Over the past three decades, the discourse on the mechanistic approach to scientific modelling and explanation has notably sidestepped the topic of simplicity and fit within the process of model selection. This paper aims to rectify this disconnect by delving into the topic of simplicity and fit within the context of mechanistic explanations. More precisely, our primary objective is to address whether simplicity metrics hold any significance within mechanistic explanations. If they do, then our inquiry extends to the suitability of (...) the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and related criteria in determining the optimal balance of fit and simplicity of mechanistic models. As our main claims, we argue that mechanistic models inherently lend themselves to considerations of simplicity, and that the AIC and BIC and related criteria are applicable to some submodels of certain kinds of mechanistic models. However, these criteria and related criteria designed for curve fitting and causal modelling are of little help for a comparative assessment of full mechanistic models, and a fundamentally different approach is needed to make determinations of this kind. (shrink)

The study of cultural evolution has taken on an increasingly interdisciplinary and diverse approach in explicating phenomena of cultural transmission and adoptions. Inspired by this computational movement, this study uses Bayesian networks analysis, combining both the frequentist and the Hamiltonian Markov chain Monte Carlo (MCMC) approach, to investigate the highly representative elements in the cultural evolution of a Vietnamese city’s architecture in the early 20th century. With a focus on the façade design of 68 old houses in Hanoi’s Old (...) Quarter (based on 78 data lines extracted from 248 photos), the study argues that it is plausible to look at the aesthetics, architecture, and designs of the house façade to find traces of cultural evolution in Vietnam, which went through more than six decades of French colonization and centuries of sociocultural influence from China. The in-depth technical analysis, though refuting the presumed model on the probabilistic dependency among the variables, yields several results, the most notable of which is the strong influence of Buddhism over the decorations of the house façade. Particularly, in the top 5 networks with the best Bayesian Information Criterion (BIC) scores and p<0.05, the variable for decorations (DC) always has a direct probabilistic dependency on the variable B for Buddhism. The paper then checks the robustness of these models using Hamiltonian MCMC method and find the posterior distributions of the models’ coefficients all satisfy the technical requirement. Finally, this study suggests integrating Bayesian statistics in the social sciences in general and for the study of cultural evolution and architectural transformation in particular. (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)

We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of idealizations are being made which can be relaxed by an appeal to Bayesian Networks.

The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in (...) terms of Wallace's Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism. Hence an important part of the attack on Bayesianism fails. (shrink)

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then (...) it is shown that the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.

Verbal learning and memory summaries of older adults have usually been used to describe neuropsychiatric complaints. Bayesian hierarchical models are modern and appropriate approaches for predicting repeated measures data where information exchangeability is considered and a violation of the independence assumption in classical statistics. Such models are complex models for clustered data that account for distributions of hyper-parameters for fixed-term parameters in Bayesian computations. Repeated measures are inherently clustered and typically occur in clinical trials, education, cognitive psychology, (...) and treatment follow-up. The Hopkins Verbal Learning Test is a general verbal knowledge and memory assessment administered repeatedly as part of a neurophysiological experiment to examine an individual’s performance outcomes at different time points. Multiple trial-based scores of verbal learning and memory tests were considered as an outcome measurement. In this article, we attempted to evaluate the predicting effect of individual characteristics in considering within and between-group variations by fitting various Bayesian hierarchical models via the hybrid Hamiltonian Monte Carlo under the Bayesian Regression Models using ‘Stan’ package of R. Comparisons of the fitted models were done using leave-one-out information criteria, Widely applicable information criterion, and K-fold cross-validation methods. The full hierarchical model with varying intercepts and slopes had the best predictive performance for verbal learning tests [from the Advanced Cognitive Training for Independent and Vital Elderly study dataset] using the hybrid Hamiltonian-Markov Chain Monte Carlo approach. (shrink)

I propose a qualitative Bayesian account of explanatory goodness that is analogous to the Bayesian account of incremental confirmation. This is achieved by means of a complexity criterion according to which an explanation h is good if the reduction in the complexity of the explanandum e brought about by h (the explanatory gain) is greater than the additional complexity introduced by h in the context of e (the explanatory cost). To illustrate the account, I apply it in (...) the context of ad hoc hypotheses. (shrink)

We develop a probabilistic criterion for belief expansion that is sensitive to the degree of contextual fit of the new information to our belief set as well as to the reliability of our information source. We contrast our approach with the success postulate in AGM-style belief revision and show how the idealizations in our approach can be relaxed by invoking Bayesian-Network models.

