UID:
almafu_9961051794202883
Umfang:
1 online resource (xvi, 478 pages) :
,
illustrations (black and white), digital, PDF file(s)
Ausgabe:
First edition.
ISBN:
9781108906067
,
1108906060
,
9781108902724
,
1108902723
Inhalt:
'The New Handbook of Mathematical Psychology' provides a rigorous introduction to the key foundational, theoretical, and applied areas of the field of mathematical psychology. Volume 3 focuses on key content areas in perceptual and cognitive processes, and effectively complements the previous volumes by covering recent developments.
Anmerkung:
Also issued in print: 2023.
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Cover -- Half-title -- Title page -- Copyright information -- Contents -- List of Contributors -- Preface -- 1 Principles and Consequences of the Initial Visual Encoding -- 1.1 Introduction -- 1.2 Scene to Retinal Image -- 1.2.1 Light Field -- 1.2.2 The Incident Light Field -- 1.2.3 Spectral Irradiance and the Plenoptic Function -- 1.2.4 The Initial Visual Encoding -- 1.3 Mathematical Principles -- 1.3.1 Linear Systems -- 1.3.2 Linearity Example: Cone Excitations and Color Matching -- 1.3.3 Matrix Formulation of Linearity -- 1.3.4 Color-Matching Functions -- 1.3.5 Noise in the Sensory Measurements -- 1.3.6 Image Formation -- 1.3.7 Shift-Invariance and Convolution -- 1.4 Computational Model of the Initial Encoding -- 1.4.1 The Value of Computational Modeling -- 1.4.2 Shift-Varying and Wavelength-Dependent Point Spreads -- 1.4.3 Shift-Varying Sampling -- 1.4.4 Spatial Derivatives of the Cone Excitations Mosaic -- 1.5 Perceptual Inference -- 1.5.1 Ambiguity and Perceptual Processing -- 1.5.2 Mathematical Principles of Inference -- 1.5.3 Thresholds and Ideal Observer Theory -- 1.5.4 Computational Observers -- 1.5.5 Image Reconstruction -- 1.5.6 Optimizing Sensory Measurements -- 1.6 Summary and Conclusions -- 1.7 Related Literature -- Acknowledgments -- References -- 2 Measuring Multisensory Integration in Selected Paradigms -- 2.1 Overview -- 2.2 Measures of Multisensory Integration: Introduction -- 2.2.1 Defining Multisensory Integration -- 2.2.2 Measuring Multisensory Integration -- 2.3 Measures for the Multisensory Neuron Response -- 2.3.1 Rules of Multisensory Integration -- 2.3.2 Multisensory Integration vs. Probability Summation -- 2.3.3 Measures of MI under PS Hypothesis -- 2.4 Measures Based on Response Speed -- 2.4.1 MI Measures in Redundant Signals Paradigms -- 2.4.2 Probability Summation in the Redundant Signals Paradigm.
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2.4.3 Measures of MI in Redundant Signals Paradigms under PS -- 2.4.4 MI Measures in Focused Attention Paradigms -- 2.5 MI Measures Based on Accuracy -- 2.5.1 MI Measures Based on Detection Accuracy -- 2.5.2 Measures for Audiovisual Speech Identification -- 2.6 Measures Based on MI Modeling of RTs -- 2.6.1 Coactivation Models -- 2.6.2 Time-Window-of-Integration Framework -- 2.7 Conclusions -- 2.8 Related Literature -- References -- 3 Fechnerian Scaling: Dissimilarity Cumulation Theory -- 3.1 Introduction -- 3.1.1 What is it About? -- 3.1.2 Unidimensional Fechnerian Scaling -- 3.1.3 Historical Digression: Fechner's Law -- 3.1.4 Observation Areas and Canonical Transformation -- 3.1.5 Same-Different Judgments -- 3.2 Notation Conventions -- 3.3 Basics of Fechnerian Scaling -- 3.3.1 Step 1 -- 3.3.2 Step 2 -- 3.3.3 Step 3 -- 3.3.4 Subsequent Development -- 3.4 Dissimilarity Function -- 3.5 Quasimetric Dissimilarity -- 3.6 Dissimilarity Cumulation in Discrete Spaces -- 3.6.1 Direct Computation of Distances -- 3.6.2 Recursive Corrections for Violations of the Triangle Inequality -- 3.7 Dissimilarity Cumulation in Path-Connected Spaces -- 3.7.1 Chains-on-Nets and Paths -- 3.7.2 Path Length through Quasimetric Dissimilarity -- 3.7.3 The Equality of the D-length and G-length of Paths -- 3.7.4 Intrinsic Metrics and Spaces with Intermediate Points -- 3.8 Dissimilarity Cumulation in Euclidean Spaces -- 3.8.1 Introduction -- 3.8.2 Submetric Function -- 3.8.3 Indicatrices -- 3.8.4 Convex Combinations and Hulls -- 3.8.5 Minimal Submetric Function and Convex Hulls of Indicatrices -- 3.8.6 Length and Metric in Euclidean Spaces -- 3.8.7 Continuously Differentiable Paths and Intrinsic Metric G -- 3.9 Dissimilarity Cumulation: Extensions and Applications -- 3.9.1 Example 1: Observational Sorites "Paradox" -- 3.9.2 Example 2: Thurstonian-Type Representations.
