Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints.

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What (...) is their performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (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)

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)

This note responds to some criticisms of my recent book In Defence of Objective Bayesianism that were provided by Gregory Wheeler in his ‘Objective Bayesian Calibration and the Problem of Non-convex Evidence’.

Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated---this invites worries about the connection between Bayesianism and rationality.

This chapter examines the role of parameterParametercalibrationCalibration in the confirmation and validation of complex computer simulation models. I examine the question to what extent calibration data can confirm or validate the calibrated model, focusing in particular on Bayesian approaches to confirmation. I distinguish several different Bayesian approaches to confirmation and argue that complex simulation models exhibit a predictivist effect: Complex computer simulation models constitute a case in which predictive success, as opposed to the mere accommodation of evidence, (...) provides a more stringent test of the model. DataData used in tuning do not validate or confirm a model to the same extent as data successfully predicted by the model do. (shrink)

We argue that concerns about double-counting—using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate—deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a Bayesian/relative-likelihood approach to (...) incremental confirmation. According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit. 1 Introduction2 Remarks about Models and Adequacy-for-Purpose3 Evidence for Calibration Can Also Yield Comparative Confirmation3.1 Double-counting I3.2 Double-counting II4 Climate Science Examples: Comparative Confirmation in Practice4.1 Confirmation due to better and worse best fits4.2 Confirmation due to more and less plausible forcings values5 Old Evidence6 Doubts about the Relevance of Past Data7 Non-comparative Confirmation and Catch-Alls8 Climate Science Example: Non-comparative Confirmation and Catch-Alls in Practice9 Concluding Remarks. (shrink)

We appeal to the theory of Bayesian Networks to model different strategies for obtaining confirmation for a hypothesis from experimental test results provided by less than fully reliable instruments. In particular, we consider (i) repeated measurements of a single test consequence of the hypothesis, (ii) measurements of multiple test consequences of the hypothesis, (iii) theoretical support for the reliability of the instrument, and (iv) calibration procedures. We evaluate these strategies on their relative merits under idealized conditions and show (...) some surprising repercussions on the variety-of-evidence thesis and the Duhem-Quine thesis. (shrink)

We argue that concerns about double-counting -- using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate --deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a (...) class='Hi'>Bayesian/relative-likelihood approach to incremental confirmation. According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit. (shrink)

This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets (...) and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics. (shrink)

According to Williamson , the difference between empirical subjective Bayesians and objective Bayesians is that, while both hold reasonable credence to be calibrated to evidence, the objectivist also takes such credence to be as equivocal as such calibration allows. However, Williamson’s prescription for equivocation generates constraints on reasonable credence that are objectionable. Herein Williamson’s calibration norm is explicated in a novel way that permits an alternative equivocation norm. On this alternative account, evidence calibrated probability functions are recognised as (...) implications of evidence calibrated density functions defined over chance hypotheses. The objective Bayesian equivocates between these calibrated density functions rather than between the calibrated probability functions themselves. The result is an objective Bayesianism that avoids the main problem afflicting Williamson’s original proposal. (shrink)

Visual aids can improve comprehension of risks associated with medical treatments, screenings, and lifestyles. Do visual aids also help decision makers accurately assess their risk comprehension? That is, do visual aids help them become well calibrated? To address these questions, we investigated the benefits of visual aids displaying numerical information and measured accuracy of self-assessment of diagnostic inferences (i.e., metacognitive judgment calibration) controlling for individual differences in numeracy. Participants included 108 patients who made diagnostic inferences about three medical tests (...) on the basis of information about the sensitivity and false-positive rate of the tests and disease prevalence. Half of the patients received the information in numbers without a visual aid, while the other half received numbers along with a grid representing the numerical information. In the numerical condition, many patients --especially those with low numeracy-- misinterpreted the predictive value of the tests and profoundly overestimated the accuracy of their inferences. Metacognitive judgment calibration mediated the relationship between numeracy and accuracy of diagnostic inferences. In contrast, in the visual aid condition, patients at all levels of numeracy showed high-levels of inferential accuracy and metacognitive judgment calibration. Results indicate that accurate metacognitive assessment may explain the beneficial effects of visual aids and numeracy --a result that accords with theory suggesting that metacognition is an essential part of risk literacy. We conclude that well-designed risk communications can inform patients about health-relevant numerical information while helping them assess the quality of their own risk comprehension. (shrink)

