In this paper we consider a Bayesian treatment of ‘Duhem's thesis’, the proposition that theories are never refuted on empirical grounds because they cannot be tested in isolation from auxiliary hypotheses about initial conditions or the operation of scientific instruments. Sawyer, Beed, and Sankey consider Duhem's thesis and its role in hypothesis testing, using four theories from economics and finance as examples. Here we consider Duhem's thesis in the context of theory choice, econometric results, and the ‘farm problem’ in agricultural (...) economics. This problem is defined as persistently low and highly variable prices, incomes, and returns in the agricultural sector as compared to the nonagricultural sector of the U.S. economy. The existence of the farm problem tends to refute an implication of general equilibrium theory — that resources flow to equate returns between sectors of the economy. We discuss Duhem's thesis in the context of demonstrating why evidence supporting the farm problem has not diminished the standing of general equilibrium theory among agricultural economists. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

Mayo (1987) sought to discredit Urbach's (1985) arguments against randomization as a universal requirement in clinical and agricultural trials. The present reply rebuts Mayo's criticisms.

While many philosophers of science have accorded special evidential significance to tests whose results are "novel facts", there continues to be disagreement over both the definition of novelty and why it should matter. The view of novelty favored by Giere, Lakatos, Worrall and many others is that of use-novelty: An accordance between evidence e and hypothesis h provides a genuine test of h only if e is not used in h's construction. I argue that what lies behind the intuition that (...) novelty matters is the deeper intuition that severe tests matter. I set out a criterion of severity akin to the notion of a test's power in Neyman-Pearson statistics. I argue that tests which are use-novel may fail to be severe, and tests that are severe may fail to be use-novel. I discuss the 1919 eclipse data as a severe test of Einstein's law of gravity. (shrink)

Evidential support is often equated with confirmation, where evidence supports hypothesis H if and only if it increases the probability of H. This article argues against this received view. As the author shows, support is a comparative notion in the sense that increase-in-probability is not. A piece of evidence can confirm H, but it can confirm alternatives to H to the same or greater degree; and in such cases, it is at best misleading to conclude that the evidence supports H. (...) The author puts forward an alternative view that defines support in terms of measures of degree of confirmation. The proposed view is both sufficiently comparative and able to accommodate the increase-in-probability aspect of support. The author concludes that the proposed measure-theoretic approach to support provides a superior alternative to the standard confirmatory approach. (shrink)

The stopping rule for a sequential experiment is the rule or procedure for determining when that experiment should end. Accordingly, the stopping rule principle (SRP) states that the evidential relationship between the final data from a sequential experiment and a hypothesis under consideration does not depend on the stopping rule: the same data should yield the same evidence, regardless of which stopping rule was used. I clarify and provide a novel defense of two interpretations of the main argument against the (...) SRP, the foregone conclusion argument. According to the first, the SRP allows for highly confirmationally unreliable experiments, which concept I make precise, to confirm highly. According to the second, it entails the evidential equivalence of experiments differing significantly in their confirmational reliability. I rebut several attempts to deflate or deflect the foregone conclusion argument, drawing connections with replication in science and the likelihood principle. (shrink)

Credal reductivism is the view that outright belief is reducible to degrees of confidence or ‘credence’. The most popular versions of credal reductivism all have the consequence that if you are near-maximally confident that p in a low-stakes situation, then you outright believe p. This paper addresses a recent objection to this consequence—the Correctness Objection— introduced by Jeremy Fantl and Matthew McGrath and further developed by Jacob Ross and Mark Schroeder. The objection is that near-maximal confidence cannot entail outright belief (...) because when you believe a false proposition, you are wrong or incorrect, whereas you can be highly confident of a false proposition in a low-stakes situation without being incorrect. Both Fantl and McGrath’s and Ross and Schoeder’s versions of the Correctness Objection admit of multiple interpretations. But it is argued that even on the most charitable interpretations the objection fails. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Several philosophers and psychologists have characterized belief in conspiracy theories as a product of irrational reasoning. Proponents of conspiracy theories apparently resist revising their beliefs given disconfirming evidence and tend to believe in more than one conspiracy, even when the relevant beliefs are mutually inconsistent. In this paper, we bring leading views on conspiracy theoretic beliefs closer together by exploring their rationality under a probabilistic framework. We question the claim that the irrationality of conspiracy theoretic beliefs stems from an inadequate (...) response to disconfirming evidence and internal incoherence. Drawing analogies to Lakatosian research programs, we argue that maintaining a core conspiracy belief can be Bayes-rational when it is embedded in a network of auxiliary beliefs, which can be revised to protect the more central belief from disconfirmation. We propose that the irrationality associated with conspiracy belief lies not in a flawed updating method, but in a failure to converge toward wellconfirmed, stable belief networks in the long run. This approach not only reconciles previously disjointed views, but also points toward more specific descriptions of why agents may be prone to adopting beliefs in conspiracy theories. (shrink)

