Bayesian models can be related to cognitive processes in a variety of ways that can be usefully understood in terms of Marr's distinction among three levels of explanation: computational, algorithmic and implementation. In this note, we discuss how an integrated probabilistic account of the different levels of explanation in cognitive science is resulting, at least for the current research practice, in a sort of unpredicted epistemological shift with respect to Marr's original proposal.

According to [Bayesian] models” in cognitive neuroscience, says a recent textbook, “the human mind behaves like a capable data scientist”. Do they? That is to say, do such model show we are rational? I argue that Bayesian models of cognition, perhaps surprisingly, do not and indeed cannot, show that we are Bayesian-rational. The key reason is that such models appeal to approximations, a fact that carries significant implications. After outlining the argument, I critique two (...) responses, seen in recent cognitive neuroscience. One says that the mind can be seen as approximately Bayes-rational, while the other reconceives norms of rationality. (shrink)

The Capgras delusion is a condition in which a person believes that an imposter has replaced some close friend or relative. Recent theorists have appealed to Bayesianism to help explain both why a subject with the Capgras delusion adopts this delusional belief and why it persists despite counter-evidence. The Bayesian approach is useful for addressing these questions; however, the main proposal of this essay is that Capgras subjects also have a delusional conception of epistemic possibility, more specifically, they think (...) more things are possible, given what is known, than non-delusional subjects do. I argue that this is a central way in which their thinking departs from ordinary cognition and that it cannot be characterized in Bayesian terms. Thus, in order to fully understand the cognitive processing involved in the Capgras delusion, we must move beyond Bayesianism. 1 The Simple Bayesian Model2 Anomalous Evidence and the Capgras Delusion3 Impaired Reasoning4 Setting Priors5 Epistemic Modality6 Delusions of Possibility7 Delusions of Possibility in Different Contexts8 How Many Factors? (shrink)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt (...) to make them consistent in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

Although some previous studies have investigated the relationship between moral foundations and moral judgment development, the methods used have not been able to fully explore the relationship. In the present study, we used Bayesian Model Averaging (BMA) in order to address the limitations in traditional regression methods that have been used previously. Results showed consistency with previous findings that binding foundations are negatively correlated with post-conventional moral reasoning and positively correlated with maintaining norms and personal interest schemas. In addition (...) to previous studies, our results showed a positive correlation for individualizing foundations and post-conventional moral reasoning. Implications are discussed as well as a detailed explanation of the novel BMA method in order to allow others in the field of moral education to be able to use it in their own studies. (shrink)

The "myside bias'' in evaluating arguments is an empirically well-confirmed phenomenon that consists of overweighting arguments that endorse one's beliefs or attack alternative beliefs while underweighting arguments that attack one's beliefs or defend alternative beliefs. This paper makes two contributions: First, it proposes a probabilistic model that adequately captures three salient features of myside bias in argument evaluation. Second, it provides a Bayesian justification of this model, thus showing that myside bias has a rational Bayesian explanation under certain (...) conditions. (shrink)

Learning is fundamentally about action, enabling the successful navigation of a changing and uncertain environment. The experience of pain is central to this process, indicating the need for a change in action so as to mitigate potential threat to bodily integrity. This review considers the application of Bayesian models of learning in pain that inherently accommodate uncertainty and action, which, we shall propose are essential in understanding learning in both acute and persistent cases of pain.

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for (...) discrete datasets. The full Bayesian significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

This paper applies Bayesian theories to critically analyse and offer reforms of intelligence analysis, collection, analysis, and decision making on the basis of Human Intelligence, Signals Intelligence, and Communication Intelligence. The article criticises the reliabilities of existing intelligence methodologies to demonstrate the need for Bayesian reforms. The proposed epistemic reform program for intelligence analysis should generate more reliable inferences. It distinguishes the transmission of knowledge from its generation, and consists of Bayesian three stages modular model for the (...) generation of reliable intelligence from multiple coherent and independent testimonial sources, and for the tracing and analysis of intelligence failures. The paper concludes with suggestions for further research, the development of artificial intellignce that may measure coherence and reliability of HUMINT sources and infer intelligence following the outlined general modular model. (shrink)

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests (...) if in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method’s sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results. (shrink)

