Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.

Not since Ernest Nagel’s 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical. Hume’s skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own (...) criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability, as well as the older classical and subjective interpretations. (shrink)

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defences, objections, and replies into a convincing defence of the core of his theory, which is that we can analyse causation by appeal to the notion of manipulation.

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

Considers that intuitive predictions follow a judgmental heuristic-representativeness. By this heuristic, people predict the outcome that appears most representative of the evidence. Consequently, intuitive predictions are insensitive to the reliability of the evidence or to the prior probability of the outcome, in violation of the logic of statistical prediction. The hypothesis that people predict by representativeness was supported in a series of studies with both naive and sophisticated university students. The ranking of outcomes by likelihood coincided with the ranking by (...) representativeness, and Ss erroneously predicted rare events and extreme values if these happened to be representative. The experience of unjustified confidence in predictions and the prevalence of fallacious intuitions concerning statistical regression are traced to the representativeness heuristic. (shrink)

Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick (...) to incrementally well confirmed theories, because incremental confirmation takes one to (the most) informative (among all) true theories. However, incremental confirmation does not further this goal in general. I close by presenting a necessary and sufficient condition for revealing the confirmational structure in almost every world when presented separating data. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory The example (...) The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

This article shows that a slight variation of the argument in Milne 1996 yields the log‐likelihood ratio l rather than the log‐ratio measure r as “the one true measure of confirmation. ” *Received December 2006; revised December 2007. †To contact the author, please write to: Formal Epistemology Research Group, Zukunftskolleg and Department of Philosophy, University of Konstanz, P.O. Box X906, 78457 Konstanz, Germany; e‐mail: franz.huber@uni‐konstanz.de.

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...) truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory. (shrink)

I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, a problem (...) that, we will see, is much more extensive than usually recognized. I will argue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief. (shrink)

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (shrink)

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...) a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...) In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals a (...) different problem for probabilistic confirmation measures, a problem that is unlikely to lend itself to formal solution. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (shrink)