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

The philosophical significance of the procedure of applying Akaike Information Criterion (AIC) to curve-fitting problems is evaluated. The theoretical justification for using AIC (the so-called Akaike's theorem) is presented in a rigorous way, and its range of validity is assessed by presenting both instances in which it is valid and counter-examples in which it is invalid. The philosophical relevance of the justification that this result gives for making one particular choice between simple and complicated hypotheses is emphasized. In (...) addition, recent claims that the methods based on Akaike's theorem are relevant to other philosophical problems associated with the notion of simplicity are presented and evaluated. (shrink)

We develop a probabilistic criterion for belief expansion that is sensitive to the degree of contextual fit of the new information to our belief set as well as to the reliability of our information source. We contrast our approach with the success postulate in AGM-style belief revision and show how the idealizations in our approach can be relaxed by invoking Bayesian-Network models.

In his discussion of minimax decision rules, Savage presents an example purporting to show that minimax applied to negative expected utility is an inadequate decision criterion for statistics; he suggests the application of a minimax regret rule instead. The crux of Savage’s objection is the possibility that a decision maker would choose to ignore even “extensive” information. More recently, Parmigiani has suggested that minimax regret suffers from the same flaw. He demonstrates the existence of “relevant” experiments that a (...) minimax regret agent would never pay a positive cost to observe. On closer inspection, I find that minimax regret is more resilient to this critique than would first appear. In particular, there are cases in which no experiment has any value to an agent employing the minimax negative income rule, while we may always devise a hypothetical experiment for which a minimax regret agent would pay. The force of Parmigiani’s critique is further blunted by the observation that “relevant” experiments exist for which a Bayesian agent would never pay. I conclude with a discussion of pessimism in the context of minimax decision rules. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

This study aimed to explore the influence of the visuospatial active working memory sub-components on early math skills in young children, followed longitudinally along the first two years of primary school. We administered tests investigating visual active working memory (jigsaw puzzle), spatial active working memory (backward Corsi), and math tasks to 43 children at the beginning of first grade (T1), at the end of first grade (T2), and at the end of second grade (T3). Math tasks were select according to (...) the children’s age and their levels of formal education: the “Battery for the evaluation of numerical intelligence from 4 to 6 years of age” (BIN 4–6) at T1 to test early numerical competence and the “Test for the evaluation of calculating and problem-solving abilities” (AC-MT 6–11) to test math skills at T2 and T3. Three regression models, in which the predictors were identified through a forward selection based on the use of the Bayesian information criterion (BIC) index, were performed to study the relationship between visual and spatial working memory and math ability at the three points in time. The results show that spatial working memory influences early numerical performance at T1, while early numerical performance is the unique predic-tor of math performance at T2. At the end of the second grade, the regression model reveals a relationship between math performance and both visual and spatial working memory and the attenuation of the importance of domain-specific predictors. The study depicts the dif-ferent implications of visual and spatial working memory predictors over the children’s de-velopment periods and brings additional evidence to the debate on the relationship between visuospatial working memory and math ability in young children. (shrink)

Acoustic emission technique is a common approach to identify the damage of the refractories; however, there is a complex problem since there are as many as fifteen involved parameters, which calls for effective data processing and classification algorithms to reduce the level of complexity. In this paper, experiments involving three-point bending tests of refractories were conducted and AE signals were collected. A new data processing method of merging the similar parameters in the description of the damage and reducing the dimension (...) was developed. By means of the principle component analysis for dimension reduction, the fifteen related parameters can be reduced to two parameters. The parameters were the linear combinations of the fifteen original parameters and taken as the indexes for damage classification. Based on the proposed approach, the Gaussian mixture model was integrated with the Bayesian information criterion to group the AE signals into two damage categories, which accounted for 99% of all damage. Electronic microscope scanning of the refractories verified the two types of damage. (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)

