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# (p. 391) Index

(p. 391) 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*, 133–135response times, 135

theories of, 124–129

Absorbing barriers, 30

Actions, in Markov decision process (MDP), 102–103

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

Anxiety, diffusion models of, 49

Anxiety-prone individuals, threat sensitivity modeling in, 352–354

Aphasia, 49–50

Ashby, F. G., 13

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

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 models.

*See also*Hierarchical models, Bayesian estimation inof 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

parsimony principle in, 309–314

of shape perception, 258–260

Bayesian parameter estimation, 348–349

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

Blood sugar reduction, 50

Bootstrapping, 105

Boundary setting across tasks, 48

Brown, S. D., 121

Brown and Heathcote’s linear ballistic accumulator model, 301

BUGS modeling specification language, 282

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

Cattell, James McKeen, 66

Chaos-theoretic modeling, 345–346

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

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

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, 108–109reward varieties, 113–114

state representation influence, 109–110

temporal difference learning, 104–105

values for states and actions, 102–103

Confidence judgments, 52–53

Conjunction probability judgment errors, 376–379

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

COVIS theory of category learning, 30–31

Criss, A. H., 165

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

Deadline tasks, 41–42

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 decisionchoice 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

Depression, diffusion models of, 49

Derivatives and integrals, 3–5

Deterministic processes, 72

Differential-deficit, psychometric-artifact problem, 360

Differential equations, 4–5

Diffusion models, 35–62

in aging studies, 48

in child development, 48–49

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

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, 1

Donders, Franciscus, 65–66

Donkin, C., 121

Double factorial paradigm, 83

Dual process models of recognition, 166

Dynamic attractor networks, 237–239

Dynamic programming, 104

Dyslexia, 50

Effective sample size (ESS) statistic, 282

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

Epistemic uncertainty, 210

Error signal, 4–5

ESS (effective sample size) statistic, 282

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

Exhaustive processing, 71–72

Expectancy Valence Learning Model (EVL), 356–357

Expectations, 7–8

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, 2

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

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

Functions, mathematical, 1–3

Galen, 64

Gate accumulator model, 327

Generalizability, measures of, 303

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

Griffiths, T. L., 187

Grouping, power of, 66

Guided search, 89

Gureckis, T. M., 99

HA-LA (higher anxiety-prone-lower anxiety-prone) group differences, 352–353

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

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

Histograms, 9

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

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

Individual differences studies, diffusion models in, 48

Infinite Relational Model (IRM), 195

Information criteria, in model comparison, 306–307

Institute for Collaborative Biotechnologies, 31

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

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

Kruschke, J. K., 279

Kullback-Leibler divergence, 306

Languages, tonal, 134

Latent Díríchlet Allocation algorithms, 244

Law of total probability, 376

Learning.

*See also*Computational reinforcement learningabsolute identification in, 130–133

associative, 194–196

Hebbian, 235

modeling human function, 202–203

relationships in continuous quantities, 200–203

Lexical decisions, diffusion models in, 46–47

Lexicographic semi-order (LS) choice rule, 213

Li, Y., 255

Likelihood ratio test, 28

Linear functions, 1–2

Logan, G. D., 320

Love, B. C., 99

LS (lexicographic semi-order) choice rule, 213

Luder’s rule, 374

“Magical number seven,” 66

Mapping, functions for, 1

Marginal discriminabilities, 23

Marginal response invariance, 22

Markov decision process (MDP), 102–104

Maskelyn, Nevil, 65

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

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 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,*71–72Minkowski power model, 144

Model-based

*versus*model-free learning, 108–109Model 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

Moving window models, 240–241

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 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

Multiple comparisons, shrinkage and, 290

Multiple linear regression, 8

Multivariate normal model, 16–17

Myopic behavior, of agents, 103

National Institute of Neurological Disorders and Stroke, 31

Natural log functions, 2

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 ofNeuro-connectionist modeling, 345

