OXFORD LIBRARY OF PSYCHOLOGY EDITED BY JEROME R BUSEMEYER ZHENG WANG JAMES T TOWNSEND & AMI EIDELS The Oxford Handbook of COMPUTATIONAL and MATHEMATICAL PSYCHOLOGY The Oxford Handbook of Computational and Mathematical Psychology OX F O R D L I B R A RY O F P S Y C H O L O G Y E D I T O R-I N-C H I E F Peter E Nathan AREA EDITORS Clinical Psychology David H Barlow Cognitive Neuroscience Kevin N Ochsner and Stephen M Kosslyn Cognitive Psychology Daniel Reisberg Counseling Psychology Elizabeth M Altmaier and Jo-Ida C Hansen Developmental Psychology Philip David Zelazo Health Psychology Howard S Friedman History of Psychology David B Baker Methods and Measurement Todd D Little Neuropsychology Kenneth M Adams Organizational Psychology Steve W J Kozlowski Personality and Social Psychology Kay Deaux and Mark Snyder OXFORD LIBRARY OF PSYCHOLOGY Editor-in-Chief peter e nathan The Oxford Handbook of Computational and Mathematical Psychology Edited by Jerome R Busemeyer Zheng Wang James T Townsend Ami Eidels Oxford University Press is a department of the University of Oxford It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trademark of Oxford University Press in the UK and certain other countries Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016 c Oxford University Press 2015 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Library of Congress Cataloging-in-Publication Data Oxford handbook of computational and mathematical psychology / edited by Jerome R Busemeyer, Zheng Wang, James T Townsend, and Ami Eidels pages cm – (Oxford library of psychology) Includes bibliographical references and index ISBN 978-0-19-995799-6 Cognition Cognitive science Psychology–Mathematical models Psychometrics I Busemeyer, Jerome R BF311.O945 2015 150.1 51–dc23 2015002254 Printed in the United States of America on acid-free paper Dedicated to the memory of Dr William K Estes (1919–2011) and Dr R Duncan Luce (1925–2012) Two of the founders of modern mathematical psychology v SHORT CONTENTS Oxford Library of Psychology ix About the Editors xi Contributors xiii Table of Contents Chapters Index xvii 1–390 391 vii OX F O R D L I B R A R Y O F P SYC H O LO GY The Oxford Library of Psychology, a landmark series of handbooks, is published by Oxford University Press, one of the world’s oldest and most highly respected publishers, with a tradition of publishing significant books in psychology The ambitious goal of the Oxford Library of Psychology is nothing less than to span a vibrant, wide-ranging field and, in so doing, to fill a clear market need Encompassing a comprehensive set of handbooks, organized hierarchically, the Library incorporates volumes at different levels, each designed to meet a distinct need At one level are a set of handbooks designed broadly to survey the major subfields of psychology; at another are numerous handbooks that cover important current focal research and scholarly areas of psychology in depth and detail Planned as a reflection of the dynamism of psychology, the Library will grow and expand as psychology itself develops, thereby highlighting significant new research that will impact on the field Adding to its accessibility and ease of use, the Library will be published in print and, later on, electronically The Library surveys psychology’s principal subfields with a set of handbooks that capture the current status and future prospects of those major subdisciplines The initial set includes handbooks of social and personality psychology, clinical psychology, counseling psychology, school psychology, educational psychology, industrial and organizational psychology, cognitive psychology, cognitive neuroscience, methods and measurements, history, neuropsychology, personality assessment, developmental psychology, and more Each handbook undertakes to review one of psychology’s major subdisciplines with breadth, comprehensiveness, and exemplary scholarship In addition to these broadlyconceived volumes, the Library also includes a large number of handbooks designed to explore in depth more specialized areas of scholarship and research, such as stress, health and coping, anxiety and related disorders, cognitive development, or child and adolescent assessment In contrast to the broad coverage of the subfield handbooks, each of these latter volumes focuses on an especially productive, more highly focused line of scholarship and research Whether at the broadest or most specific level, however, all of the Library handbooks offer synthetic coverage that reviews and evaluates the relevant