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)

(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.

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian cognitive (...) science, where probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account (...) optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. (shrink)

This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues that, although often useful in specific settings, most of these approaches are limited in their ability to give a general assessment of models. This article argues that hierarchical methods, generally, and hierarchical Bayesian (...) methods, specifically, can provide a more thorough evaluation of models in the cognitive sciences. This article presents two worked examples of hierarchical Bayesian analyses to demonstrate how the approach addresses key questions of descriptive adequacy, parameter interference, prediction, and generalization in principled and coherent ways. (shrink)

Gut microbiome plays a significant role in defining the health status of subjects, and recent studies highlight the importance of using time series strategies to analyse microbiome dynamics. In this paper, we develop a Bayesian model for microbiota longitudinal data, based on Dirichlet distribution with time-varying parameters, that take into account the compositional paradigm and consider principal balances. The proposed model can be effective for predicting the future dynamics of a microbial community in the short term and for analysing (...) the microbial interactions using the value of the estimated parameters. The usefulness of the proposed model is illustrated with six different datasets, and a comparison study with four alternative models is provided. (shrink)

In most decision-making situations, there is a plethora of information potentially available to people. Deciding what information to gather and what to ignore is no small feat. How do decision makers determine in what sequence to collect information and when to stop? In two experiments, we administered a version of the German cities task developed by Gigerenzer and Goldstein (1996), in which participants had to decide which of two cities had the larger population. Decision makers were not provided with the (...) names of the cities, but they were able to collect different kinds of cues for both response alternatives (e.g., “Does this city have a university?”) before making a decision. Our experiments differed in whether participants were free to determine the number of cues they examined. We demonstrate that a novel model, using hierarchical latent mixtures and Bayesian inference (Lee & Newell, 2011) provides a more complete description of the data from both experiments than simple conventional strategies, such as the take–the–best or the Weighted Additive heuristics. (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)

Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘para- digms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian (...) tradition, particularly the idea that higher-level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. (shrink)

While Conviction Narrative Theory correctly criticizes utility-based accounts of decision-making, it unfairly reduces probabilistic models to point estimates and treats affect and narrative as mechanistically opaque yet explanatorily sufficient modules. Hierarchically nested Bayesian accounts offer a mechanistically explicit and parsimonious alternative incorporating affect into a single biologically plausible precision-weighted mechanism that tunes decision-making toward narrative versus sensory dependence under varying uncertainty levels.

Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher‐level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, (...) particularly the idea that higher‐level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. *Received July 2009; revised October 2009. †To contact the authors, please write to: Leah Henderson, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 32D‐808, Cambridge, MA 02139; e‐mail: [email protected]. (shrink)

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis (...) can provide a unifying explanation of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models. (shrink)

In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski :559–582, 2016) and Gładziejewski and Miłkowski, to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing (...) that it is consistent with approaches implicit in theories of unsupervised learning in neural networks. In the course of this discussion, we argue that the structural representation proposal, properly understood, has more in common with functional-role than with causal/informational or teleosemantic theories. In the remainder of the paper, we describe the PEM framework for approximate Bayesian inference in some detail, and discuss how structural representations might arise within the proposed Bayesian hierarchies. After explicating the notion of variational inference, we define a subjectively accessible measure of misrepresentation for hierarchical Bayesian networks by appeal to the Kullbach–Leibler divergence between posterior generative and approximate recognition densities, and discuss a related measure of objective misrepresentation in terms of correspondence with the facts. (shrink)

The Recursive Bayesian Net formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in (...) particular how a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis. (shrink)

This article proposes a formal model that integrates cognitive and psychodynamic psychotherapeutic models of psychopathy to show how two major psychopathic traits called lacks remorse and self-aggrandizing can be understood as a form of abnormal Bayesian inference about the self. This model draws on the predictive coding (i.e., active inference) framework, a neurobiologically plausible explanatory framework for message passing in the brain that is formalized in terms of hierarchical Bayesian inference. In summary, this model proposes that (...) these two cardinal psychopathic traits reflect entrenched maladaptive Bayesian inferences about the self, which defend against the experience of deep-seated, self-related negative emotions, specifically shame and worthlessness. Support for the model in extant research on the neurobiology of psychopathy and quantitative simulations are provided. Finally, we offer a preliminary overview of a novel treatment for psychopathy that rests on our Bayesian formulation. (shrink)

The Recursive Bayesian Net (RBN) formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show (...) in particular how a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis. (shrink)