ABSTRACT: It will be argued that Eric Winsberg has created a problem where nobody is in the position to rationally support the Anthropogenic Climate Change hypothesis, since he demands the normal lay public defer to experts but, from Winsberg’s philosophical commitments, experts are precluded from having the ability to rationally conclude that a hypothesis is superior to an alternative. Winsberg’s difficulties can be resolved with a little help from Bayesian Confirmation Theory. A Bayesian analysis will be provided which (...) allows for the evaluation of climate models that uses Winsberg’s analysis of robustness. (shrink)

Compared with traditional statistics, only a few social scientists employ Bayesian analyses. The existing software programs for implementing Bayesian analyses such as OpenBUGS, WinBUGS, JAGS, and rstanarm can be daunting given that their complex computer codes involve a steep learning curve. In contrast, this paper introduces a new open software for implementing Bayesian network modelling and analysis: the bayesvl R package. The package aims at providing an intuitive gateway for beginners of Bayesian statistics to construct and (...) analyse mathematical models in social sciences... (shrink)

It has been argued recently that dogmatism in epistemology is incompatible with Bayesianism. That is, it has been argued that dogmatism cannot be modelled using traditional techniques for Bayesian modelling. I argue that our response to this should not be to throw out dogmatism, but to develop better modelling techniques. I sketch a model for formal learning in which an agent can discover a posteriori fundamental epistemic connections. In this model, there is no formal objection to dogmatism.

The exponential growth of social data both in volume and complexity has increasingly exposed many of the shortcomings of the conventional frequentist approach to statistics. The scientific community has called for careful usage of the approach and its inference. Meanwhile, the alternative method, Bayesian statistics, still faces considerable barriers toward a more widespread application. The bayesvl R package is an open program, designed for implementing Bayesian modeling and analysis using the Stan language’s no-U-turn (NUTS) sampler. The package combines (...) the ability to construct Bayesian network models using directed acyclic graphs (DAGs), the Markov chain Monte Carlo (MCMC) simulation technique, and the graphic capability of the ggplot2 package. As a result, it can improve the user experience and intuitive understanding when constructing and analyzing Bayesian network models. A case example is offered to illustrate the usefulness of the package for Big Data analytics and cognitive computing. (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 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)

Bayesian epistemologists support the norms of probabilism and conditionalization using Dutch book and accuracy arguments. These arguments assume that rationality requires agents to maximize practical or epistemic value in every doxastic state, which is evaluated from a subjective point of view (e.g., the agent’s expectancy of value). The accuracy arguments also presuppose that agents are opinionated. The goal of this paper is to discuss the assumptions of these arguments, including the measure of epistemic value. I have designed AI agents (...) based on the Bayesian model and a nonmonotonic framework and tested how they achieve practical and epistemic value in conditions in which an alternative set of assumptions holds. In one of the tested conditions, the nonmonotonic agent, which is not opinionated and fulfills neither probabilism nor conditionalization, outperforms the Bayesian in the measure of epistemic value that I argue for in the paper (α-value). I discuss the consequences of these results for the epistemology of rationality. (shrink)

The data analyzed in this paper are part of the results described in Bueno et al. (2000). Three cytogenetics endpoints were analyzed in three populations of a species of wild rodent – Akodon montensis – living in an industrial, an agricultural, and a preservation area at the Itajaí Valley, State of Santa Catarina, Brazil. The polychromatic/normochromatic ratio, the mitotic index, and the frequency of micronucleated polychromatic erythrocites were used in an attempt to establish a genotoxic profile of each area. It (...) was assumed that the three populations were in the same conditions with respect to the influence of confounding factors such as animal age, health, nutrition status, presence of pathogens, and intra- and inter-populational genetic variability. Therefore, any differences found in the endpoints analyzed could be attributed to the external agents present in each area. The statistical models used in this paper are mixtures of negative-binomials and Poisson variables. The Poisson variables are used as approximations of binomials for rare events. The mixing distributions are beta densities. The statistical analyzes are under the bayesian perspective, as opposed to the frequentist ones often considered in the literature, as for instance in Bueno et al. (2000). (shrink)

The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an asymmetric (...) way—ruling out “streaky” hypotheses more quickly than “switchy” ones. As a result, the majority (and the average) exhibit the gambler’s fallacy. If they have limited memory, this tendency persists even with arbitrarily-large amounts of data. Indeed, such Bayesians exhibit a variety of the empirical trends found in studies of the gambler’s fallacy: they expect switches after short streaks but continuations after long ones; these nonlinear expectations vary with their familiarity with the causal system; their predictions depend on the sequence they’ve just seen; they produce sequences that are too switchy; and they exhibit greater rates of gambler’s reasoning when forming binary predictions than when forming probability estimates. In short: what’s been thought to be evidence for irrationality may instead be rational responses to limited data and memory. (shrink)

