Approximate Bayesian inference in and for computational models of cognition: a simulation-based perspective

Abstract

Bayesian inference provides a normative framework for reasoning under uncertainty, combining prior beliefs with observed evidence into posterior beliefs. Despite its theoretical elegance, Bayesian inference can be intractable, which presents problems both for Bayesian data analysis and Bayesian accounts of human inference under uncertainty.

This work explores two complementary themes: First, how approximate Bayesian inference can answer challenges to traditional Bayesian models of cognition; Second, how we can perform Bayesian analyses of expressive models of human cognition.

Both themes are examined through the lens of simulation-based inference, which can benefit computational models of cognition.

The first theme addresses a fundamental paradox in human cognition: How do people routinely solve seemingly intractable inference problems in everyday life?

We begin by examining human causal structure learning from events and their timings, accounting for potential hidden causes and cyclic causal structures.

Next, we study human causal learning from event sequences, comparing traditional associative models to resource-rational models adopting an inference-by-sampling perspective. Finally, we investigate the apparent dichotomy between heuristics and Bayesian models, proposing to resolve this tension by viewing heuristics through the lens of likelihood-free inference and summary statistics.

The second theme focuses on developing methodological tools to support richer, simulation-based theories of cognition. As models grow in complexity, intuiting and designing informative experiments becomes increasingly challenging.

We present a methodology for Bayesian optimal experimental design (BOED) to address these issues, providing researchers with robust tools for developing and testing sophisticated cognitive models. Through a case study on models of human behavior in multi-armed bandit tasks, we demonstrate the approach’s usefulness and provide guidance for its practical adoption.

The themes explored in this thesis – approximate Bayesian inference in and for computational models of cognition – are inherently complementary. As theories become more expressive, they necessitate more sophisticated tools, while advances in methodology may inspire novel theories about how people tackle challenging inference problems.