past and present research and anticipates research in the future Each handbook in the Library includes introductory and concluding chapters written by its editor to provide a roadmap to the handbook’s table of contents and to offer informed anticipations of significant future developments in that field ix INDEX Abductive reasoning in clinical cognitive science, 343–344 Absolute identification absolute and relative judgment, 129–130 intertrial interval and sequential effects, 136–138 learning, 130–133 perfect pitch versus, 133–135 response times, 135 theories of, 124–129 Absorbing barriers, 30 Accumulator models, 321–322, 327–328 Across-trial variability, 37–38, 46, 56–57 Actions, in Markov decision process (MDP), 102–103 ACT-R architectures, 126, 219, 301 Additive factors method, 69–70, 89 ADHD, 49–50 Affine transformation, 28 Aging studies, diffusion models in, 48 Akaike information criterion (AIC), 306–308 Alcohol consumption, 50 Aleatory uncertainty, 210 Algom, D., 63 Allais paradox, 219 ANCHOR-based exemplar model of absolute identification, 126 Anderson’s ACT-R model, 126, 219, 301 Anxiety, diffusion models of, 49 Anxiety-prone individuals, threat sensitivity modeling in, 352–354 Aphasia, 49–50 Ashby, F G., 13 Assimilation and contrast, in absolute identification, 123–124, 128 Associative learning, 194–196 Associative recognition, 47 Attention allocation differences data, 291–292 descriptive model and parameters, 292–293 overview, 290–291 posterior distribution interpretation, 293–295 Attention-weight parameters, 144 Attraction, as context effect in DFT, 225–226 Austerweil, J L., 187 Autism spectrum disorders, 354–356 Automaticity, 143, 148–150, 325 Autonomous search models, 178–179 Bandit tasks, 111 Basa ganglia model, 51 Baseball batting example, 282–290 data, 283 descriptive model and parameters, 283–285 overview, 282–283 posterior distribution interpretation, 285–290 shrinkage and multiple comparisons, 290 Basis functions, 201 Bayesian information criterion (BIC), 9, 21, 306–308 Bayesian models See also Hierarchical models, Bayesian estimation in of cognition, 187–208 clustering observations, 192–196 conclusions, 203–204 continuous quantities, 200–203 features as perceptual units, 196–200 future directions, 204 mathematical background, 188–192 overview, 187–188 overview, 40, 169 parsimony principle in, 309–314 of shape perception, 258–260 Bayesian parameter estimation, 348–349 Bayes’ rule, 6, 281–282 BEAGLE (Bound Encoding of the Aggregate Language Environment) model, 243–244, 248 Bellman equation, 103 Benchmark model, 74–75 Benchmark phenomena, in perceptual judgment, 122–124 Berlin Institute of Physiology, 64 Bernoulli, Daniel, 210–211 Bessel, F W., 65 Bias-variance trade-off, 190–191 BIC (Bayesian information criterion), 9, 21, 306–308 Blood sugar reduction, 50 Bootstrapping, 105 Boundary setting across tasks, 48 Bound Encoding of the Aggregate Language Environment (BEAGLE) model, 243–244, 248 Bow effects, in absolute identification, 123, 128 Brown, S D., 121 Brown and Heathcote’s linear ballistic accumulator model, 301 BUGS modeling specification language, 282 Busemeyer, J R., 1, 369 Calculus, 3–5 Candidate decision processes, 14 Capacity coefficient, 72–74 Capacity limitations, in absolute identification, 122–123 Capacity reallocation model, 69 Capacity theory, 90–91 Catastrophe theory, 346 Categorization, 29, 325 See also Bayesian models; Exemplar-based random walk (EBRW) model Category learning, 30–31, 189 Cattell, James McKeen, 66 Chaos-theoretic modeling, 345–346 391 Child development, diffusion models in, 48–49 Chinese restaurant process (CRP) metaphor, 193–195 Choice axiom testing, 211–214 Choice behavior, 199–200 Cholesky transformation, 20 “Chunking,” 66 Clinical psychology, mathematical and computational modeling in, 341–368 contributions of, 349–359 cognition in autism spectrum disorders, 354–356 cognitive modeling of routinely used measures, 356–357 multinomial processing tree modeling of memory, 350–352 in pathocognition and functional neuroimaging, 357–359 threat sensitivity modeling of anxiety-prone individuals, 352–354 distinctions in, 343–346 overview, 341–343 parameter estimation in, 346–349 special considerations, 359–361 Clustering observations, 192–196 Coactivation, 73 COALS (Correlated Occurrence Analogue to Lexical Semantics) model, 241, 248 Coexistence model (CXM), 303–304, 306, 308–309, 313 Cognition See Bayesian models; Quantum models of cognition and decision Cognitive control of perceptual decisions, 330, 334 Cognitive modeling, 219–226 