Though individual categorization or decision processes have been studied separately in many previous investigations, few studies have investigated how they interact by using a two-stage task of first categorizing and then deciding. To address this issue, we investigated a categorization-decision task in two experiments. In both, participants were shown six faces varying in width, first asked to categorize the faces, and then decide a course of action for each face. Each experiment was designed to include three groups, and for each (...) group, we manipulated the probabilistic contingencies between stimulus, category assignments, and decision consequences. For each group, each participant received three different sequences of category response, category feedback, decision response, and decision feedback. We found that participants were only partially responsive in the appropriate directions to the contingencies assigned to each group. Comparisons of results from different sequences provided evidence for empirical interference effects of categorization on decisions. The empirical interference effect is defined as the difference between the probability of taking a hostile action in decision-alone conditions and the total probability of taking a hostile action in categorization-decision conditions. To test competing accounts for multiple empirical results, including two-stage choice probabilities and empirical interference effects, we compared a quantum cognition model versus a two-stage exemplar categorization model at both aggregate and individual levels. Using a Bayesian information criterion, we found that the quantum model provided an overall better model fit than the exemplar model. Although both models predicted empirical interference effects, the exemplar model was able to generate probabilistic deviation by incorporating category information of the first stage into the feature representation of the subsequent decision stage, while the quantum model produced interference effect by superposition, measurement, and quantum entanglement. (shrink)

We show how the Full Bayesian Significance Test (FBST) can be used as a model selection criterion. The FBST was presented by Pereira and Stern as a coherent Bayesian significance test. Key Words: Bayesian test; Evidence; Global optimization; Information; Model selection; Numerical integration; Posterior density; Precise hypothesis; Regularization. AMS: 62A15; 62F15; 62H15.

We examine in detail three classic reasoning fallacies, that is, supposedly ``incorrect'' forms of argument. These are the so-called argumentam ad ignorantiam, the circular argument or petitio principii, and the slippery slope argument. In each case, the argument type is shown to match structurally arguments which are widely accepted. This suggests that it is not the form of the arguments as such that is problematic but rather something about the content of those examples with which they are typically justified. This (...) leads to a Bayesian reanalysis of these classic argument forms and a reformulation of the conditions under which they do or do not constitute legitimate forms of argumentation. (shrink)

The rational status of the Bayesian calculus for revising likelihoods is compromised by the common but still unfamiliar phenomenon of information distortion. This bias is the distortion in the evaluation of a new datum toward favoring the currently preferred option in a decision or judgment. While the Bayesian calculus requires the independent combination of the prior probability and a new datum, information distortion invalidates such independence (because the prior influences the datum). Although widespread, information distortion (...) has not generally been recognized. First, individuals are not aware when they themselves commit this bias. In addition, it is often hidden in more obvious suboptimal phenomena. Finally, the Bayesian calculus is usually explained only with undistortable data like colored balls drawn randomly. Partly because information distortion is unrecognized by the individuals exhibiting it, no way has been devised for eliminating it. Partial reduction is possible in some situation such as presenting all data simultaneously rather than sequentially with revision after each datum. The potential dangers of information distortion are illustrated for three professional revision tasks: forecasting, predicting consumer choices from internet data, and statistical inference from experimental results. The optimality of the Bayesian calculus competes with people’s natural desire that their belief systems remain coherent in the face of new data. Information distortion provides this coherence by biasing those data toward greater agreement with the currently preferred position – but at the cost of Bayesian optimality. (shrink)

Suppose that several observations “coincide,” meaning that they are similar in some interesting respect. Is this coinciding a mere coincidence, or does it derive from a common cause? Those who reason about this kind of question—whether they embrace the first answer or the second—often deploy a mode of inference that I call probabilistic modus tollens. In this chapter I criticize probabilistic modus tollens and consider likelihood and Bayesian frameworks for reasoning about coincidences. I also consider the perspective offered by (...) model selection theory (including the Akaike information criterion), and argue that model selection often provides important insights. (shrink)

