Models for behavior: Stochastic processes in psychology
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Francisco
Freeman
1982
|
| Schriftenreihe: | A series of books in psychology.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 353 S. graph. Darst. |
| ISBN: | 0716713527 0716713535 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804118044818014208 |
|---|---|
| adam_text | Titel: Models for behavior
Autor: Wickens, Thomas D.
Jahr: 1982
Contents
Glossary of Symbols xi
Preface xiii
1 Theories and Markov Models 1
1.1 An Example: The AH-or-None Model 1
1.2 Theories and Models 6
1.3 Markov Models 9
The State Space I Transitions Between States I
The Markov Property
1.4 Overview of This Book 16
2 Representation of Psychological Processes as Markov Models 18
2.1 Markov Models 19
2.2 Simple Models of Learning 24
The All-or-S one Association Model ¦ AH-or-None Learning
on Errors ; The Linear Model The Random-Trials-
Increment Model
2.3 Two-Stage Learning Models 32
An Intermediate State i The Long-and-Short Model /
Multiple Transition Operators
vi Contents
2.4 Choice Models 39
Single Choices I Sequences of Choices I
Probability Learning
2.5 Random Walks 46
3 Algebraic Analysis of Finite Markov Chains 51
3.1 State Probabilities 52
3.2 Response Probabilities 58
3.3 The Number of Errors 60
3.4 Sequential Response Probabilities 65
3.5 Item Variability 68
4 Matrix Methods 77
4.1 Representation and State Probabilities 78
4.2 Transitions Among Sets of States 82
State Sets as Responses I Likelihoods of Response
Strings i The Fundamental Matrix
4.3 Distributions of Some Summary Statistics 92
The Number of Errors I The Trial of Last Error I
Latency of Responses
4.4 Selection of Items Taking Particular Paths 98
Likelihoods Again I The Backward Learning Curve I
The Backward Latency Curve
5 Estimation of Parameters 108
5.1 The Estimation Problem 109
5.2 Method-of-Moments Estimators 113
5.3 Maximum-Likelihood Estimators 116
5.4 Minimum Chi-Square Estimators 123
5.5 Finding Numerical Extrema 126
Contents vii
6 Statistical Testing 135
6.1 Goodness-of-Fit Tests 137
6.2 Tests of Parameters and Comparison of Models 141
6.3 Examples of Likelihood-Ratio Testing 145
7 Identification of Models and Parameters 151
7.1 Unidentifiable Parameters and Equivalent Models 152
7.2 Vector-Space Representation 158
7.3 Treatment of Identifiability Problems 162
Equivalence Classes of Models I Parametric Restrictions I
Analysis in a Broader Domain
8 Markov Chains Without Absorbing States 171
8.1 Classification of Markov States and Chains 172
8.2 State Probabilities 176
Transient States I Ergodic States and Chains I
Periodic States
8.3 Renewal Properties of a Finite Markov Chain 185
Recurrence Probabilities I Recurrence of Transient
States I Expected Return Times I Matrix Formulation
9 Markov Chains with Unbounded State Spaces 199
9.1 Random Walks 200
State Probabilities I Asymptotic Behavior I State Types
and Recurrence Probabilities
9.2 A Queuing Example 206
9.3 Learning Models 208
9.4 Generating Functions 211
Properties of Generating Functions I Difference Equations
and State Probabilities I The RTI Model I Recurrence
Probabilities
viii Contents
10 Continuous-Time Markov Processes 226
10.1 The Poisson Process 227
Definition of a Poisson Process I The State Distribution I
Waiting Times I Erlang Processes
10.2 Birth Processes with State-Dependent Rates 238
Yule Processes I Death Processes
10.3 Processes with Arrivals and Departures 246
A Simple Queue I State Proportional Rates I
Multiple-Step Transitions
A Summary of Probability Theory 254
A.I Fundamental Definitions 254
A.2 Random Variables 256
Expected Values
A3 Some Discrete Distributions 261
The Geometric Distribution I Sums of Geometric Series I
The Binomial Distribution I The Negative Binomial
Distribution I The Poisson Distribution
A.4 Some Continuous Distributions 271
Distributions from Statistics: The Chi-Square
and the Normal I The Exponential Distribution I
The Gamma Distribution I The Beta Distribution
B Difference Equations 280
B.I Homogeneous Difference Equations 282
B.2 Nonhomogeneous Difference Equations 285
B.3 Simultaneous Difference Equations 288
C Introduction to Linear Algebra 291
C.I Basic Definitions 292
C.2 Fundamental Operations 294
Contents ix
C.3 Matrix Inversion 299
C.4 Partitioned Matrices 303
C.5 Vector Spaces, Bases, and Transformations 304
C.6 Eigenvalues and Eigenvectors 308
D Some Concepts from Calculus 314
D.I The Derivative 315
Finding Extrema of Functions I Finding Derivatives
D.2 Integration 321
Integrals as Weighted Combinations I The Relation
of the Integral to the Derivative I Calculation of Integrals
D.3 Differential Equations 327
E The Greek Alphabet 329
F Chi-Square and Normal Distributions 330
Solutions to Problems 331
References 343
Index 347
|
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| id | DE-604.BV003700035 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:03Z |
| institution | BVB |
| isbn | 0716713527 0716713535 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002355104 |
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| physical | XIII, 353 S. graph. Darst. |
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| series2 | A series of books in psychology. |
| spelling | Wickens, Thomas D. 1942- Verfasser (DE-588)137361602 aut Models for behavior Stochastic processes in psychology Thomas D. Wickens San Francisco Freeman 1982 XIII, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A series of books in psychology. Chaîne de Markov Markov-processen gtt Modèle statistique Probabilité Processus stochastique Psychologie - Modèles mathématiques Psychologie gtt Psychométrie Mathematisches Modell Markov processes Probability Psychology Mathematical models Psychometrics Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Psychologie (DE-588)4047704-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002355104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wickens, Thomas D. 1942- Models for behavior Stochastic processes in psychology Chaîne de Markov Markov-processen gtt Modèle statistique Probabilité Processus stochastique Psychologie - Modèles mathématiques Psychologie gtt Psychométrie Mathematisches Modell Markov processes Probability Psychology Mathematical models Psychometrics Stochastischer Prozess (DE-588)4057630-9 gnd Psychologie (DE-588)4047704-6 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4047704-6 |
| title | Models for behavior Stochastic processes in psychology |
| title_auth | Models for behavior Stochastic processes in psychology |
| title_exact_search | Models for behavior Stochastic processes in psychology |
| title_full | Models for behavior Stochastic processes in psychology Thomas D. Wickens |
| title_fullStr | Models for behavior Stochastic processes in psychology Thomas D. Wickens |
| title_full_unstemmed | Models for behavior Stochastic processes in psychology Thomas D. Wickens |
| title_short | Models for behavior |
| title_sort | models for behavior stochastic processes in psychology |
| title_sub | Stochastic processes in psychology |
| topic | Chaîne de Markov Markov-processen gtt Modèle statistique Probabilité Processus stochastique Psychologie - Modèles mathématiques Psychologie gtt Psychométrie Mathematisches Modell Markov processes Probability Psychology Mathematical models Psychometrics Stochastischer Prozess (DE-588)4057630-9 gnd Psychologie (DE-588)4047704-6 gnd |
| topic_facet | Chaîne de Markov Markov-processen Modèle statistique Probabilité Processus stochastique Psychologie - Modèles mathématiques Psychologie Psychométrie Mathematisches Modell Markov processes Probability Psychology Mathematical models Psychometrics Stochastischer Prozess |
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