of clinical science measures, 356–357 context effects example, 225–226 decision field theory for multialternative choice problems, 222–225 multi-attribute, 221–222 overview, 220–221 “horse race,” 356 392 index Cognitive-psychological complementarity, 87–90 Cognitive psychometrics, 290 Cohen’s PDP model, 301 Cold cognition, 361 Commutativity, 375 Competing accumulator models, 322 Complication experiment, 66–68 Component power laws model, 301 Compositional semantics, 249 Compromise, as context effect in DFT, 225–226 Computational reinforcement learning (CRL), 99–117 decision environment, 102 exploration and exploitation balance, 106 goal of, 101 good decision making, 103–104 historical perspective, 100–101 neural correlates of, 106–108 Q-learning, 105–106 research issues, 108–114 human exploration varieties, 110–113 model-based versus model-free learning, 108–109 reward varieties, 113–114 state representation influence, 109–110 temporal difference learning, 104–105 values for states and actions, 102–103 Conditioning, 101–103, 111, 195 Confidence judgments, 52–53 Conjunction probability judgment errors, 376–379 Connectionist models decision field theory as, 223, 225 of semantic memory, 234–239 Constancy, in shape perception, 256–257 Constructed semantics model (CSM), 247 Context, 175–178 Context-noise models, 172 Contingency table, 6f Continuous quantities, relationships of, 200–203 Contrast and assimilation, in absolute identification, 123–124, 128 Correlated Occurrence Analogue to Lexical Semantics (COALS) model, 241, 248 COVIS theory of category learning, 30–31 Credit assignment problem, in reinforcement learning, 100–101, 103 Criss, A H., 165 CRL (Computational reinforcement learning) See Computational reinforcement learning (CRL) CrossCat model, 195 CRP (Chinese restaurant process) metaphor, 193–195 Crude two-part code, in MDL, 307–308 CSM (constructed semantics model), 247 Cued recall models of episodic memory, 173–174 Cumulative prospect theory, 217–219 CXM (coexistence model), 303–304, 306, 308–309, 313 Deadline tasks, 41–42 Decisional separability, 15–16, 22f, 23 Decision-boundary models, 30, 142 Decision field theory (DFT), 220–225 Decision-making models, 209–231 See also Computational reinforcement learning; Perceptual decision making, neurocognitive modeling of; Quantum models of cognition and decision choice axiom testing, 211–214 cognitive models context effects example, 225–226 decision field theory, 220–221 decision field theory for multialternative choice problems, 222–225 multi-attribute decision field theory, 221–222 overview, 219–220 historical development of, 210–211 overview, 209–210 rational choice models, 214–219 Decision rules for Bayesian posterior distribution, 287 Dennis, S., 232 Density estimation, in Bayesian models, 188–190 Depression, diffusion models of, 49 Derivatives and integrals, 3–5 Destructive updating model (DUM), 303–304, 306, 308–309, 313 Deterministic processes, 72 Diederich, A., 1, 209 Differential-deficit, psychometric-artifact problem, 360 Differential equations, 4–5 Diffusion models, 35–62 in aging studies, 48 in child development, 48–49 in clinical applications, 49–50, 352 competing two-choice models, 51–56 failure of, 50–51 in homeostatic state manipulations, 49–50 in individual differences studies, 48 in lexical decision, 46–47 optimality, 44–45 in perceptual tasks, 45–46 for practice effects, 301 for rapid decisions, 35–44 accuracy and RT distribution expressions, 38–41 drift rate, 36–38 overview, 35–36 standard two-choice task, 41–44 in recognition memory, 46 in semantic and recognition priming effects, 47 in value-based judgments, 47–48 Diffusion process, 30 Díríchlet-process mixture model, 192–194, 244 Disjunction probability judgment errors, 376–379 Dissociations, in categorization and recognition, 158–159 Distributional models of semantic memory, 239–247 latent semantic analysis, 239–240 moving window models, 240–241 probabilistic topic models, 243–246 random vector models, 241–243 retrieval-based semantics, 246–247 Domain of the function, Donders, Franciscus, 65–66 Donkin, C., 121 Double factorial paradigm, 83 Drift rates accumulator model assumptions about, 321–322 across-trial variability in, 56–57 in perceptual decision making, 36–38, 45, 325–327 Dual process models of recognition, 166 DUM (destructive updating model), 303–304, 306, 308–309, 313 Dynamic attractor networks, 237–239 Dynamic decision models, 219–220 See also Decision-making models Dynamic programming, 104 Dyslexia, 50 Effective sample size (ESS) statistic, 282 