Neuroeconomics, 48

Neuroscience, decision making understanding from, 53–58

Newton-Raphson method, 19

Nietzsche, Friedrich, 64

Nonlinear dynamical system modeling, 345–346

Normal distribution, 7

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

Overfitting, 190–191

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*, 71Parallel-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

neural locus of drift rates, 325–327

overview, 320–323

saccadic eye movements and, 323–325

Perceptual expertise, automaticity and, 148–150

Perceptual judgment, 121–141

absolute identification issues, 129–139

absolute and relative judgment, 129–130

absolute identification

*versus*perfect pitch, 133–135intertrial 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 units, features as, 196–200

Perfect pitch, absolute identification

*versus*, 133–135Pizlo, Z., 255

Pleskac, T. J., 209

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, 2

Power law, 300

*Principles of Psychology*(James), 64

Probability density function, 72

Probability judgment error, 377–379

Probability mass function, 7

Probability weighting function, 214–216

Problem of Points, 210

Procedural learning, 30–31

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 inPsychomotor vigilance task (PVT), 53

Quadratic functions, 2

Quantile-probability plots, 40

Quantum models of cognition and decision, 369–389

classical probabilities

*versus*, 373–377concepts, 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

Rank-dependent utility theory, 209

Ratanalysis, 188

Ratcliff, R., 35

Ratcliff’s diffusion model, 301

Reaction time distributions, 83–87

Region of practical equivalence (ROPE), in decision rules, 286

Regularization methods, in shape perception, 258–260

Release-from-inhibition model, 50–51

Response signal tasks, 41–42

Response times (RT)

cognitive-psychological complementarity, 87–90

in diffusion models, 38–41

example of, 78–79

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

quantitative expressions of, 70–75

stopping rule distinctions based on set-size functions, 82–87

theoretical distinctions, 79–82

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

ROPE (region of practical equivalence), in decision rules, 286

RPM (Random Permutations Model), 244

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

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

Serial processing mathematics supported by, 76–77

parallel processing

*versus*, 71parallel-serial mimicry ignored, 87–90

parallel-serial testing paradigm, 82

SFT (Systems Factorial Technology), 354–355

Shape perception, 255–276

constancy, 256–257

constraints in regularization and Bayesian methods, 258–260

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

Sichuan University, 134

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 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, 5

Stochastic independence, 72

Stochastic transitivity, 212–213

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

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

Systematic exploration, 113

Systems Factorial Technology (SFT), 354–355

TAX (transfer of attention exchange) model, 219

Temporal Context Model (TCM), 244

Tenenbaum, J. B., 187

Test of English as a Foreign Language (TOEFL), 240

Theorizing process, 1

Threat sensitivity modeling in anxiety-prone individuals, 352–354

Time-varying processing, 44

TOEFL (Test of English as a Foreign Language), 240

Tolman, Edwin, 93

Tonal languages, 134

Total probability, law of, 375–376

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

Two-choice models, diffusion models

*versus*, 51–56Two-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

Uniqueness, in shape perception, 255–256

Unlimited capacity and independent, parallel processing channels (UCIP), 74–75

U.S. Army Research Office, 31

Value-based judgments, diffusion models in, 47–48

Vandekerckhove, J., 300

Vanpaemel, W., 279

Venn diagrams, 6

Vickers accumulator model, 36

Visual search experiments, 69

Visual short-term memory (VSTM), 45

Vitalism, 64

von Helmholtz, Hermann, 64

VSTM (visual short-term memory), 45

Wagenmakers, E.-J., 300

WAIS vocabulary, 48

Wallsten, T. S., 209

Weighted additive utility model, 220

William of Occam, 302

Willits, J., 232

Woodworth, R. S., 63–64

Word frequency effects in (REM) model, 170–171

Word recognition, 47

Word-Similarity software for semantic memory modeling, 246

Wundt, Wilhem, 65