The target article provides important theoretical contributions to psychology and Bayesian modeling. Despite the article's excellent points, we suggest that it succumbs to a few misconceptions about evolutionary psychology (EP). These include a mischaracterization of evolutionary psychology's approach to optimality; failure to appreciate the centrality of mechanism in EP; and an incorrect depiction of hypothesis testing. An accurate characterization of EP offers more promise for successful integration with Bayesian modeling.

Bayesian paradigm has been widely acknowledged as a coherent approach to learning putative probability model structures from a finite class of candidate models. Bayesian learning is based on measuring the predictive ability of a model in terms of the corresponding marginal data distribution, which equals the expectation of the likelihood with respect to a prior distribution for model parameters. The main controversy related to this learning method stems from the necessity of specifying proper prior distributions for all unknown (...) parameters of a model, which ensures a complete determination of the marginal data distribution. Even for commonly used models, subjective priors may be difficult to specify precisely, and therefore, several automated learning procedures have been suggested in the literature. Here we introduce a novel Bayesian learning method based on the predictive entropy of a probability model, that can combine both subjective and objective probabilistic assessment of uncertain quantities in putative models. It is shown that our approach can avoid some of the limitations of the earlier suggested objective Bayesian methods. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases (...) of the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)

The mechanisms by which delusion and anxiety affect the tendency to make hasty decisions (Jumping-to-Conclusions bias) remain unclear. This paper proposes a Bayesian computational model that explores the assignment of evidence weights as a potential explanation of the Jumping-to-Conclusions bias using the Beads Task. We also investigate the Beads Task as a repeated measure by varying the key aspects of the paradigm. The Bayesian model estimations from two online studies showed that higher delusional ideation promoted reduced belief updating (...) but the impact of general and social anxiety on evidence weighting was inconsistent. The altered evidence weighting as a result of a psychopathological trait appeared insufficient in contributing to the Jumping-to-Conclusions bias. Variations in Beads Task aspects significantly affected subjective certainty at the point of decisions but not the number of draws to decisions. Repetitions of the Beads Task are feasible if one assesses the Jumping-to-Conclusions bias using number of draws to decisions. (shrink)

A long tradition suggests a fundamental distinction between situations of risk, where true objective probabilities are known, and unmeasurable uncertainties where no such probabilities are given. This distinction can be captured in a Bayesian model where uncertainty is represented by the agent’s subjective belief over the parameter governing future income streams. Whether uncertainty reduces to ordinary risk depends on the agent’s ability to smooth consumption. Uncertainty can have a major behavioral and economic impact, including precautionary behavior that may appear (...) overly conservative to an outside observer. We argue that one of the main characteristics of uncertain beliefs is that they are not empirical, in the sense that they cannot be objectively tested to determine whether they are right or wrong. This can confound empirical methods that assume rational expectations. (shrink)

This article explores some of the philosophical implications of the Bayesian modeling paradigm. In particular, it focuses on the ramifications of the fact that Bayesian models pre‐specify an inbuilt hypothesis space. To what extent does this pre‐specification correspond to simply ‘‘building the solution in''? I argue that any learner must have a built‐in hypothesis space in precisely the same sense that Bayesian models have one. This has implications for the nature of learning, Fodor's puzzle of concept acquisition, (...) and the role of modeling in cognitive science. (shrink)

Bayesian approaches to legal reasoning propose causal models of the relation between evidence, the credibility of evidence, and ultimate hypotheses, or verdicts. They assume that legal reasoning is the process whereby one infers the posterior probability of a verdict based on observed evidence, or facts. In practice, legal reasoning does not operate quite that way. Legal reasoning is also an attempt at inferring applicable rules derived from legal precedents or statutes based on the facts at hand. To make such (...) an inference, legal reasoning follows syllogistic logic and first order transitivity. This paper proposes a Bayesian model of legal syllogistic reasoning that complements existing Bayesian models of legal reasoning using a Bayesian network whose variables correspond to legal precedents, statutes, and facts. We suggest that legal reasoning should be modelled as a process of finding the posterior probability of precedents and statutes based on available facts. (shrink)

How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common (...) Bayesian formalism. The concepts we review are ambiguities, fusion, multimodality, conflicts, modularity, hierarchies and loops. First, each of these concepts is introduced briefly using some examples from the neuroscience, psychophysics or robotics literature. Then, the concept is formalized using a template Bayesian model. The assumptions and common features of these models, as well as their major differences, are outlined and discussed. (shrink)

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)

(2013). Hierarchical Bayesian models as formal models of causal reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 36-45. doi: 10.1080/19462166.2012.700321.

We argue that the authors’ call to integrate Bayesian models more strongly with algorithmic- and implementational-level models must go hand in hand with a call for a fully developed account of algorithmic rationality. Without such an account, the integration of levels would come at the expense of the explanatory benefit that rational models provide.

