Likelihood-Free Methods for Cognitive Science

Abstract

Computational Approaches to Cognition and Perception is a series that aims to publish books that represent comprehensive, up-to-date overviews of specific research and developments as it applies to cognitive and theoretical psychology. The series as a whole provides a rich foundation, with an emphasis on computational methods and their application to various fields of psychology. Works exploring decision-making, problem solving, learning, memory, and language are of particular interest. Submitted works will be considered as well as solicited manuscripts, with all be subject to external peer review.Books in this series serve as must-have resources for Upper-level undergraduate and graduate students of cognitive psychology, theoretical psychology, and mathematical psychology. Books in this series will also be useful supplementary material for doctoral students and post-docs, and researchers in academic settings. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paperThis Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland ForewordThis book provides a concise overview of recent developments in likelihoodfree inference, thereby opening a new chapter in the field of cognitive modeling. With the easy availability of computers, researchers in the field introduced a glut of mechanistic models of cognition that have no closed-form expression of the likelihood function, placing them outside of the standard statistical realm. As such, it is not generally possible to fit a mechanistic model to observed data by maximum likelihood estimation or Markov chain Monte Carlo based Bayesian methods.Instead, as a provisional step, the best-fitting parameter values of the model of interest were estimated in the frequentist fra...

Computational Models of Retrieval Processes in Sentence Processing

“…The participant-level estimates of the interference effect were computed from a hierarchical Bayesian model [86]. The average facilitatory interference effect is shown as a 95% credible interval (labeled Observed effect), and the range of predicted values from the activation model are also shown as a 95% credible interval (labeled Model prediction); the model predictions are computed using Approximate Bayesian Computation [85,87,88]. We see the predicted facilitatory interference effect even at the individual participant level, but different participants show varying magnitudes.…”

Parallel probability density approximation

“…Most (though not all) past methods of achieving this have typically been limited to relatively simple models which have tractable likelihood functions. More recently however, new simulation based methods have been developed (Palestro, Sederberg, Osth, van Zandt, & Turner, 2018) that utilize modern computational power to significantly expand the scope of models that quantitative fitting can be applied to. Here, we describe a highly efficient, GPU enabled parallel implementation of canonical Bayesian Markov chain Monte Carlo (MCMC) methods utilizing the Probability Density Approximation (PDA) (Holmes, 2015;Turner & Sederberg, 2014).…”

Reconciling similarity across models of continuous selections

“…Instead, we use an approach for model fitting based on kernel density estimation to turn the simulated data into a truly continuous, 2-dimensional distribution of responses and response times. This method has been effectively used to approximate the likelihoods of several types of simulation-based models (Palestro et al, 2018;Turner & Van Zandt, 2012;Turner & Sederberg, 2014), is reasonably efficient especially with the addition of signal processing methods (Holmes, 2015;Lin et al, 2019), and can be easily adapted to a two-dimensional joint distribution like the one produced by the SCDM and GDM. For these models, we can simulate a large number of trials from the model, use the kernel density method to generate an approximate likelihood, and then impute the likelihood of each combination of response and response time in the observed data set.…”