We model scientific theories as Bayesian networks. Nodes carry credences and function as abstract representations of propositions within the structure. Directed links carry conditional probabilities and represent connections between those propositions. Updating is Bayesian across the network as a whole. The impact of evidence at one point within a scientific theory can have a very different impact on the network than does evidence of the same strength at a different point. A Bayesian model allows us to envisage (...) and analyze the differential impact of evidence and credence change at different points within a single network and across different theoretical structures. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as (...) a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (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)

The Fully Bayesian Significance Test (FBST) is a coherent Bayesian significance test for sharp hypotheses. This paper explores the FBST as a model selection tool for general mixture models, and gives some computational experiments for Multinomial-Dirichlet-Normal-Wishart models.

International trade enables countries to expand their markets, access more products, improve resource allocation, and boost economic growth by leveraging comparative advantage and specialization. The aim of this article is to analyze the primary factors that influence Malawi’s international trade flows. The study is relevant because it examines Malawi’s trade patterns with its main partners, which include surrounding nations and traditional trade allies. The novelty is that, through the analysis, the research offers valuable insights into the primary factors that influence (...) Malawi’s international commerce. Panel data is gathered from various sources, including the International Monetary Fund (IMF) and World Bank, covering the period from 2000 to 2023 for 11 countries that are trading partners with Malawi. We employ the Bayesian Mindsponge gravity methodology. The results show that the economic size (characterized by the gross domestic product) of the origin and destination countries, bilateral agreements, and the population size of the destination country have a beneficial impact on Malawi’s exports. In conclusion, Malawi’s export performance is significantly enhanced by the economic size of both Malawi and its trading partners, the existence of bilateral agreements, and the population size of the destination countries, underscoring the importance of strategic economic partnerships and targeted trade policies in boosting Malawi’s international trade. We recommend Malawi authorities focus on strengthening bilateral agreements and targeting trade relationships with larger and more populous economies to boost international trade. (shrink)

There are two distinct approaches to Bayesian modelling in cognitive science. Black-box approaches use Bayesian theory to model the relationship between the inputs and outputs of a cognitive system without reference to the mediating causal processes; while mechanistic approaches make claims about the neural mechanisms which generate the outputs from the inputs. This paper concerns the relationship between these two approaches. We argue that the dominant trend in the philosophical literature, which characterizes the relationship between black-box and mechanistic (...) approaches to Bayesian cognitive science in terms of the dichotomy between instrumentalism and realism, is misguided. We propose that the two distinctions are orthogonal: black-box and mechanistic approaches to Bayesian modelling can each be given either an instrumentalist or a realist interpretation. We argue that the current tendency to conflate black-box approaches with instrumentalism and mechanistic approaches with realism stems from unwarranted assumptions about the nature of scientific explanation, the ontological commitments of scientific theories, and the role of abstraction and idealization in scientific models. We challenge each of these assumptions to reframe the debates over Bayesian modelling in cognitive science. (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)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the (...) evidence calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful (...) and convincing results”. The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

Politics is rife with motivated cognition. People do not dispassionately engage with the evidence when they form political beliefs; they interpret it selectively, generating justifications for their desired conclusions and reasons why contrary evidence should be ignored. Moreover, research shows that epistemic ability (e.g. intelligence and familiarity with evidence) is correlated with motivated cognition. Bjørn Hallsson has pointed out that this raises a puzzle for the epistemology of disagreement. On the one hand, we typically think that epistemic ability in an (...) interlocutor gives us reason to downgrade our belief upon learning that we disagree. On the other hand, if our interlocutor is under the sway of motivated cognition, then we have reason to discount his opinion. In this paper, I argue that Hallsson's puzzle is solved by adopting a Bayesian approach to disagreement. If an interlocutor is under the sway of motivated cognition, his disagreement should not affect our beliefs--no matter his ability. Because we implicitly and to high accuracy know his beliefs before he reveals them to us, disagreement provides us with no new information on which to conditionalize. I advance a model which accommodates the motivated cognition dynamic and other key epistemic features of disagreement. (shrink)

