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.

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.

I extend Jones & Love's (J&L's) critique of Bayesian models and evaluate the conceptual foundations on which they are built. I argue that: (1) the “Bayesian” part of Bayesian models is scientifically trivial; (2) “computational level” theory is a fiction that arises from an inappropriate programming metaphor; and (3) the real scientific problems lie outside Bayesian theorizing.

We agree with Jones & Love (J&L) that much of Bayesian modeling has taken a fundamentalist approach to cognition; but we do not believe in the potential of Bayesianism to provide insights into psychological processes. We discuss the advantages of associative explanations over Bayesian approaches to causal induction, and argue that Bayesian models have added little to our understanding of human causal reasoning.

Grounded cognition offers a natural approach for integrating Bayesian accounts of optimality with mechanistic accounts of cognition, the brain, the body, the physical environment, and the social environment. The constructs of simulator and situated conceptualization illustrate how Bayesian priors and likelihoods arise naturally in grounded mechanisms to predict and control situated action.

Jones & Love (J&L) suggest that Bayesian approaches to the explanation of human behavior should be constrained by mechanistic theories. We argue that their proposal misconstrues the relation between process models, such as the Bayesian model, and mechanisms. While mechanistic theories can answer specific issues that arise from the study of processes, one cannot expect them to provide constraints in general.

We argue that Bayesian models are best categorized as methodological or theoretical. That is, models are used as tools to constrain theories, with no commitment to the processes that mediate cognition, or models are intended to approximate the underlying algorithmic solutions. We argue that both approaches are flawed, and that the Enlightened Bayesian approach is unlikely to help.

If Bayesian Fundamentalism existed, Jones & Love's (J&L's) arguments would provide a necessary corrective. But it does not. Bayesian cognitive science is deeply concerned with characterizing algorithms and representations, and, ultimately, implementations in neural circuits; it pays close attention to environmental structure and the constraints of behavioral data, when available; and it rigorously compares multiple models, both within and across papers. J&L's recommendation of Bayesian Enlightenment corresponds to past, present, and, we hope, future practice in Bayesian cognitive science.

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.

The only viable formulation of perception, thinking, and action under uncertainty is statistical inference, and the normative way of statistical inference is Bayesian. No wonder, then, that even seemingly non-Bayesian computational frameworks in cognitive science ultimately draw their justification from Bayesian considerations, as enlightened theorists know fully well.

We highlight one way in which Jones & Love (J&L) misconstrue the Bayesian program: Bayesian models do not represent a rejection of mechanism. This mischaracterization obscures the valid criticisms in their article. We conclude that computational-level Bayesian modeling should not be rejected or discouraged a priori, but should be held to the same empirical standards as other models.

Bayesian psychology follows an old instrumentalist tradition most infamously illustrated by Osiander's preface to Copernicus's masterpiece. Jones & Love's (J&L's) criticisms are, if anything, understated, and their proposals overoptimistic.

My research program proposes that children have representations and learning mechanisms that can be characterized as causal models of the world – coherent, structured hypotheses with consistent relationships to probabilistic patterns of evidence. We also propose that Bayesian inference is one mechanism by which children learn these models from data. These proposals are straightforward psychological hypotheses and far from “Bayesian Fundamentalism.”

Bayesian accounts are currently popular in the field of inductive reasoning. This commentary briefly reviews the limitations of one such account, the Rational Model (Anderson 1991b), in explaining how inferences are made about objects whose category membership is uncertain. These shortcomings are symptomatic of what Jones & Love (J&L) refer to as “fundamentalist” Bayesian approaches.

It is timely to assess Bayesian models, but Bayesianism is not a religion. Bayesian modeling is typically used as a tool to explain human data. Bayesian models are sometimes equivalent to other models, but have the advantage of explicitly integrating prior hypotheses with new observations. Any lack of representational or neural assumptions may be an advantage rather than a disadvantage.

We support Enlightenment Bayesianism's commitment to grounding Bayesian analysis in empirical details of psychological and neural mechanisms. Recent philosophical accounts of mechanistic science illuminate some of the challenges this approach faces. In particular, mechanistic decomposition of mechanisms into their component parts and operations gives rise to a notion of levels distinct from and more challenging to accommodate than Marr's.

The field of causal learning and reasoning (largely overlooked in the target article) provides an illuminating case study of how the modern Bayesian framework has deepened theoretical understanding, resolved long-standing controversies, and guided development of new and more principled algorithmic models. This progress was guided in large part by the systematic formulation and empirical comparison of multiple alternative Bayesian models.

According to Jones & Love (J&L), Bayesian theories are too often isolated from other theories and behavioral processes. Here, we highlight examples of two types of isolation from the field of word learning. Specifically, Bayesian theories ignore emergence, critical to development theory, and have not probed the behavioral details of several key phenomena, such as the “suspicious coincidence” effect.

Jones & Love (J&L) should have given more attention to Agnostic uses of Bayesian methods for the statistical analysis of models and data. Reliance on the frequentist analysis of Bayesian models has retarded their development and prevented their full evaluation. The Ecumenical integration of Bayesian statistics to analyze Bayesian models offers a better way to test their inferential and predictive capabilities.

Cognitive models focus on information and the computational manipulation of information. Rational models optimize the function that relates the input of a process to the output. In contrast, efficient algorithms minimize the computational cost of processing in terms of time. Minimizing time is a better criterion for normative models, because it reflects the energy costs of a physical system.