EGCM (extended generalized context model) of absolute identification, 126, 143 Eidels, A., 1, 63 Emotional bias, 49 Episodic memory, 165–183 cued recall models of, 173–174 free recall models of, 174–179 future directions, 179 overview, 165–166 recognition memory models, 166–172 context-noise models, 172 global matching models, 167–168 retrieving effectively from memory (REM) model, 168–171 updating consequences, 171–172 Epistemic uncertainty, 210 Error signal, 4–5 ESS (effective sample size) statistic, 282 EUT (expected utility theory), 209, 211 EVL (Expectancy Valence Learning Model), 356–357 Exemplar-based random walk (EBRW) model of absolute identification, 125–126 of categorization and recognition, 142–164 automaticity and perceptual expertise, 148–150 old-new recognition RTs predicted by, 152–157 overview, 142–144 probabilistic feedback to contrast predictions, 150–152 research goals, 157–159 in response times, 144–146 similarity and practice effects, 146–148 in perceptual decision making, 325 Exemplar models of absolute identification, 125–126, 129 Exhaustive processing, 71–72 Expectancy Valence Learning Model (EVL), 356–357 Expectations, 7–8 Expected utility theory (EUT), 209, 211 Experience-based decision making, 215–216 Experimental Psychology (Woodworth), 83 Exploration/exploitation balance experiments in, 100 human varieties of, 110–113 in reinforcement learning, 106 Exponential functions, Extended generalized context model (EGCM) of absolute identification, 126, 143 Eye movements, saccadic, 323–325 False alarm rates, 23 Feature inference, 196–199 Feature integration theory, 87 Feature-list models, 233–234 Fechnerian paradigm, 257–258 Fechner’s law of psychophysics, 307 Feed-forward networks, 235 FEF (frontal eye field), 321, 323 Fermat, Pierre de, 210 Flexibility-to-fit data, of models, 93 fMRI category-relevant dimensions shown by, 158 in clinical psychology, 357–359 context word approach and, 241 diffusion models and, 57 model-based analysis of, 107–108 Free recall models of episodic memory, 174–179 Frequentist methods, 281 Frontal eye field (FEF), 321, 323 Functions, mathematical, 1–3 index 393 Gabor patch orientation discrimination, 50 Galen, 64 Gate accumulator model, 327 Gaussian distribution, 189, 192 Generalizability, measures of, 303 Generalized context model (GCM), 126, 143, 152, 325 General recognition theory (GRT) application of, 14 applied to data, 17–21 empirical example, 24–28 multivariate normal distributions assumed by, 16 neural implementations of, 30–31 overview, 15–16 response accuracy and response time accounted for, 28–30 summary statistics approach, 22–24 GenSim software for semantic memory modeling, 246 Gershman, S J., 187 Global matching models, 167–168 Go/No-Go Discrimination Task, 44, 349, 356 Goodness of fit evaluation, 20–21, 302 Grice inequality, 74–75, 92 Griffiths, T L., 187 Grouping, power of, 66 GRT (general recognition theory) See General recognition theory (GRT) Guided search, 89 Gureckis, T M., 99 HA-LA (higher anxiety-prone-lower anxiety-prone) group differences, 352–353 HAL (Hyperspace Analogue to Language) model, 240–241, 245, 248 Hamilton, Sir William, 66 Hawkins, R X D., 63 HDI (highest density interval), 285 Heathcote, A., 121 Hebbian learning, 235 HiDEx software for semantic memory modeling, 246 Hierarchical models, Bayesian estimation in, 279–299 attention allocation differences example, 290–295 data, 291–292 394 index descriptive model and parameters, 292–293 overview, 290–291 posterior distribution interpretation, 293–295 baseball batting example, 282–290 data, 283 descriptive model and parameters, 283–285 overview, 282–283 posterior distribution interpretation, 285–290 shrinkage and multiple comparisons, 290 comparison of, 295–297 ideas in, 279–282 Higher anxiety-prone-lower anxiety-prone (HA-LA) group differences, 352–353 Highest density interval (HDI), 285 Hilbert space, in quantum theory, 371–372, 374–375 Histograms, Homeostatic state manipulations, 49–50 “Horse race” model of cognitive processes, 356 Hot cognition, 361 Howard, M W., 165 Human function learning, 202–203 Human information processing, 63–70 Donder’s complication experiment, 66–68 Sternberg’s work in, 68–70 von Helmholtz’s measurement of nerve impulse speed, 64–65 Wundt’s reaction time studies, 65–66 Human neuroscience, diffusion models for, 56–58 Hyperspace Analogue to Language (HAL) model, 240–241, 245, 248 IBP (Indian buffet process) metaphor, 194–195, 197–200, 203 Identification data, fitting GRT to, 18–21 Identification hit rate, 23 Importance sampling