Clearing algorithms are at the core of modern payment systems, facilitating the settling of multilateral credit messages with (near) minimum transfers of currency. Traditional clearing procedures use batch processing based on MILP - mixed-integer linear programming algorithms. The MILP approach demands intensive computational resources; moreover, it is also vulnerable to operational risks generated by possible defaults during the inter-batch period. This paper presents TORC3 - the Token-Ring Clearing Algorithm for Currency Circulation. In contrast to the MILP approach, TORC3 is a (...) real time heuristic procedure, demanding modest computational resources, and able to completely shield the clearing operation against the participating agents’ risk of default. (shrink)

*PSA 2016, symposium on “Data in Time: Epistemology of Historical Data” organized by Sabina Leonelli, 5 November 2016* *See published version: "Radiocarbon Dating in Archaeology: Triangulation and Traceability" in Data Journeys in the Sciences (2020) - link below* Archaeologists put a premium on pressing “legacy data” into service, given the notoriously selective and destructive nature of their practices of data capture. Legacy data consist of material and records that been assembled over decades, sometimes centuries, often by means and for purposes (...) long since discredited or superseded. The primary strategies by which archaeologists put the data to work for new purposes are, I argue, secondary retrieval, recontextualization, and experimental modelling. I focus here on a particularly telling and complex example of secondary retrieval: the extraction of new data from old by means of radiocarbon dating. This is by no means a straightforward process of retrieving physical samples from legacy data to which 14C techniques can be applied that can, on their own, decisively settle chronological questions. When Libby’s post-war radiocarbon revolution got under way, it was expected to establish an absolute chronology that would render obsolete the local and relative chronologies on which archaeologists had long relied. Transformative though it has been, bringing these tools of physical dating to bear on archaeological problems has been a long, tortuous process, now described as proceeding through two subsequent radiocarbon revolutions. The second was an extended process of calibration by which 14C chronologies were corrected and refined, often against the very lines of evidence they were meant to displace. The most recent, a “pragmatic Bayesian” approach to archaeological dating, is motivated by concern that, no matter how much it is refined, radiocarbon dating cannot on its own resolve the chronological problems that archaeologists address; the challenge, its advocates argue, is to ‘fully integrate archaeological information with 14C dating in order to address archaeologically relevant timescales and episodes’. This is a genre of “robustness” reasoning that illustrates its epistemic risks as well as its appeal. As recent philosophical debate makes clear, it depends on appeals to the convergence of independent lines of evidence that may have more rhetorical than epistemic force and that may be spurious. Drawing on this philosophical literature I identify a set of conditions that must be met if these risks are to be avoided, all of which are an explicit focus of debate in cases of contestation about and reconciliation of chronologies based on legacy data. (shrink)

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective (...) Bayesianism are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem. (shrink)

We often evaluate belief-forming processes, agents, or entire belief states for reliability. This is normally done with the assumption that beliefs are all-or-nothing. How does such evaluation go when we’re considering beliefs that come in degrees? I consider a natural answer to this question that focuses on the degree of truth-possession had by a set of beliefs. I argue that this natural proposal is inadequate, but for an interesting reason. When we are dealing with all-or-nothing belief, high reliability leads to (...) high levels of truth-possession. However, when it comes to degrees of belief, reliability and truth-possession part ways. The natural answer thus fails to be a good way to evaluate degrees of belief for reliability. I propose and develop an alternative method based on the notion of calibration, suggested by Frank Ramsey, which does not have this problem and consider why we should care about such assessments of reliability even if they are not tied directly to truth-possession. (shrink)

Objective Bayesians hold that degrees of belief ought to be chosen in the set of probability functions calibrated with one’s evidence. The particular choice of degrees of belief is via some objective, i.e., not agent-dependent, inference process that, in general, selects the most equivocal probabilities from among those compatible with one’s evidence. Maximising entropy is what drives these inference processes in recent works by Williamson and Masterton though they disagree as to what should have its entropy maximised. With regard to (...) the probability function one should adopt as one’s belief function, Williamson advocates selecting the probability function with greatest entropy compatible with one’s evidence while Masterton advocates selecting the expected probability function relative to the density function with greatest entropy compatible with one’s evidence. In this paper we discuss the significant relative strengths of these two positions. In particular, Masterton’s original proposal is further developed and investigated to reveal its significant properties; including its equivalence to the centre of mass inference process and its ability to accommodate higher order evidence. (shrink)