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3.9.3 Example 3: Universality of Corrections for Violations of the Triangle Inequality -- 3.9.4 Example 4: Data Analysis -- 3.9.5 Example 5: Ultrametric Fechnerian Scaling -- 3.10 Related Literature -- Appendix: Select Proofs -- References -- 4 Mathematical Models of Human Learning -- 4.1 Early Models of Human Learning -- 4.2 Neuroscience Breakthroughs -- 4.2.1 Discovery of LTP and LTD -- 4.2.2 Discovery of Multiple Learning and Memory Systems -- 4.3 Modern Approaches to Modeling Human Learning -- 4.3.1 Descriptive- and Process-Level Approaches -- 4.3.2 Implementational-Level Approaches -- 4.4 Descriptive and Process Models of Human Learning -- 4.4.1 Reinforcement Learning -- 4.4.2 Bayesian Modeling of Human Learning Under Uncertainty -- 4.4.3 Supervised-Learning Models of Sensorimotor Adaptation -- 4.5 Implementational Models of Human Learning -- 4.5.1 Physiology of DA-Dependent Two- and Three-Factor Synaptic Plasticity -- 4.5.2 Models Based on Two-Factor Plasticity -- 4.5.3 Models Based on DA-Dependent Three-Factor Plasticity -- 4.5.4 Models Based on Plasticity that Mimics Supervised Learning -- 4.5.5 Models of Human Learning that Include Multiple Forms of Plasticity -- 4.6 Empirical Testing -- 4.7 Conclusions -- 4.8 Related Literature -- Acknowledgments -- References -- 5 Formal Models of Memory Based on Temporally-Varying Representations -- 5.0.1 Associations in the Mind and Brain -- 5.0.2 Cognitive Models of Memory -- 5.0.3 Beyond Associations: Representing Temporal Relationships in the Mind and Brain -- 5.0.4 A Brief History of Mathematical Models of Memory -- 5.1 "Simple" Associations in the Mind and Brain -- 5.1.1 Hebbian Learning -- 5.1.2 Forgetting -- 5.2 Short-Term Memory and Temporal Context Models -- 5.2.1 The Recency Effect and Two-Store Models -- 5.2.2 The Contiguity Effect Across Delays -- 5.2.3 Temporal Context Models.