A generalized Bayesian inference nets model is proposed to aid researchers to construct Bayesian inference nets for various applications. The benefit of such a model is well demonstrated by applying GBINM in constructing a hierarchical Bayesian fuzzy inference nets to diagnose five important types of cardiovascular diseases. The patients' medical records with doctors' confirmed diagnostic results obtained from two hospitals in China are used to design and verify HBFIN. Bayesian theorem is used to calculate the (...) propagation of probability and address the uncertainties involved in each sequential stage of inference nets to deduce the disease. The validity and effectiveness of proposed approach is witnessed clearly from testing results obtained. (shrink)

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)

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent (...) to some of the earlier, possibilistic models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions. (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)

A recent critique of hierarchical Bayesian models of delusion argues that, contrary to a key assumption of these models, belief formation in the healthy (i.e., neurotypical) mind is manifestly non-Bayesian. Here we provide a deeper examination of the empirical evidence underlying this critique. We argue that this evidence does not convincingly refute the assumption that belief formation in the neurotypical mind approximates Bayesian inference. Our argument rests on two key points. First, evidence that purports (...) to reveal the most damning violation of Bayesian updating in human belief formation is counterweighted by substantial evidence that indicates such violations are the rare exception—not a common occurrence. Second, the remaining evidence does not demonstrate convincing violations of Bayesian inference in human belief updating; primarily because this evidence derives from study designs that produce results that are not obviously inconsistent with Bayesian principles. (shrink)

Learning to understand a single causal system can be an achievement, but humans must learn about multiple causal systems over the course of a lifetime. We present a hierarchical Bayesian framework that helps to explain how learning about several causal systems can accelerate learning about systems that are subsequently encountered. Given experience with a set of objects, our framework learns a causal model for each object and a causal schema that captures commonalities among these causal models. The (...) schema organizes the objects into categories and specifies the causal powers and characteristic features of these categories and the characteristic causal interactions between categories. A schema of this kind allows causal models for subsequent objects to be rapidly learned, and we explore this accelerated learning in four experiments. Our results confirm that humans learn rapidly about the causal powers of novel objects, and we show that our framework accounts better for our data than alternative models of causal learning. (shrink)

This chapter explores to what extent some core ideas of predictive processing can be applied to the phenomenology of time consciousness. The focus is on the experienced continuity of consciously perceived, temporally extended phenomena (such as enduring processes and successions of events). The main claim is that the hierarchy of representations posited by hierarchical predictive processing models can contribute to a deepened understanding of the continuity of consciousness. Computationally, such models show that sequences of events can be (...) represented as states of a hierarchy of dynamical systems. Phenomenologically, they suggest a more fine-grained analysis of the perceptual contents of the specious present, in terms of a hierarchy of temporal wholes. Visual perception of static scenes not only contains perceived objects and regions but also spatial gist; similarly, auditory perception of temporal sequences, such as melodies, involves not only perceiving individual notes but also slightly more abstract features (temporal gist), which have longer temporal durations (e.g., emotional character or rhythm). Further investigations into these elusive contents of conscious perception may be facilitated by findings regarding its neural underpinnings. Predictive processing models suggest that sensorimotor areas may influence these contents. (shrink)

The focus of this commentary is what Andy Clark takes to be the most groundbreaking of the philosophical import of the ‘bidirectional hierarchical model of brain functions’, namely, the claim that perceptual representations represent probabilities. This is what makes his account Bayesian and this is a philosophical or theoretical conclusion that neuroscientists and psychologists are also quick and happy to draw. My claim is that nothing in the ‘bidirectional hierarchical models of brain functions’ implies that perceptual (...) representations are probabilistic, or that they represent or ‘encode probability density distributions’. There is a much more parsimonious way of describing the representations in the bidirectional hierarchical model of brain functions: they attribute properties to objects (or to the perceived scene) that are not fully determinate. (shrink)

Hohwy et al.’s (2008) model of binocular rivalry (BR) is taken as a classic illustration of predictive coding’s explanatory power. I revisit the account and show that it cannot explain the role of reward in BR. I then consider a more recent version of Bayesian model averaging, which recasts the role of reward in (BR) in terms of optimism bias. If we accept this account, however, then we must reconsider our conception of perception. On this latter view, I argue, (...) organisms engage in what amounts to policy-driven, motivated perception. (shrink)