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the (...) ‘principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. *Received February 2007; revised July 2007. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA 15260; e-mail: [email protected]. (shrink)

The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing (...) a generalized approach to conditionalization. The technique is illustrated by application to simple examples. (shrink)

Several philosophers and psychologists have characterized belief in conspiracy theories as a product of irrational reasoning. Proponents of conspiracy theories apparently resist revising their beliefs given disconfirming evidence and tend to believe in more than one conspiracy, even when the relevant beliefs are mutually inconsistent. In this paper, we bring leading views on conspiracy theoretic beliefs closer together by exploring their rationality under a probabilistic framework. We question the claim that the irrationality of conspiracy theoretic beliefs stems from an inadequate (...) response to disconfirming evidence and internal incoherence. Drawing analogies to Lakatosian research programs, we argue that maintaining a core conspiracy belief can be Bayes-rational when it is embedded in a network of auxiliary beliefs, which can be revised to protect the more central belief from disconfirmation. We propose that the (ir)rationality associated with conspiracy belief lies not in a flawed updating method, but in their failure to converge toward well-confirmed, stable belief networks in the long run. This approach not only reconciles previously disjointed views, but also points toward more specific hypotheses explaining why some agents may be prone to adopting beliefs in conspiracy theories. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

This collection of essays is a Festschrift for Ernest W. Adams, and is based on a symposium that was held in his honor in 1993. As the title suggests, most of the essays focus on probability and the logic of conditionals, and the relationship between them; they draw their inspiration from Adams’s seminal work on the subject. As a computer scientist, I was struck by just how much the topics discussed play a major role in much recent work in computer (...) science, and how relevant much recent work in computer science is to some of the issues discussed here. (shrink)

This collection of essays is a Festschrift for Ernest W. Adams, and is based on a symposium that was held in his honor in 1993. As the title suggests, most of the essays focus on probability and the logic of conditionals, and the relationship between them; they draw their inspiration from Adams’s seminal work on the subject. As a computer scientist, I was struck by just how much the topics discussed play a major role in much recent work in computer (...) science, and how relevant much recent work in computer science is to some of the issues discussed here. (shrink)

Kuhn's theory of paradigm reveals a pattern of scientific progress, in which normal science alternates with scientific revolution. But Kuhn underrated too much the function of scientific test in his pattern, because he focuses all his attention on the hypothetico-deductive schema instead of Bayesian schema. This paper employs Bayesian schema to re-examine Kuhn's theory of paradigm, to uncover its logical and rational components, and to illustrate the tensional structure of logic and belief, rationality and irrationality, in the process of scientific (...) revolution. (shrink)

Evidence-Based Medicine is a relatively new movement that seeks to put clinical medicine on a firmer scientific footing. I take it as uncontroversial that medical practice should be based on best evidence—the interesting questions concern the details. This paper tries to move towards a coherent and unified account of best evidence in medicine, by exploring in particular the EBM position on RCTs.

The evidence from randomized controlled trials (RCTs) is widely regarded as supplying the ‘gold standard’ in medicine—we may sometimes have to settle for other forms of evidence, but this is always epistemically second-best. But how well justified is the epistemic claim about the superiority of RCTs? This paper adds to my earlier (predominantly negative) analyses of the claims produced in favour of the idea that randomization plays a uniquely privileged epistemic role, by closely inspecting three related arguments from leading contributors (...) to the burgeoning field of probabilistic causality—Papineau, Cartwright and Pearl. It concludes that none of these further arguments supplies any practical reason for thinking of randomization as having unique epistemic power. IntroductionWhy the issue is of great practical importance—the ECMO casePapineau on the ‘virtues of randomization’Cartwright on causality and the ‘ideal’ randomized experimentPearl on randomization, nets and causesConclusion. (shrink)