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5.2.4 Contiguity Effect -- 5.2.5 Neural Evidence for Temporal Context Models -- 5.2.6 Memory is Scale-Invariant -- Exponential Functions are Not -- 5.3 Scale-Invariant Temporal History -- 5.3.1 Estimating Temporal Relationships Using the Laplace Transform -- 5.3.2 Behavioral Models Using Scale-Invariant Temporal History -- 5.3.3 Evidence for Scale-Invariant Temporal History in the Brain -- 5.3.4 Going Forward -- 5.4 Related Literature -- References -- 6 Statistical Decision Theory -- 6.1 Introduction -- 6.2 Historical Precedents -- 6.3 One Dimension: Signal Detection Theory -- 6.3.1 The Receiver Operating Characteristic -- 6.3.2 Application to Other Tasks -- 6.3.3 Extensions -- 6.4 Two or More Dimensions: General Recognition Theory -- 6.4.1 Identification versus Categorization -- 6.4.2 Modeling Perceptual and Decisional Interactions -- 6.4.3 Applications to Categorization Tasks -- 6.4.4 Applications to Identification Tasks -- 6.4.5 Extensions to Response Time -- 6.4.6 Extensions to Neuroscience -- 6.5 Concluding Remarks -- 6.6 Related Literature -- Acknowledgments -- References -- 7 Modeling Response Inhibition in the Stop-Signal Task -- 7.1 Response Inhibition and the Stop-Signal Task -- 7.2 Some Typical Data Patterns in the Stop-Signal Paradigm -- 7.2.1 Inhibitions Function -- 7.2.2 Reaction Times to Go and Stop Signal -- 7.3 Modeling the Stop-Signal Task -- 7.3.1 The General Race Model -- 7.3.2 The (Complete) Independent Race Model -- 7.3.3 Nonparametric Estimation of Stop-Signal Distribution under Independence -- 7.4 Parametric Independent Race Models -- 7.4.1 Exponential Model -- 7.4.2 Ex-Gaussian Model -- 7.4.3 Hanes-Carpenter Race Model -- 7.4.4 Diffusion Race Model Including its Extension to Choice RT -- 7.5 Parametric Dependent Race Models -- 7.5.1 Evidence Against Independence: The Paradox -- 7.5.2 Interactive Race Model.
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7.5.3 Linking Propositions -- 7.6 Related (Non-race) Models -- 7.6.1 Blocked-Input Model -- 7.6.2 DINASAUR Model -- 7.6.3 Diffusion-Stop Model -- 7.7 Semi-parametric Race Models -- 7.7.1 The Role of Copulas -- 7.7.2 Equivalence with Dependent Censoring -- 7.7.3 Perfect Negative Dependency Race Model -- 7.8 Miscellaneous Aspects -- 7.8.1 Variants of the Stop-Signal Paradigm -- 7.8.2 Modeling Trigger Failures -- 7.8.3 Sequential (After Effects) Effects -- 7.9 Concluding Remarks -- 7.10 Related Literature -- References -- 8 Approximate Bayesian Computation -- 8.1 Introduction -- 8.1.1 Increasing Sophistication of Models -- 8.1.2 Statement of the Problem -- 8.1.3 A Motivating Example: The Activation-Suppression Race Model of Conflict -- 8.2 Approximate Bayesian Computation -- 8.2.1 Conceptual Basis -- 8.2.2 How it Works -- 8.2.3 Likelihood-Informed Markov Chain Monte Carlo -- 8.3 Three ABC Algorithms -- 8.3.1 Rejection ABC -- 8.3.2 Population Monte Carlo -- 8.3.3 Probability Density Approximation -- 8.3.4 Summary Results -- 8.4 Conclusions -- Acknowledgments -- References -- 9 Cognitive Diagnosis Models -- 9.1 Introduction -- 9.1.1 Basic Ideas -- 9.1.2 Model Estimation -- 9.1.3 CDM Applications -- 9.2 Q-Matrix Specification -- 9.2.1 Initial Q-Matrix Specification -- 9.2.2 Empirical Q-Matrix Validation -- 9.3 Model Fit Evaluation -- 9.3.1 Absolute Fit -- 9.3.2 Relative Fit -- 9.4 Examinee Classification, Reliability, and Validity -- 9.4.1 Examinee Classification -- 9.4.2 Reliability -- 9.4.3 Validity -- 9.5 Discussion and Future Directions -- 9.6 Related Literature -- References -- 10 Encoding Models in Neuroimaging -- 10.1 Introduction -- 10.2 Voxel-Based Encoding Models -- 10.2.1 Encoding Model -- 10.2.2 Measurement Model -- 10.2.3 Population Receptive Fields -- 10.2.4 Feature Spaces and Model Interpretation -- 10.3 Model Inversion.
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10.3.1 Population Response Reconstruction.
Weitere Ausg.:
ISBN 9781108830676
Weitere Ausg.:
ISBN 1108830676
Sprache:
Englisch
DOI:
10.1017/9781108902724
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