Many climate scientists have made claims that may suggest that evidence used in tuning or calibrating a climate model cannot be used to evaluate the model. By contrast, the philosophers Katie Steele and Charlotte Werndl have argued that, at least within the context of Bayesian confirmation theory, tuning is simply an instance of hypothesis testing. In this paper I argue for a weak predictivism and in support of a nuanced reading of climate scientists’ concerns about tuning: there are cases, (...) model-tuning among them, in which predictive successes are more highly confirmatory of a model than accommodation of evidence. (shrink)

Computational theories of vision typically rely on the analysis of two aspects of human visual function: (1) object and shape recognition (2) co-calibration of sensory measurements. Both these approaches are usually based on an inverse-optics model, where visual perception is viewed as a process of inference from a 2D retinal projection to a 3D percept within a Euclidean space schema. This paradigm has had great success in certain areas of vision science, but has been relatively less successful in understanding (...) perceptual representation, namely, the nature of the perceptual encoding. One of the drawbacks of inverse-optics approaches has been the difficulty in defining the constraints needed to make the inference computationally tractable (e.g. regularity assumptions, Bayesian priors, etc.). These constraints, thought to be learned assumptions about the nature of the physical and optical structures of the external world, have to be incorporated into any workable computational model in the inverse-optics paradigm. But inference models that employ an inverse optics plus structural assumptions approach inevitably result in a na. (shrink)

According to the subjective Bayesian interpretation of quantum mechanics, the instruments used to measure quantum systems are to be regarded as an extension of the senses of the agent who is using them, and quantum states describe the agent’s expectations for what they will experience through these extended senses. How can QBism then account for the fact that instruments must be calibrated before they can be used to ‘sense’ anything; some instruments are more precise than others; more precise instruments (...) can lead to discovery of new systems? Furthermore, is the agent ‘incoherent’ if they prefer to use a less precise instrument? Here we provide answers to these questions. (shrink)

Many examples of calibration in climate science raise no alarms regarding model reliability. We examine one example and show that, in employing Classical Hypothesis-testing, it involves calibrating a base model against data that is also used to confirm the model. This is counter to the "intuitive position". We argue, however, that aspects of the intuitive position are upheld by some methods, in particular, the general Cross-validation method. How Cross-validation relates to other prominent Classical methods such as the Akaike Information (...) Criterion and Bayesian Information Criterion is also discussed. (shrink)

The thesis that agents should calibrate their beliefs in the face of higher-order evidence—i.e., should adjust their first-order beliefs in response to evidence suggesting that the reasoning underlying those beliefs is faulty—is sometimes thought to be in tension with Bayesian approaches to belief update: in order to obey Bayesian norms, it’s claimed, agents must remain steadfast in the face of higher-order evidence. But I argue that this claim is incorrect. In particular, I motivate a minimal constraint on a (...) reasonable treatment of the evolution of self-locating beliefs over time and show that calibrationism is compatible with any generalized Bayesian approach that respects this constraint. I then use this result to argue that remaining steadfast isn’t the response to higher-order evidence that maximizes expected accuracy. (shrink)

In this concise book based on his Arne Ryde Lectures in 2002, Young suggests a conceptual framework for studying strategic learning and highlights theoretical developments in the area. He discusses the interactive learning problem; reinforcement and regret; equilibrium; conditional no-regret learning; prediction, postdiction, and calibration; fictitious play and its variants; Bayesian learning; and hypothesis testing. Young's framework emphasizes the amount of information required to implement different types of learning rules, criteria for evaluating their performance, and alternative notions of (...) equilibrium to which they converge. He also stresses the limits of what can be achieved: for a given type of game and a given amount of information, there may exist no learning procedure that satisfies certain reasonable criteria of performance and convergence. In short, Young has provided a valuable primer that delineates what we know, what we would like to know, and the limits of what we can know, when we try to learn about a system that is composed of other learners. (shrink)

Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting (...) formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss. (shrink)