for Bayes factor, 312–313 Independence, axioms of, 211–212 Independent parallel, limited-capacity (IPLC) processing system, 353 Independent race model, 74–75 Indian buffet process (IBD) metaphor, 194–195, 197–200, 203 Individual differences studies, diffusion models in, 48 Infinite Relational Model (IRM), 195 Information criteria, in model comparison, 306–307 Instance theory, 301, 325 Institute for Collaborative Biotechnologies, 31 Instrumental conditioning, 101, 111 Integrals and derivatives, 3–5 Integrate-and-fire neurons, 39 Intercompletion time equivalence, 77–78 Intertrial interval, sequential effects and, 136–138 Inverse problem, shape perception as, 256–263 Iowa Gambling Task, 349, 356 IPLC (independent parallel, limited-capacity) processing system, 353 IRM (Infinite Relational Model), 195 James, William, 64 Jefferson, B., 63 Jeffreys weights, 313 Jones, M N., 232 Kinnebrook, David, 65 Kolmogorov axioms, 307, 370, 373–374 Kruschke, J K., 279 Kullback-Leibler divergence, 306 Languages, tonal, 134 Latent Díríchlet Allocation algorithms, 244 Latent semantic analysis (LSA), 239–240, 245, 248–249 Law of total probability, 376 LBA (Linear Ballistic Accumulator) model, 52, 301 Leaky competing accumulator (LCA) model, 36, 51–52, 128, 223–225, 327 Learning See also Computational reinforcement learning absolute identification in, 130–133 associative, 194–196 Hebbian, 235 modeling human function, 202–203 procedural, 30–31 relationships in continuous quantities, 200–203 Lexical decisions, diffusion models in, 46–47 Lexicographic semi-order (LS) choice rule, 213 Li, Y., 255 Likelihood function, 18–19, 280, 296 Likelihood ratio test, 28 Limited capacity, 70, 73 Linear Ballistic Accumulator (LBA) model, 52, 301 Linear functions, 1–2 Linear regression, 8, 200–202 Logan, G D., 320 Love, B C., 99 LSA (latent semantic analysis), 239–240, 245, 248–249 LS (lexicographic semi-order) choice rule, 213 Lüder’s rule, 374 “Magical number seven,” 66 Mapping, functions for, Marginal discriminabilities, 23 Marginal response invariance, 22 Markov Chain Monte Carlo (MCMC) algorithms, 244, 281–282, 293 Markov decision process (MDP), 102–104 Markov dynamic model for two-stage gambles, 382–383, 385–387 Maskelyn, Nevil, 65 Matched filter model, 167, 173 Mathematical concepts, review of, 1–10 derivatives and integrals, 3–5 expectations, 7–8 mathematical functions, 1–3 maximum likelihood estimation, 8–9 probability theory, 5–7 Matrix reasoning, 48 Matzke, D., 300 Maximum likelihood estimation (MLE), 8–9, 281, 347 MCMC (Markov Chain Monte Carlo) algorithms, 244, 281–282, 293 MDL (minimum description length), in model comparison, 307–309 MDP (Markov decision process), 102–104 MDS (multidimensional scaling), 143 Mean interaction contrast, 83–84 Measures of generalizability, 303 Memory, 350–352 See also Episodic memory; Semantic memory Memory interference models example, 303–306 Méré, Chevalier de, 210 Meyer, Irwin, Osman, and Kounios partial information paradigm, 42–44 Miller, George, 66 Minimum description length (MDL), in model comparison, 307–309 Minimum-time stopping rule, exhaustive processing versus, 71–72 Minkowski power model, 144 MLE (maximum likelihood estimation), 8–9, 281, 347 Model-based versus model-free learning, 108–109 Modeling See Parsimony principle in model comparison; specifically named models Model mimicking degenerative, 80 ignoring parallel-serial, 87–90 prediction overlaps from, 75–78 in psychological science, 91–93 Moderate stochastic transitivity (MST), 212–213 Moment matching, in parameter estimation, 347–348 Monte-Carlo methods, 104, 311–313 Movement-related neurons, in FEF, 321, 323, 325–326, 328 Moving window models, 240–241 MPM (multiplicative prototype model), 290, 292 MPTs (multinomial processing tree models) See Multinomial processing tree models (MPTs) MST (moderate stochastic transitivity), 212–213 Müller, Johannes, 64 Multialternative choice problems, decision field theory for, 222–225 Multi-armed bandit tasks, 111 Multi-attribute decision field theory, 221–222 Multichoice-decision-making, 52–53 Multidimensional scaling (MDS), 143, 273 Multidimensional signal detection theory, 13–34 general recognition theory applied to data, 17–21 empirical example, 24–28 neural implementations of, 30–31 overview, 15–16 response accuracy and response time accounted for, 28–30 summary statistics approach, 22–24 multivariate normal model, 16–17 overview, 13–15 Multinomial processing tree models (MPTs), 301, 304–305, 307–311, 350–352 Multiple comparisons, shrinkage and, 290 Multiple linear