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)

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)

Thats logic. LEWIS CARROLL, Through the Looking Glass 1-1. The fundamental problem of this work is the question of the nature of scientific inference.

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute a posterior distribution over languages by combining a prior (representing their inductive biases) with the evidence provided by linguistic data. We show that when learners sample languages from this posterior (...) distribution, iterated learning converges to a distribution over languages that is determined entirely by the prior. Under these conditions, iterated learning is a form of Gibbs sampling, a widely-used Markov chain Monte Carlo algorithm. The consequences of iterated learning are more complicated when learners choose the language with maximum posterior probability, being affected by both the prior of the learners and the amount of information transmitted between generations. We show that in this case, iterated learning corresponds to another statistical inference algorithm, a variant of the expectation-maximization (EM) algorithm. These results clarify the role of iterated learning in explanations of linguistic universals and provide a formal connection between constraints on language acquisition and the languages that come to be spoken, suggesting that information transmitted via iterated learning will ultimately come to mirror the minds of the learners. (shrink)

Introduction: Something on the State of the Art 1 I. Functionalism and Realism 1. Operationalism and Ordinary Language 35 2. The Appeal to Tacit Knowledge in Psychological Explanations 63 3. What Psychological States are Not 79 4. Three Cheers for Propositional Attitudes 100 II. Reduction and Unity of Science 5. Special Sciences 127 6. Computation and Reduction 146 III. Intensionality and Mental Representation 7. Propositional Attitudes 177 8. Tom Swift and His Procedural Grandmother 204 9. Methodological Solipsism Considered as a (...) Research Strategy in Cognitive Psychology 225 IV. Nativism 10. The Present Status of the Innateness Controversy 257 Notes 317. (shrink)

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

Probability, Frequency and Reasonable Expectation.