It is surely obvious that medicine, like any other rational activity, must be based on evidence. The interest is in the details: how exactly are the general principles of the logic of evidence to be applied in medicine? Focussing on the development, and current claims of the ‘Evidence-Based Medicine’ movement, this article raises a number of difficulties with the rationales that have been supplied in particular for the ‘evidence hierarchy’ and for the very special role within that hierarchy of randomized (...) controlled trials (and meta-analyses of the results of randomized controlled trials). The point is not at all to question the application of a scientific approach to evidence in medicine, but, on the contrary, to indicate a number of areas where philosophers of science can contribute to a proper implementation of exactly that scientific-evidential approach. (shrink)

This paper explores how data serve as evidence for phenomena. In contrast to standard philosophical models which invite us to think of evidential relationships as logical relationships, I argue that evidential relationships in the context of data-to-phenomena reasoning are empirical relationships that depend on holding the right sort of pattern of counterfactual dependence between the data and the conclusions investigators reach on the phenomena themselves.

Much philosophical progress has been made in elucidating the idea of evolutionary contingency in a recent re-burgeoning of the debate. However, additional progress has been impaired on three fronts. The first relates to its characterisation: the under-specification of various contingency claims has made it difficult to conceptually pinpoint the scope to which ‘contingency’ allegedly extends, as well as which biological forms are in contention. That is—there appears to be no systematic means with which to fully specify contingency claims which has (...) led to a tendency for authors to talk past each other. Secondly, on the matter of evidence, recent research has focused on the evidential import of convergent evolution which is taken to disconfirm the evolutionary contingency thesis. However, there has been a neglect of convergent evolution’s converse: ‘evolutionary idiosyncrasies’ or the singular evolution of certain forms, which I argue is evidentially supportive of evolutionary contingency. Thirdly, evolutionary contingency has often been claimed to vary in degrees and that the debate, itself, is a matter of ‘relative significance’. However, there has been no formal method of evaluating the strength of contingency and its relative significance in a particular domain. In this paper, I address all three issues by proposing a systematic means of fully specifying contingency theses with the concept of the modal range. Secondly, I propose an account of evolutionary idiosyncrasies, investigate the explanations for their occurrences, and, subsequently, spell out their significance with respect to the evolutionary contingency thesis. Finally, having been equipped with the evidential counterpart to convergent evolution, I shall sketch a likelihood framework for evaluating, precisely on the basis of a sequence of opposing data, the strength and relative significance of evolutionary contingency in a particular domain. With this in hand, the relative observations of idiosyncrasies and convergences can be informative of the strength and relative significance of contingency in any particular domain. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

We argued that explanatoriness is evidentially irrelevant in the following sense: Let H be a hypothesis, O an observation, and E the proposition that H would explain O if H and O were true. Then our claim is that Pr = Pr. We defended this screening-off thesis by discussing an example concerning smoking and cancer. Climenhaga argues that SOT is mistaken because it delivers the wrong verdict about a slightly different smoking-and-cancer case. He also considers a variant of SOT, called (...) “SOT*”, and contends that it too gives the wrong result. We here reply to Climenhaga’s arguments and suggest that SOT provides a criticism of the widely held theory of inference called “inference to the best explanation”. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...) emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

I aim to provide some evidence that Husserl’s description of perceptual updating actually fits very nicely into the Bayesian Brain paradigm, articulated by Karl Friston and others, and that that paradigm, in turn, can be taken as an excellent example of “Neurophenomenology”. The apparently un-phenomenological Helmholtzian component of the Bayesian Brain paradigm, according to which what one consciously seems to see is a product of unconscious causal reasoning to the best explanation of one’s sensory stimulations, can be finessed, I claim, (...) in a way that makes it compatible with a phenomenological orientation. I begin by roughly characterizing the Bayesian Brain paradigm as it relates to perceptual cognition. I then show how Husserl’s descriptions of the conscious perceptual process relate to the paradigm. I conclude with some considerations about how to understand the relation between conscious and unconscious brain process in the present case and in relation to Neurophenomenology generally. (shrink)

The principle of indifference has fallen from grace in contemporary philosophy, yet some papers have recently sought to vindicate its plausibility. This paper follows suit. In it, I articulate a version of the principle and provide what appears to be a novel argument in favour of it. The argument relies on a thought experiment where, intuitively, an agent’s confidence in any particular outcome being true should decrease with the addition of outcomes to the relevant space of possible outcomes. Put simply: (...) the greater the number of outcomes, the weaker your confidence should be in any one of those outcomes. The argument holds that this intuition favours the principle of indifference. I point out that, in contrast, the intuition is also incompatible with a major alternative to the principle which prescribes imprecise credences: the so-called wide interval view. Consequently, the argument may also be seen as an argument against the wide interval view. (shrink)

