cambridge: Cambridge University Press, 2016, 147pp, £14.99 (paperback).

5th International Symposium on Imprecise …, 2007

2008

We study two notions of independence in evidence theory: random set independence and strong independence. We show their relation for special models (Bayesian basic assignments and consonant bodies of evidence) a well as in general case.

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayes-ian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga's rebuttal to Belot's analysis, which focuses attention on the role that the assumption of countable additivity plays in Belot's criticisms. 1. Introduction. Consider the following compound result about asymp-totic statistical inference. A community of Bayesian investigators who begin an investigation with conflicting opinions about a common family of statistical hypotheses use shared evidence to achieve a consensus about which hypothesis is the true one. Specifically, suppose the investigators agree on a partition of statistical hypotheses and share observations of an increasing sequence of random samples with respect to whichever is the true statistical hypothesis from this partition. 1 Then, under various combinations of formal conditions that we review in this essay, ex ante (i.e., before accepting the new evidence) it is practically certain that each of the investigators' conditional probabilities approach 1 for the one true hypothesis in the partition. The result is compound: individual investigators achieve asymptotic certainty about the unknown, true statistical hypothesis. Second, the shared ev

Philosophy of statistics, handbook of …, 2011

Wheeler, Gregory and Williamson, Jon (2011) Evidential probability and objective Bayesian epistemology. In: Philosophy of statistics. Handbook of the Philosophy of Science . Elsevier, pp. 307-331. ... The full text of this publication is not available from this repository.

Philosophy Compass, 2011

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemology, and statistics, and criticisms of these applications.

Synthese, 2007