regression, Multiplicative prototype model (MPM), 290, 292 Multivariate normal model, 16–17 Myopic behavior, of agents, 103 National Institute of Neurological Disorders and Stroke, 31 Natural log functions, NCM (no-conflict model), 303, 305–306, 308–309, 313 Nested models, comparing, 313–314 Neufeld, R W J., 341 Neural evidence of computational reinforcement learning, 106–108 of exemplar-based random walk, 158 of GRT, 30–31 in perceptual decision making, 325–330 Neurocognitive modeling of perceptual decision making See Perceptual decision making, neurocognitive modeling of Neuro-connectionist modeling, 345 Neuroeconomics, 48 Neuroscience, decision making understanding from, 53–58 Newton-Raphson method, 19 Nietzsche, Friedrich, 64 No-conflict model (NCM), 303, 305–306, 308–309, 313 Noise, in perceptual systems, 15, 36 index 395 Nondecision time, 48–50, 57 Nonlinear dynamical system modeling, 345–346 Nonparametric models, 189–192, 194–195 Normal distribution, Nosofsky, R M., 142 Null list strength effects in (REM) model, 170–171 Numerosity discrimination task, 50 Observations, clustering, 192–196 Occam’s razor, 301–302 One-choice decisions, 53 Operant conditioning, 101 Optimality, 44–45 Optimal planning, 113 Ornstein-Uhlenbeck (OU) diffusion process, 50, 55 Overfitting, 190–191 Palmeri, T J., 142, 320 Parallelism, 68 Parallel processing in benchmark model, 74–75 mathematics supported by, 77 parallel-serial mimicry ignored, 87–90 partial processing as basis of, 80–81 serial processing versus, 71 Parallel-Serial Tester (PST) paradigm, 82 Parametric models, 189–190 Parsimony principle in model comparison, 300–319 Bayes factors, 309–314 comparison of model comparisons, 314–315 information criteria, 306–307 memory interference models example, 303–306 minimum description length, 307–309 overview, 300–303 Partial information paradigm, 42–44 Pascal, Blaise, 210 Pathocognition, 357–359 Pavlovian conditioning, 195 PBRW (prototype-based random walk) model, 151–152 Perceptual decision making, neurocognitive modeling of, 320–340 architectures for, 327–328 conclusions, 333–336 control over, 330–333 neural dynamics, predictions of, 328–330 396 index neural locus of drift rates, 325–327 overview, 320–323 saccadic eye movements and, 323–325 Perceptual expertise, automaticity and, 148–150 Perceptual independence, 15–16, 23 Perceptual judgment, 121–141 absolute identification issues, 129–139 absolute and relative judgment, 129–130 absolute identification versus perfect pitch, 133–135 intertrial interval and sequential effects, 136–138 learning, 130–133 response times, 135 absolute identification theories, 124–129 benchmark phenomena, 122–124 overview, 121–122 Perceptual separability, 15, 22f Perceptual tasks, diffusion models in, 36, 45–46 Perceptual units, features as, 196–200 Perfect pitch, absolute identification versus, 133–135 Perspective See Shape perception Pizlo, Z., 255 Pleskac, T J., 209 Poisson counter model, 36, 55 Poisson shot noise process, 55 Policies, in decision making, 103–104 Polynomial regression, 302–303 Posterior distribution in attention allocation differences, 293–295 in baseball batting example, 285–290 Monte Carlo sampling for, 311–313 in tests for model-parameter differences, 356 Pothos, E., 369 Power functions, Power law, 300 Practice effects, 146–148, 300–301 Prediction error, 105, 107–108 Principles of Psychology (James), 64 Probabilistic topic models, 243–246, 248, 250 Probability density function, 72 Probability judgment error, 377–379 Probability mass function, Probability theory, 5–7, 373–377 See also Bayesian models; Decision-making models Probability weighting function, 214–216 Problem of Points, 210 Procedural learning, 30–31 Prospect theory, 209, 214, 216–219 Prototype-based random walk (PBRW) model, 151–152 Prototype models, 142 PST (Parallel-Serial Tester) paradigm, 82 Psychology, mathematical and computational modeling in See Clinical psychology, mathematical and computational modeling in Psychomotor vigilance task (PVT), 53 Q-learning, 104–106, 109, 111 Quadratic functions, Quantile-probability plots, 40 Quantum models of cognition and decision, 369–389 classical probabilities versus, 373–377 concepts, definitions, and notation, 371–373 decision making applications, 381–387 Markov dynamic model for two-stage gambles, 382–383 model comparisons, 385–387 quantum dynamic model for two-stage gambles, 384–385 two-stage gambling paradigm, 381–382 dynamical principles, 379–381 probability judgment error applications, 377–379 reasons for, 369–371 Race model inequality, 