A common methodological adage holds that diverse evidence better confirms a hypothesis than does the same amount of similar evidence. Proponents of Bayesian approaches to scientific reasoning such as Horwich, Howson and Urbach, and Earman claim to offer both a precise rendering of this maxim in probabilistic terms and an explanation of why the maxim should be part of the methodological canon of good science. This paper contends that these claims are mistaken and that, at best, Bayesian accounts of diverse (...) evidence are crucially incomplete. This failure should lend renewed force to a long-neglected global worry about Bayesian approaches. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation” which later on he called ‘OP’(Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion left Lewis uneasy, because he thought that an inverse form of NP is “quite messy”, whereas an inverse form of OP, namely the simple and intuitive PP, is “the key to our concept of chance”. I argue that, (...) even if OP should be discarded, PP need not be. Moreover, far from being messy, an inverse form of NP is a simple and intuitive Conditional Principle (CP). Finally, both PP and CP are special cases of a General Principle (GP); it follows that so are PP and NP, which are thus compatible rather than competing. (shrink)

Quine and Putnam argued for mathematical realism on the basis of the indispensability of mathematics to science. They claimed that the mathematics that is used in physical theories is confirmed along with those theories and that scientific realism entails mathematical realism. I argue here that current theories of confirmation suggest that mathematics does not receive empirical support simply in virtue of being a part of well confirmed scientific theories and that the reasons for adopting a realist view of scientific theories (...) do not support realism about mathematical entities, despite the use of mathematics in formulating scientific theory. (shrink)

According to Margaret Gilbert’s collective epistemology, we should take attributions of beliefs to groups seriously, rather than metaphorically or as reducible to individual belief. I argue that, similarly, attributions of belief to markets ought to be taken seriously and not merely as reports of the average beliefs of market participants. While many of Gilbert’s purported examples of group belief are better thought of as instances of acceptance, some collectives, such as courts and markets, genuinely believe. Such collectives enact truth-aimed processes (...) that are beyond the control of any single individual. These processes produce beliefs that are distinct from any individual belief and do not merely report the “average” or “majority” view of the group. In the case of markets, beliefs are indicated by prices, though it is often difficult to infer beliefs from prices and those inferences are almost always uncertain. Reliabilism is the best available standard of justification for market beliefs. In some cases market beliefs are reliable and prove to be true. Thus, in some cases markets can know. (shrink)

According to Margaret Gilbert’s collective epistemology, we should take attributions of beliefs to groups seriously, rather than metaphorically or as reducible to individual belief. I argue that, similarly, attributions of belief to markets ought to be taken seriously and not merely as reports of the average beliefs of market participants. While many of Gilbert’s purported examples of group belief are better thought of as instances of acceptance, some collectives, such as courts and markets, genuinely believe. Such collectives enact truth-aimed processes (...) that are beyond the control of any single individual. These processes produce beliefs that are distinct from any individual belief and do not merely report the “average” or “majority” view of the group. In the case of markets, beliefs are indicated by prices, though it is often difficult to infer beliefs from prices and those inferences are almost always uncertain. Reliabilism is the best available standard of justification for market beliefs. In some cases market beliefs are reliable and prove to be true. Thus, in some cases markets can know. (shrink)

Scientific articles exemplify standard functional units constraining argumentative structures. Severe space limitations demand every paragraph and illustration contribute to establishing the paper's claims. Philosophical testing and confirmation models should take into account each paragraph, table, and illustration. Hypothetico-Deductive, Bayesian Inductive, and Inference-to-the-Best-Explanation models do not, garbling the logic of papers. Micro-analysis of the fundamental paper in plate tectonics reveals an argumentative structure commonplace in science but ignored by standard philosophical accounts that cannot be dismissed as mere rhetorical embellishment. Papers with (...) illustrations often display a second argumentative structure differing from the text's. Constraints on adequate testing and confirmation analyses are adduced. "Experiments are about the assembly of persuasive arguments, ones that will stand up in court.... The task at hand is to capture the building-up of a persuasive argument about the world even in the absence of the logician's certainty." --Galison, How Experiments End, 277. (shrink)