When faced with an ambiguous pronoun, an addressee must interpret it by identifying a suitable referent. It has been proposed that the interpretation of pronouns can be captured using Bayes’ Rule: P ∝ PP. This approach has been successful in English and Mandarin Chinese. In this study, we further the cross-linguistic evidence for the Bayesian model by applying it to German personal and demonstrative pronouns, and provide novel quantitative support for the model by assessing model performance in a (...) class='Hi'>Bayesian statistical framework that allows implementation of a fully hierarchical structure, providing the most conservative estimates of uncertainty. Data from two story-continuation experiments showed that the Bayesian model overall made more accurate predictions for pronoun interpretation than production and next-mention biases separately. Furthermore, the model accounts for the demonstrative pronoun dieser as well as the personal pronoun, despite the demonstrative having different, and more rigid, resolution preferences. (shrink)

Hierarchical cognitive mechanisms underlie sophisticated behaviors, including language, music, mathematics, tool-use, and theory of mind. The origins of hierarchical logical reasoning have long been, and continue to be, an important puzzle for cognitive science. Prior approaches to hierarchical logical reasoning have often failed to distinguish between observable hierarchical behavior and unobservable hierarchical cognitive mechanisms. Furthermore, past research has been largely methodologically restricted to passive recognition tasks as compared to active generation tasks that are stronger tests (...) of hierarchical rules. We argue that it is necessary to implement learning studies in humans, non-human species, and machines that are analyzed with formal models comparing the contribution of different cognitive mechanisms implicated in the generation of hierarchical behavior. These studies are critical to advance theories in the domains of recursion, rule-learning, symbolic reasoning, and the potentially uniquely human cognitive origins of hierarchical logical reasoning. (shrink)

Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows (...) for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way. (shrink)

this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recursive Bayesian Net can be used to model mechanisms (...) in cancer science. The highest level of the proposed model will contain variables at the clinical level, while a middle level will map the structure of the DNA damage response mechanism and the lowest level will contain information about gene expression. (shrink)

Does perceptual consciousness require cognitive access? Ned Block argues that it does not. Central to his case are visual memory experiments that employ post-stimulus cueing—in particular, Sperling's classic partial report studies, change-detection work by Lamme and colleagues, and a recent paper by Bronfman and colleagues that exploits our perception of ‘gist’ properties. We argue contra Block that these experiments do not support his claim. Our reinterpretations differ from previous critics' in challenging as well a longstanding and common view of visual (...) memory as involving declining capacity across a series of stores. We conclude by discussing the relation of probabilistic perceptual representations and phenomenal consciousness. (shrink)

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely (...) observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution model can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory model, which extends the Quantum Episodic Memory model developed by Brainerd, Wang, and Reyna. We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory. (shrink)

Many clinical and psychological constructs are conceptualized to have multivariate higher-order constructs that give rise to multidimensional lower-order traits. Although recent measurement models and computing algorithms can accommodate item response data with a higher-order structure, there are few measurement models and computing techniques that can be employed in the context of complex research synthesis, such as meta-analysis of individual participant data or integrative data analysis. The current study was aimed at modeling complex item responses that can arise when (...) underlying domain-specific, lower-order traits are hierarchically related to multiple higher-order traits for individual participant data from multiple studies. We formulated a multi-group, multivariate higher-order item response theory (HO-IRT) model from a Bayesian perspective and developed a new Markov chain Monte Carlo (MCMC) algorithm to simultaneously estimate the (a) structural parameters of the first- and second-order latent traits across multiple groups and (b) item parameters of the model. Results from a simulation study support the feasibility of the MCMC algorithm. From the analysis of real data, we found that a bivariate HO-IRT model with different correlation/covariance structures for different studies fit the data best, compared to a univariate HO-IRT model or other alternate models with unreasonable assumptions (i.e., the same means and covariances across studies). Although more work is needed to further develop the method and to disseminate it, the multi-group multivariate HO-IRT model holds promise to derive a common metric for individual participant data from multiple studies in research synthesis studies for robust inference and for new discoveries. (shrink)

Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter. Previous work has used Gaussian processes—a statistical framework that extends Bayesian nonparametric approaches to regression—to model human function learning. We build on this work, modeling the process of (...) learning to learn functions as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters. (shrink)

Mechanisms are usually viewed as inherently hierarchical, with lower levels of a mechanism influencing, and decomposing, its higher-level behaviour. In order to adequately draw quantitative predictions from a model of a mechanism, the model needs to capture this hierarchical aspect. The recursive Bayesian network formalism was put forward as a means to model mechanistic hierarchies by decomposing variables. The proposal was recently criticized by Gebharter and Gebharter and Kaiser, who instead propose to decompose arrows. In this paper, (...) I defend the RBN account from the criticism and argue that it offers a better representation of mechanistic hierarchies than the rival account. (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)

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)

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)

Hierarchical Bayesian models provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly (...) the idea that higher-level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. (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)

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)

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 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)

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)