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the (...) problem of old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)

Recent years have seen a Bayesian revolution in cognitive science. This should be of interest to metaphysicians of science, whose naturalist project involves working out the metaphysical implications of our leading scientific accounts, and in advancing our understanding of those accounts by drawing on the metaphysical frameworks developed by philosophers. Toward these ends, in this paper I develop a metaphysics of the Bayesian mind. My central claim is that the Bayesian approach supports a novel empirical argument for (...) normativism, the thesis that belief has a normative essence, with the norms in question being those of rationality. The argument I develop draws in part on the causal powers subset account of realization defended by Wilson and Shoemaker, with the link being that Bayesians often appeal to Marr’s framework of levels of analysis, which carries with it multiple realizability claims that can be understood in terms of the subset model. I then use the view developed, with its appeal to normativism and subset realization, to explain how Bayesians can accommodate empirical findings of irrationality that are sometimes thought to pose a problem for their view. (shrink)

ABSTRACTRational agents have consistent beliefs. Bayesianism is a theory of consistency for partial belief states. Rational agents also respond appropriately to experience. Dogmatism is a theory of how to respond appropriately to experience. Hence, Dogmatism and Bayesianism are theories of two very different aspects of rationality. It's surprising, then, that in recent years it has become common to claim that Dogmatism and Bayesianism are jointly inconsistent: how can two independently consistent theories with distinct subject matter be jointly inconsistent? In this (...) essay I argue that Bayesianism and Dogmatism are inconsistent only with the addition of a specific hypothesis about how the appropriate responses to perceptual experience are to be incorporated into the formal models of the Bayesian. That hypothesis isn't essential either to Bayesianism or to Dogmatism, and so Bayesianism and Dogmatism are jointly consistent. That leaves the matter of how experiences and credences are related, a... (shrink)

The Fully Bayesian Significance Test (FBST) is a coherent Bayesian significance test for sharp hypotheses. This paper proposes the FBST as a model selection tool for general mixture models, and compares its performance with Mclust, a model-based clustering software. The FBST robust performance strongly encourages further developments and investigations.

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)

Extant literature suggests a positive correlation between social trust (also called generalized trust) and life satisfaction. However, the psychological pathways underlying this relationship can be complex. Using the Bayesian Mindsponge Framework (BMF), we examined the influence of social trust in a high-violence environment. Employing Bayesian analysis on a sample of 1237 adults in Cali, Colombia, we found that in a linear relationship, generalized trust is positively associated with life satisfaction. However, in a model including the interactions between trust (...) and education level as well as between trust and socioeconomic status, generalized trust is found to be negatively associated with life satisfaction. In this non-linear relationship, both education level and socioeconomic status have moderating effects against the negative association between generalized trust and life satisfaction. In other words, less educated people living in worse socioeconomic conditions are more likely to have lower life satisfaction when they have higher levels of social trust. In contrast, highly educated people living in better socioeconomic conditions are more likely to have higher life satisfaction when they have higher levels of social trust. Due to the facilitating function of trust in information processing, lowering the rigor of the filtering system in a high-violence social environment will likely put an individual at risk. Based on our findings, we suggest that policymakers should consider the impacts of social contexts when advocating for increasing social trust. We also recommend that researchers carefully examine the psychological mechanism underlying an observed association before making suggestions for policymaking. (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.

Much contemporary epistemology is informed by a kind of confirmational holism, and a consequent rejection of the assumption that all confirmation rests on experiential certainties. Another prominent theme is that belief comes in degrees, and that rationality requires apportioning one's degrees of belief reasonably. Bayesian confirmation models based on Jeffrey Conditionalization attempt to bring together these two appealing strands. I argue, however, that these models cannot account for a certain aspect of confirmation that would be accounted for (...) in any adequate holistic confirmation theory. I then survey the prospects for constructing a formal epistemology that better accommodates holistic insights. (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)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s (...) erotetic account are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