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)

This paper provides a model of belief representation in which ambiguity and unambiguity are endogenously distinguished in a purely subjective setting where objects of choices are, as usual, maps from states to consequences. Specifically, I first extend the maxmin expected utility theory and get a representation of beliefs such that the probabilistic beliefs over each ambiguous event are represented by a non-degenerate interval, while the ones over each unambiguous event are represented by a number. I then consider a class of (...) the biseparable preferences. Two representation results are achieved and can be used to identify the unambiguity in the context of the biseparable preferences. Finally a subjective definition of ambiguity is suggested. It provides a choice theoretic foundation for the Knightian distinction between ambiguity and unambiguity. (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)

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We (...) present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally. (shrink)

We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites (...) paradox, with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)

Bayesian epistemology provides a popular and powerful framework for modeling rational norms on credences, including how rational agents should respond to evidence. The framework is built on the assumption that ideally rational agents have credences, or degrees of belief, that are representable by numbers that obey the axioms of probability. From there, further constraints are proposed regarding which credence assignments are rationally permissible, and how rational agents’ credences should change upon learning new evidence. While the details are hotly disputed, (...) all flavors of Bayesianism purport to give us norms of ideal rationality. This raises the question of how exactly these norms apply to you and me, since perfect compliance with those ideal norms is out of reach for human thinkers. A common response is that Bayesian norms are ideals that human reasoners are supposed to approximate – the closer they come to being ideally rational, the better. To make this claim plausible, we need to make it more precise. In what sense is it better to be closer to ideally rational, and what is an appropriate measure of such closeness? This article sketches some possible answers to these questions. (shrink)

How do teachers learn about what learners already know? How do learners aid teachers by providing them with information about their background knowledge and what they find confusing? We formalize this collaborative reasoning process using a hierarchical Bayesian model of pedagogy. We then evaluate this model in two online behavioral experiments (N = 312 adults). In Experiment 1, we show that teachers select examples that account for learners' background knowledge, and adjust their examples based on learners' feedback. In Experiment (...) 2, we show that learners strategically provide more feedback when teachers' examples deviate from their background knowledge. These findings provide a foundation for extending computational accounts of pedagogy to richer interactive settings. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. (...) Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Recent studies suggest that learners who are asked to predict the outcome of an event learn more than learners who are asked to evaluate it retrospectively or not at all. One possible explanation for this “prediction boost” is that it helps learners engage metacognitive reasoning skills that may not be spontaneously leveraged, especially for individuals with still-developing executive functions. In this paper, we combined multiple analytic approaches to investigate the potential role of executive functions in elementary school-aged children's science learning. (...) We performed an experiment that investigates children's science learning during a water displacement task where a “prediction boost” had previously been observed—children either made an explicit prediction or evaluated an event post hoc (i.e., postdiction). We then considered the relation of executive function measures and learning, which were collected following the main experiment. Via mixed effects regression models, we found that stronger executive function skills (i.e., stronger inhibition and switching scores) were associated with higher accuracy in Postdiction but not in the Prediction Condition. Using a theory-based Bayesian model, we simulated children's individual performance on the learning task (capturing “belief flexibility”), and compared this “flexibility” to the other measures to understand the relationship between belief revision, executive function, and prediction. Children in the Prediction Condition showed near-ceiling “belief flexibility” scores, which were significantly higher than among children in the Postdiction Condition. We also found a significant correlation between children's executive function measures to our “belief flexibility” parameter, but only for children in the Postdiction Condition. These results indicate that when children provided responses post hoc, they may have required stronger executive function capacities to navigate the learning task. Additionally, these results suggest that the “prediction boost” in children's science learning could be explained by increased metacognitive flexibility in the belief revision process. (shrink)

Bayesian Rationality (Oaksford & Chater 2007) illustrates the strengths of Bayesian models of cognition: the systematicity of rational explanations, transparent assumptions about human learners, and combining structured symbolic representation with statistics. However, the book also highlights some of the challenges this approach faces: of providing psychological mechanisms, explaining the origins of the knowledge that guides human learning, and accounting for how people make genuinely new discoveries.

According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this article is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of the epistemological challenges to these claims; and some of the implications of these claims. We address two questions: (i) How are Bayesian models used in theoretical neuroscience? (ii) From (...) the use of Bayesian models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people's performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the three-level framework laid out by David Marr ( [1982] ). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects' perceptual performance and features of the underlying neural mechanisms. (shrink)

Bayesian model selection has frequently been the focus of philosophical inquiry (e.g., Forster, Br J Philos Sci 46:399–424, 1995; Bandyopadhyay and Boik, Philos Sci 66:S390–S402, 1999; Dowe et al., Br J Philos Sci 58:709–754, 2007). This paper argues that Bayesian model selection procedures are very diverse in their inferential target and their justification, and substantiates this claim by means of case studies on three selected procedures: MML, BIC and DIC. Hence, there is no tight link between Bayesian (...) model selection and Bayesian philosophy. Consequently, arguments for or against Bayesian reasoning based on properties of Bayesian model selection procedures should be treated with great caution. (shrink)

We comment on the contributions of Dahlman and of Fenton et al., who both suggested a Bayesian approach to analyze the Simonshaven case. We argue that analyzing a full case with a Bayesian approach is not feasible, and that there are serious problems with assigning actual numbers to probabilities and priors. We also discuss the nature of Bayesian thinking in court, and the nature and interpretation of the likelihood ratio. In particular, we discuss what it could mean (...) that a likelihood ratio is in some sense uncertain. (shrink)