Consider two agents who want to be Bayesians with a common prior, but who cannot due to computational limitations. If these agents agree that their estimates are consistent with certain easy-to-compute consistency constraints, then they can agree to disagree about any random variable only if they also agree to disagree, to a similar degree and in a stronger sense, about an average error. Yet average error is a state-independent random variable, and one agent's estimate of it is also agreed to (...) be state-independent. Thus suggests that disagreements are not fundamentally due to differing information about the state of the world. (shrink)

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts’ probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects (...) were more likely to invariably choose the category to which they assigned the higher probability of a target’s membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments. (shrink)

ObjectiveTo compare techniques for computing clustering and switching scores in terms of agreement, correlation, and empirical value as predictors of incident cognitive impairment.MethodsWe transcribed animal and letter F fluency recordings on 640 cases of ICI and matched controls from a national epidemiological study, amending each transcription with word timings. We then calculated clustering and switching scores, as well as scores indexing speed of responses, using techniques described in the literature. We evaluated agreement among the techniques with Cohen’s κ and calculated (...) correlations among the scores. After fitting a base model with raw scores, repetitions, and intrusions, we fit a series of Bayesian logistic regression models adding either clustering and switching scores or speed scores, comparing the models in terms of several metrics. We partitioned the ICI cases into acute and progressive cases and repeated the regression analysis for each group.ResultsFor animal fluency, we found that models with speed scores derived using the slope difference algorithm achieved the best values of the Watanabe–Akaike Information Criterion, but with good net reclassification improvement only for the progressive group. For letter fluency, different models excelled for prediction of acute and progressive cases. For acute cases, NRI was best for speed scores derived from a network model, while for progressive cases, the best model used clustering and switching scores derived from the same network model. Combining variables from the best animal and letter F models led to marginal improvements in model fit and NRI only for the all-cases and acute-cases analyses.ConclusionSpeed scores improve a base model for predicting progressive cognitive impairment from animal fluency. Letter fluency scores may provide complementary information. (shrink)

Moral hypocrisy is typically viewed as an ethical accusation: Someone is applying different moral standards to essentially identical cases, dishonestly claiming that one action is acceptable while otherwise equivalent actions are not. We suggest that in some instances the apparent logical inconsistency stems from different evaluations of a weak argument, rather than dishonesty per se. Extending Corner, Hahn, and Oaksford's (2006) analysis of slippery slope arguments, we develop a Bayesian framework in which accusations of hypocrisy depend on inferences of (...) shared category membership between proposed actions and previous standards, based on prior probabilities that inform the strength of competing hypotheses. Across three experiments, we demonstrate that inferences of hypocrisy increase as perceptions of the likelihood of shared category membership between precedent cases and current cases increase, that these inferences follow established principles of category induction, and that the presence of self-serving motives increases inferences of hypocrisy independent of changes in the actions themselves. Taken together, these results demonstrate that Bayesian analyses of weak arguments may have implications for assessing moral reasoning. (shrink)

A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of in-ference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (stu-dents’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many (...) systematic deviations from this model (biases, e.g. base-rate neglect, inverse fallacy) are reported in literature on Bayesian reasoning. In a teacher’s situation the information (hypotheses, priors, likelihoods) is usually not explicitly represented numerically (as in most research on Bayesian reasoning), but only by qualitative esti-mations in the mind of the teacher. In our study, we ask to which extent individuals (approximately) apply a rational Bayesian strategy or resort on other biased strategies of processing information for their diagnostic judgments. We explicitly pose this question with respect to non-numerical settings. To investigate this question, we developed a scenario that visually displays all relevant information (hypotheses, priors, likelihoods) in a graphically displayed hypothesis space (called “hypothegon”) – without recurring to numerical representations or mathematical procedures. 42 pre-service teach-ers were asked to judge the plausibility of different misconceptions of six students based on their responses to decimal comparison tasks (e.g. 3.39 > 3.4). Applying a Bayesian classification proce-dure, we identified three updating strategies: A Bayesian update strategy (BUS, processing all probabilities), a combined evidence strategy (CES, ignoring the prior probabilities but including all likelihoods), and a single evidence strategy (SES, only using the likelihood of the most probable hypothesis). In study 1, an instruction on the relevance of using all probabilities (priors and likelihoods) only weakly increased the processing of more information. In study 2, we found strong evidence that a visual explication of the prior-likelihood interaction led to an increase of processing the interaction of all relevant information. These results show that the phenomena found in general research on Bayesian reasoning in numerical settings extend to diagnostic judgments in non-numerical settings. (shrink)