74 Rae, B., 121 Random Permutations Model (RPM), 244 Random variables with continuous distribution, 7–8 Random vector models, 241–243 Random walk, 39 See also Exemplar-based random walk (EBRW) model Range of the function, Rank-dependent utility theory, 209 Rapid decisions See Diffusion models Ratanalysis, 188 Ratcliff, R., 35 Ratcliff ’s diffusion model, 301 Rational choice models, 47, 214–219 Reaction time distributions, 83–87 Recognition and categorization See Exemplar-based random walk (EBRW) model Recognition memory models, 46, 166–172 Region of practical equivalence (ROPE), in decision rules, 286 Regularization methods, in shape perception, 258–260 Reinforcement learning (RL) See Computational reinforcement learning Relative judgment models of absolute identification, 126–127, 129t, 136 Release-from-inhibition model, 50–51 REM (retrieving effectively from memory) model See Retrieving effectively from memory (REM) model Rescorla-Wagner model, 111, 194 Response accuracy, 28–30, 90–91 Response signal tasks, 41–42 Response times (RT) absolute identification and, 128, 135 cognitive-psychological complementarity, 87–90 in diffusion models, 38–41 example of, 78–79 exemplar-based random walk model of, 144–146, 152–157 GRT to account for, 28–30 human information processing studied by, 63–70 Donder’s complication experiment, 66–68 Sternberg’s work in, 68–70 von Helmholtz’s measurement of nerve impulse speed, 64–65 Wundt’s reaction time studies, 65–66 metatheory expansion to encompass accuracy, 90–91 model mimicking, 75–78, 91–93 quantitative expressions of, 70–75 stopping rule distinctions based on set-size functions, 82–87 theoretical distinctions, 79–82 Restricted capacity models of absolute identification, 127–128, 129t, 136 Retrieval-based semantics, 246–247 Retrieved context models, 177–178 Retrieving effectively from memory (REM) model consequences of updating in, 171–172 overview, 168–170 word frequency and null list strength effects in, 170–171 Reward prediction error hypothesis, 107 Reward-rate optimality, 45 Reward varieties, in reinforcement learning, 113–114 Rickard’s component power laws model, 301 Risk in decision making See Decision-making models RL (reinforcement learning) See Computational reinforcement learning ROPE (region of practical equivalence), in decision rules, 286 RPM (Random Permutations Model), 244 RT (response times) See Response times (RT) RT-distance hypothesis, 29, 150 Rule-plus-exception models, 142 Rumelhart networks, 235–237 Saccadic eye movements, 323–325 SAMBA (Selective Attention, Mapping, and Ballistic Accumulators) model of absolute identification, 128–129, 133, 135–138 Sampling independence test, 24 Savage-Dickey approximation to Bayes factor, 313–314 Sawada, T., 255 SBME (strength-based mirror effect), 171–172 Schall, J D., 320 Schizophrenia, stimulus-encoding elongation in, 357–359 SCM (similarity-choice model), 21 SD (social desirability) contamination of scores, 361 Second-order conditioning, 102–103, 111 Selective Attention, Mapping, and Ballistic Accumulators (SAMBA) model of absolute identification, 128–129, 133, 135–138 Selective influence, 85 Semantic and recognition priming effects, 47 Semantic memory, 232–254 compositional semantics, 249 connectionist models of, 234–239 distributional models of, 239–247 latent semantic analysis, 239–240 moving window models, 240–241 probabilistic topic models, 243–246 random vector models, 241–243 retrieval-based semantics, 246–247 future directions, 249–250 grounding semantic models, 247–249 overview, 232–233 research models and themes, 233–234 Semantic networks, 233–234 SEMMOD software for semantic memory modeling, 246 Sensory preconditioning, 194–195 Sequential effects, 123–124, 136–138 Sequential-sampling models See Diffusion models Serial processing mathematics supported by, 76–77 parallel processing versus, 71 parallel-serial mimicry ignored, 87–90 parallel-serial testing paradigm, 82 SEUT (subjective expected utility theory), 209, 211 SFT (Systems Factorial Technology), 354–355 Shape perception, 255–276 constancy, 256–257 constraints in regularization and Bayesian methods, 258–260 index 397 Shape perception (Cont.) eye and camera geometry, 260–263 Fechnerian paradigm inadequacy, 257–258 new definition of, 273–274 perspective and orthographic projection, 263–265 3D mirror-symmetrical shape recovery from 2D images, 269–273 3D symmetry and 2D orthographic and perspective projections, 265–269 uniqueness, 255–256 Shrinkage and multiple comparisons, 286–288, 290 Sichuan University, 134 Signal