This article argues that common intuitions regarding (a) the specialness of ‘use-novel’ data for confirmation and (b) that this specialness implies the ‘no-double-counting rule’, which says that data used in ‘constructing’ (calibrating) a model cannot also play a role in confirming the model’s predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuitive claims in (...) light of prominent accounts of confirmation of model predictions. We show that on the Bayesian account of confirmation, and also on the standard classical hypothesis-testing account, claims (a) and (b) are not generally true; but for some select cases, it is possible to distinguish data used for calibration from use-novel data, where only the latter confirm. The more specialized classical model-selection methods, on the other hand, uphold a nuanced version of claim (a), but this comes apart from (b), which must be rejected in favour of a more refined account of the relationship between calibration and confirmation. Thus, depending on the framework of confirmation, either the scope or the simplicity of the intuitive position must be revised. (shrink)

This article argues that common intuitions regarding (a) the specialness of ‘use-novel’ data for confirmation and (b) that this specialness implies the ‘no-double-counting rule’, which says that data used in ‘constructing’ (calibrating) a model cannot also play a role in confirming the model’s predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuitive claims in (...) light of prominent accounts of confirmation of model predictions. We show that on the Bayesian account of confirmation, and also on the standard classical hypothesis-testing account, claims (a) and (b) are not generally true; but for some select cases, it is possible to distinguish data used for calibration from use-novel data, where only the latter confirm. The more specialized classical model-selection methods, on the other hand, uphold a nuanced version of claim (a), but this comes apart from (b), which must be rejected in favour of a more refined account of the relationship between calibration and confirmation. Thus, depending on the framework of confirmation, either the scope or the simplicity of the intuitive position must be revised. 1 Introduction2 A Climate Case Study3 The Bayesian Method vis-à-vis Intuitions4 Classical Tests vis-à-vis Intuitions5 Classical Model-Selection Methods vis-à-vis Intuitions 5.1 Introducing classical model-selection methods 5.2 Two cases6 Re-examining Our Case Study7 Conclusion. (shrink)

We give an overview of the practice of developing and using complex climate models, as seen from experiences in a major climate modelling center and through participation in the Coupled Model Intercomparison Project. We discuss the construction and calibration of models; their evaluation, especially through use of out-of-sample tests; and their exploitation in multi-model ensembles to identify biases and make predictions. We stress that adequacy or utility of climate models is best assessed via their skill against more naïve predictions. (...) The framework we use for making inferences about reality using simulations is naturally Bayesian, and has many points of contact with more familiar examples of scientific epistemology. While the use of complex simulations in science is a development that changes much in how science is done in practice, we argue that the concepts being applied fit very much into traditional practices of the scientific method, albeit those more often associated with laboratory work. (shrink)

The "prevailing opinion" among decision theorists, according to John Harsanyi, is to use the Bayesian rule, even in situations of uncertainty. I want to argue that the prevailing opinion is wrong, at least in the case of societal risks under uncertainty. Admittedly Bayesian rules are better in many cases of individual risk or certainty. (Both Bayesian and maximin strategies are sometimes needed.) Although I shall not take the time to defend all these points in detail, I shall (...) argue (1) that there are compelling reasons for rejecting Harsanyi's defense of the Bayesian strategy under uncertainty; (2) that it is more rational, in specific types of situations, to prefer the maximin strategy; and (3) that calibrating expert opinions is superior to using the equiprobability assumption or subjective probabilities. (shrink)

When radiocarbon dating techniques were applied to archaeological material in the 1950s they were hailed as a revolution. At last archaeologists could construct absolute chronologies anchored in temporal data backed by immutable laws of physics. This would make it possible to mobilize archaeological data across regions and time-periods on a global scale, rendering obsolete the local and relative chronologies on which archaeologists had long relied. As profound as the impact of 14C dating has been, it has had a long and (...) tortuous history now described as proceeding through three revolutions, each of which addresses distinct challenges of capturing, processing and packaging radiogenic data for use in resolving chronological puzzles with which archaeologists has long wrestled. In practice, mobilizing radiogenic data for archaeological use is a hard-won achievement; it involves multiple transformations that, at each step of the way, depend upon a diverse array of technical expertise and background knowledge. I focus on strategies of triangulation and traceability that establish the integrity of these data and their relevance as anchors for evidential reasoning in archaeology. (shrink)