This article seeks, first, to show that much of the existing normative work on argument from expert opinion (AEO) is problematic for failing to be properly informed by empirical findings on expert performance. Second, it seeks to show how, with the analytic tool of Bayesian reasoning, the problem diagnosed can be remedied to circumvent some of the problems facing the scheme-based treatment of AEOs. To establish the first contention, we will illustrate how empirical studies on factors conditioning expert reliability (...) can be drawn upon to re-construct. Walton’s critical questions matching the scheme of AEOs. To establish the second contention, we will illustrate how Walton’s re-constructed set of critical questions can be formalized within a Bayesian network. Finally, we will highlight how the specific ways in which the Bayesian framework we propose is both continuous with and distinct from the models of source reliability put forward by theorists like Bovens and Hartmann (2003). (shrink)

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements (...) traditional epistemology; it does not re- place it or aim at replacing it. (shrink)

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal (...) study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions. (shrink)

BackgroundBayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.MethodsThe sample consisted of 102 mother-adolescent dyads. (...) Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.ResultsThe prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.ConclusionA systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations, and may also be affected by pragmatic considerations regarding the impact of the previous results at hand. (shrink)

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all (...) class='Hi'>information spread over the individuals without the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71.. (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the (...) nature of the information sources. Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

Bayesian cognitive science is a research programme that relies on modelling resources from Bayesian statistics for studying and understanding mind, brain, and behaviour. Conceiving of mental capacities as computing solutions to inductive problems, Bayesian cognitive scientists develop probabilistic models of mental capacities and evaluate their adequacy based on behavioural and neural data generated by humans (or other cognitive agents) performing a pertinent task. The overarching goal is to identify the mathematical principles, algorithmic procedures, and causal mechanisms that (...) enable cognitive agents to take uncertainty into account and weigh it appropriately in producing adaptive behaviour. -/- The appeal of Bayesian cognitive science derives from its transparency, normativity, and unifying power. Resources from Bayesian statistics allow cognitive scientists to characterise transparently, in terms of random variables and probabilistic dependencies between them, the inductive problems that many mental capacities are presumed to solve. Given this characterisation, researchers can define an upper bound on one’s performance on that problem and use it as a benchmark for interpreting experimental results, formulating hypotheses about why and when deviations from optimal performance should be expected, and seeking explanations of mental capacities within one encompassing theoretical framework. -/- Although critics question the testability, explanatory power, and plausibility of Bayesian models of mental capacities, Bayesian cognitive science has proved itself to be an incredibly fruitful research programme. Fuelled by empirical and theoretical results from psychology, neuroscience, philosophy, computer science, artificial intelligence, and evolution, Bayesian cognitive science has: advanced our understanding of why cognitive systems should keep track of uncertainty and use it to facilitate adaptive behaviour; clarified how the brain might encode information about the uncertainty of its stimuli and perform computations with probability distributions; and crystallised the insight that cognitive agents’ management of uncertainty might be grounded in predictive processes aimed at avoiding surprising exchanges with the environment. (shrink)

We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of (...) agreeing on what data streams are algorithmically random, two Bayesian agents can thus be taken to concur on what global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. (shrink)

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of (...) the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results. (shrink)

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon (...) to be explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (shrink)