detection theory See Multidimensional signal detection theory Sign-dependent utility theory, 209 Similarity as context effect in DFT, 225–226 kernels of, 201 practice effects and, 146–148 as search determinant, 89 similarity-choice model (SCM), 21 Single cell recording data, 54 Sleep deprivation, 50 Social desirability (SD) contamination of scores, 361 Soto, F A., 13 Span of attention, 66 Spatial models, 233–234 Speed-accuracy tradeoff, 90–91 Speeded classification, 29, 146–148 Speeded visual search, 89 Sperling, George, 66 S-Space software for semantic memory modeling, 246 SST (strong stochastic transitivity), 212–213 State representation influence, in reinforcement learning, 109–110 States, in Markov decision process (MDP), 102–103 Sternberg, Saul, 68 Steven’s law of psychophysics, 307 Stimulus dimensionality, 133 Stimulus-response learning, 101 Stochastic difference equation, 398 index Stochastic dominance, 217–218, 221–222 Stochastic independence, 72 Stochastic transitivity, 212–213 Stopping rule exhaustive processing versus, 71–72 set-size functions and, 82–87 Stop signal paradigm, 330, 332–333 St Petersburg paradox, 210–211 Strength-based mirror effect (SBME), 171–172 Strong inference tactic, 92 Strong stochastic transitivity (SST), 212–213 Structural MRI, 57 Subjective expected utility theory (SEUT), 209, 211 Subtraction, method of, 66–69 Summary statistics approach to GRT, 22–24 Super capacity, 73 SuperMatrix software for semantic memory modeling, 246 Supertaskers, 75 Survivor interaction contrast, 84–85 Symmetry See Shape perception Systematic exploration, 113 Systems Factorial Technology (SFT), 354–355 TAX (transfer of attention exchange) model, 219 Temporal Context Model (TCM), 244 Temporal difference learning, 104–105, 109, 111 Tenenbaum, J B., 187 Test of English as a Foreign Language (TOEFL), 240 Theorizing process, Threat sensitivity modeling in anxiety-prone individuals, 352–354 3D symmetry See Shape perception Thurstonian models of absolute identification, 124–125, 129, 136 Time-varying processing, 44 TOEFL (Test of English as a Foreign Language), 240 Tolman, Edwin, 93 Tonal languages, 134 Topic models, 243–246, 248, 250 Total probability, law of, 375–376 Townsend, J T., 1, 63 Townsend’s capacity reallocation, 69 Transfer of attention exchange (TAX) model, 219 Transformations, perspective projection as, 261 Transition probabilities, in Markov decision process (MDP), 102 Transitivity, axioms of, 211–214 Trial independent “random” exploration, 112–113 Trial-to-trial variability, 37 Trigonometric functions, 2–3 2D orthographic and perspective projections See Shape perception Two-choice models, diffusion models versus, 51–56 Two-choice tasks, 41–44 Two-stage gambles Markov dynamic model for, 382–383 model comparisons for, 385–387 overview, 381–382 quantum dynamic model for, 384–385 Uncertainty, 281 See also Decision-making models Uniqueness, in shape perception, 255–256 Unlimited capacity and independent, parallel processing channels (UCIP), 74–75 U.S Army Research Office, 31 Utility function, 211, 216–217 Value-based judgments, diffusion models in, 47–48 Vandekerckhove, J., 300 Vanpaemel, W., 279 Venn diagrams, Veridical perception, 255, 258 Vickers accumulator model, 36 Visually responsive neurons, in FEF, 321, 323, 325–326 Visual search experiments, 69 Visual short-term memory (VSTM), 45 Vitalism, 64 von Helmholtz, Hermann, 64 von Neumann axioms, 371, 373 VSTM (visual short-term memory), 45 Wagenmakers, E.-J., 300 WAIS vocabulary, 48 Wallsten, T S., 209 Wang, Z., 1, 369 Weak stochastic transitivity (WST), 212–213 Weighted additive utility model, 220 Wickens, T D., 14, 19 William of Occam, 302 Willits, J., 232 Wisconsin Card Sorting Test, 349, 356–357 Woodworth, R S., 63–64 Word frequency effects in (REM) model, 170–171 Word recognition, 47 Word-Similarity software for semantic memory modeling, 246 Workload capacity, 72–74, 85–87 Wundt, Wilhem, 65 index 399 ... FA C E Computational and mathematical psychology has enjoyed rapid growth over the past decade Our vision for the Oxford Handbook of Computational and Mathematical Psychology is to invite and organize... Distinguished Rudy Professor of Psychology at Indiana University He was the president of Society for Mathematical Psychology and editor of the Journal of Mathematical Psychology His theoretical contributions... reasoning The complexity of theorizing and data often requires the aid of computers and computational languages Computational models and mathematical models can be thought of as a continuum of a theorizing