The causal view of categories assumes that categories are represented by features and their causal relations. To study the effect of causal knowledge on categorization, researchers have used Bayesian causal models. Within that framework, categorization may be viewed as dependent on a likelihood computation (i.e., the likelihood of an exemplar with a certain combination of features, given the category's causal model) or as a posterior computation (i.e., the probability that the exemplar belongs to the category, given its features). Across (...) three experiments, in combination with computational modeling, we offer evidence that categorization is better accounted for by assuming that people compute posteriors and not likelihoods, though both probabilities are closely related. This result contrasts with existing analyses of causal-based categorization, which assume that likelihood computations give a good approximation of human judgments. We also find that people are able to compute likelihoods in a closely related task that elicits judgments of consistency rather than category membership judgments. Our analyses show that people do use causal probabilistic information as prescribed by a Bayesian model but that they flexibly compute likelihoods or posteriors depending on the task. We discuss our results in relation to the relevant literature on the topic. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

This paper presents a new kind of problem in the ethics of distribution. The problem takes the form of several “calibration dilemmas,” in which intuitively reasonable aversion to small-stakes inequalities requires leading theories of distribution to recommend intuitively unreasonable aversion to large-stakes inequalities. We first lay out a series of such dilemmas for prioritarian theories. We then consider a widely endorsed family of egalitarian views and show that they are subject to even more forceful calibration dilemmas than prioritarian (...) theories. Finally, we show that our results challenge common utilitarian accounts of the badness of inequalities in resources. (shrink)

Fine-tuning in physics and cosmology is often used as evidence that a theory is incomplete. For example, the parameters of the standard model of particle physics are “unnaturally” small, which has driven much of the search for physics beyond the standard model. Of particular interest is the fine-tuning of the universe for life, which suggests that our universe’s ability to create physical life forms is improbable and in need of explanation, perhaps by a multiverse. This claim has been challenged on (...) the grounds that the relevant probability measure cannot be justified because it cannot be normalized, and so small probabilities cannot be inferred. We show how fine-tuning can be formulated within the context of Bayesian theory testing in the physical sciences. The normalizability problem is seen to be a general problem for testing any theory with free parameters, and not a unique problem for fine-tuning. Physical theories in fact avoid such problems in one of two ways. Dimensional parameters are bounded by the Planck scale, avoiding troublesome infinities, and we are not compelled to assume that dimensionless parameters are distributed uniformly, which avoids non-normalizability. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...) has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, (...) relate to the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively. (shrink)

Recently in epistemology a number of authors have mounted Bayesian objections to dogmatism. These objections depend on a Bayesian principle of evidential confirmation: Evidence E confirms hypothesis H just in case Pr(H|E) > Pr(H). I argue using Keynes' and Knight's distinction between risk and uncertainty that the Bayesian principle fails to accommodate the intuitive notion of having no reason to believe. Consider as an example an unfamiliar card game: at first, since you're unfamiliar with the game, you (...) assign credences based on the indifference principle. Later you learn how the game works and discover that the odds dictate you assign the very same credences. Examples like this show that if you initially have no reason to believe H, then intuitively E can give you reason to believe H even though Pr(H|E) ≤ Pr(H). I show that without the principle, the objections to dogmatism fail. (shrink)

In this paper, it is argued that the most fruitful approach to developing normative models of argument quality is one that combines the argumentation scheme approach with Bayesian argumentation. Three sample argumentation schemes from the literature are discussed: the argument from sign, the argument from expert opinion, and the appeal to popular opinion. Limitations of the scheme-based treatment of these argument forms are identified and it is shown how a Bayesian perspective may help to overcome these. At the (...) same time, the contributions of the standard scheme-based approach are highlighted, and it is argued that only a combination of the insights of different traditions will yield a complete normative theory of argument quality. (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)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing (...) how it answers or sidesteps problems that have been raised for previous work in this area. (shrink)

The paper presents and defends a Bayesian theory of trust in social networks. In the first part of the paper, we provide justifications for the basic assumptions behind the model, and we give reasons for thinking that the model has plausible consequences for certain kinds of communication. In the second part of the paper we investigate the phenomenon of overconfidence. Many psychological studies have found that people think they are more reliable than they actually are. Using a simulation environment (...) that has been developed in order to make our model computationally tractable we show that in our model inquirers are indeed sometimes better off from an epistemic perspective overestimating the reliability of their own inquiries. We also show, by contrast, that people are rarely better off overestimating the reliability of others. On the basis of these observations we formulate a novel hypothesis about the value of overconfidence. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic (...) in character and are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)