Moral circles help define the boundaries of one’s moral consideration. One’s moral circle may provide insight into how one perceives or treats other entities. A data-driven model exploration was conducted to explore predictors and prediction models. Candidate predictors were built upon past research using moral foundations and political orientation. Moreover, we also employed additional moral psychological indicators, i.e., moral reasoning, moral identity, and empathy, based on prior research in moral development and education. We used model exploration methods, i.e., (...) class='Hi'>Bayesian model exploration, Bayesian model averaging, and elastic-net regression. The study successfully replicated past research supporting the relationship between moral foundations, political orientation, and the moral circle. Additional moral psychological constructs, such as post-conventional moral reasoning and moral identity, significantly predicted the moral circle width. The identified components of the moral circle were conceptually related to phronesis, i.e., practical wisdom. We discussed the educational implications of the findings, particularly those related to moral education focusing on phronesis cultivation, multiculturalism and global citizenship, and climate justice. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is (...) a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

We study Compositional Models based on Dirichlet Regression where, given a (vector) covariate x, one considers the response variable, y, to be a positive vector with a conditional Dirichlet distribution, y | X We introduce a new method for estimating the parameters of the Dirichlet Covariate Model given a linear model on X, and also propose a Bayesian model selection approach. We present some numerical results which suggest that our proposals are more stable and robust than traditional approaches.

According to standard rational choice theory, as commonly used in political science and economics, an agent's fundamental preferences are exogenously fixed, and any preference change over decision options is due to Bayesian information learning. Although elegant and parsimonious, such a model fails to account for preference change driven by experiences or psychological changes distinct from information learning. We develop a model of non-informational preference change. Alternatives are modelled as points in some multidimensional space, only some of whose dimensions play (...) a role in shaping the agentís preferences. Any change in these "motivationally salient" dimensions can change the agent's preferences. How it does so is described by a new representation theorem. Our model not only captures a wide range of frequently observed phenomena, but also generalizes some standard representations of preferences in political science and economics. (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)

Decoupling is a general principle that allows us to separate simple components in a complex system. In statistics, decoupling is often expressed as independence, no association, or zero covariance relations. These relations are sharp statistical hypotheses, that can be tested using the FBST - Full Bayesian Significance Test. Decoupling relations can also be introduced by some techniques of Design of Statistical Experiments, DSEs, like randomization. This article discusses the concepts of decoupling, randomization and sparsely connected statistical models in (...) the epistemological framework of cognitive constructivism. (shrink)

We explored the relationship between 24 character strengths measured by the Global Assessment of Character Strengths (GACS), which was revised from the original VIA instrument, and moral functioning comprising postconventional moral reasoning, empathic traits and moral identity. Bayesian Model Averaging (BMA) was employed to explore the best models, which were more parsimonious than full regression models estimated through frequentist regression, predicting moral functioning indicators with the 24 candidate character strength predictors. Our exploration was conducted with a dataset (...) collected from 666 college students at a public university in the Southern United States. Results showed that character strengths as measured by GACS partially predicted relevant moral functioning indicators. Performance evaluation results demonstrated that the best models identified by BMA performed significantly better than the full models estimated by frequentist regression in terms of AIC, BIC, and cross-validation accuracy. We discuss theoretical and methodological implications of the findings for future studies addressing character strengths and moral functioning. (shrink)

In engineering, as in other scientific fields, researchers seek to confirm their models with real-world data. It is common practice to assess models in terms of the distance between the model outputs and the corresponding experimental observations. An important question that arises is whether the model should then be ‘tuned’, in the sense of estimating the values of free parameters to get a better fit with the data, and furthermore whether the tuned model can be confirmed with the (...) same data used to tune it. This dual use of data is often disparagingly referred to as ‘double-counting’. Here, we analyse these issues, with reference to selected research articles in engineering. Our example studies illustrate more and less controversial practices of model tuning and double-counting, both of which, we argue, can be shown to be legitimate within a Bayesian framework. The question nonetheless remains as to whether the implied scientific assumptions in each case are apt from the engineering point of view. (shrink)

The concept of non-arbitrage plays an essential role in finance theory. Under certain regularity conditions, the Fundamental Theorem of Asset Pricing states that, in non-arbitrage markets, prices of financial instruments are martingale processes. In this theoretical framework, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender arbitrage conditions. Assuming an underlying Variance Gamma statistical model, this study aims to test, using the FBST - Full (...) Bayesian Significance Test, if there is a relevant price difference between essentially the same financial asset traded at two distinct locations. Specifically, we investigate and compare the behavior of call options on the BOVESPA Index traded at (a) the Equities Segment and (b) the Derivatives Segment of BM&FBovespa. Our results seem to point out significant statistical differences. To what extent this evidence is actually the expression of perennial arbitrage opportunities is still an open question. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)