In the process of scientific discovery, knowledge ampliation is pursued by means of non-deductive inferences. When ampliative reasoning is performed, probabilities cannot be assigned objectively. One of the reasons is that we face the problem of the unconceived alternatives: we are unable to explore the space of all the possible alternatives to a given hypothesis, because we do not know how this space is shaped. So, if we want to adequately account for the process of knowledge ampliation, we need to (...) develop an account of the process of scientific discovery which is not exclusively based on probability calculus. We argue that the analytic view of the method of science advocated by Cellucci is interestingly suited to this goal, since it rests on the concept of plausibility. In this perspective, in order to account for how probabilities are in fact assigned in uncertain contexts and knowledge ampliation is really pursued, we have to take into account plausibility-based considerations. (shrink)

Robustness is a common platitude: hypotheses are better supported with evidence generated by multiple techniques that rely on different background assumptions. Robustness has been put to numerous epistemic tasks, including the demarcation of artifacts from real entities, countering the “experimenter’s regress,” and resolving evidential discordance. Despite the frequency of appeals to robustness, the notion itself has received scant critique. Arguments based on robustness can give incorrect conclusions. More worrying is that although robustness may be valuable in ideal evidential circumstances (i.e., (...) when evidence is concordant), often when a variety of evidence is available from multiple techniques, the evidence is discordant. †To contact the author, please write to: Jacob Stegenga, Department of Philosophy, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093; e‐mail: [email protected]. (shrink)

Robustness arguments hold that hypotheses are more likely to be true when they are confirmed by diverse kinds of evidence. Robustness arguments require the confirming evidence to be independent. We identify two kinds of independence appealed to in robustness arguments: ontic independence —when the multiple lines of evidence depend on different materials, assumptions, or theories—and probabilistic independence. Many assume that OI is sufficient for a robustness argument to be warranted. However, we argue that, as typically construed, OI is not a (...) sufficient independence condition for warranting robustness arguments. We show that OI evidence can collectively confirm a hypothesis to a lower degree than individual lines of evidence, contrary to the standard assumption undergirding usual robustness arguments. We employ Bayesian networks to represent the ideal empirical scenario for a robustness argument and a variety of ways in which empirical scenarios can fall short of this ideal. (shrink)

Critics of Bayesianism often assert that scientists are not Bayesians. The widespread use of Bayesian statistics in the field of radiocarbon calibration is discussed in relation to this charge. This case study illustrates the willingness of scientists to use Bayesian statistics when the approach offers some advantage, while continuing to use orthodox methods in other contexts. The case of radiocarbon calibration, therefore, suggests a picture of statistical practice in science as eclectic and pragmatic rather than rigidly adhering to any one (...) theoretical position. (shrink)

In a recent essay (1995), Andrew Wayne charges that Bayesian attempts to account for the rule that, ceteris paribus, diverse evidence confirms better than narrow evidence are inadequate. I reply to these criticisms and argue that, on the contrary, one of the Bayesian approaches considered by Wayne does an excellent job of explaining why, and under what circumstances, diverse evidence is valuable.

Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from the (...) search for the top quark. A point in favor of the error statistical theory is its ability, demonstrated here, to explicate such methodological problems and suggest solutions, within the framework of an objective theory of evidence. (shrink)

According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...) adequately answer this question. According to Popper, corroboration is different from probability-raising, and grounded in the predictive success and testability of a hypothesis. As such, corroboration becomes an indicator of the scientific value of a hypothesis and guides our practical preferences over hypotheses that have been subjected to severe tests. This article proves two impossibility results for corroboration measures based on statistical relevance. The generality of these results shows that Popper’s qualitative characterization of corroboration must be misguided. I explore what a more promising and scientifically useful concept of corroboration could look like. (shrink)

Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: it opens the door to the influence of values and biases, evidence judgments can vary substantially between scientists, it is not suited for informing policy decisions. My paper rebuts these concerns by connecting the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference with null hypothesis significance tests. Second, (...) the criticisms are based on specific senses of objectivity with unclear epistemic value. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity—most notably by increasing the transparency of scientific reasoning. (shrink)

To what extent does the design of statistical experiments, in particular sequential trials, affect their interpretation? Should postexperimental decisions depend on the observed data alone, or should they account for the used stopping rule? Bayesians and frequentists are apparently deadlocked in their controversy over these questions. To resolve the deadlock, I suggest a three‐part strategy that combines conceptual, methodological, and decision‐theoretic arguments. This approach maintains the pre‐experimental relevance of experimental design and stopping rules but vindicates their evidential, postexperimental irrelevance. †To (...) contact the author, please write to: Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e‐mail: [email protected]. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)