Diffusion process models of decision making : fundamental processes. Volume 1 / Philip L. Smith, Roger Ratcliff. [electronic resource]

Format:

Book

Author/Creator:

Smith, Philip L., author.

Ratcliff, Roger, author.

Language:

English

Subjects (All):

Decision making--Mathematical models.

Decision making.

Diffusion processes.

Physical Description:

1 online resource (xviii, 533 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2025.

Summary:

Diffusion decision models are widely used to characterize the cognitive and neural processes involved in making rapid decisions about objects and events in the environment. These decisions, which are made hundreds of times a day without prolonged deliberation, include recognition of people and things as well as real-time decisions made while walking or driving. Diffusion models assume that the processes involved in making such decisions are noisy and variable and that noisy evidence is accumulated until there is enough for a decision. This volume provides the first comprehensive treatment of the theory, mathematical foundations, numerical methods, and empirical applications of diffusion process models in psychology and neuroscience. In addition to the standard Wiener diffusion model, readers will find a detailed, unified treatment of the cognitive theory and the neural foundations of a variety of dynamic diffusion process models of two-choice, multiple choice, and continuous outcome decisions.

Contents:

Cover

Half Title Page

Title Page

Imprints Page

Dedication

Contents

List of Figures

Preface

1 Overview

1.1 The Origins of Diffusion Process Models

1.2 Psychology's Two Ubiquitous Dependent Variables

1.3 The Variability of Behavior: Some Essential History

1.4 Organization of This Book

2 Basic Concepts and Data

2.1 What Do We Wish to Explain?

2.1.1 The Effects of Stimulus Discriminability on Mean RT and Accuracy

2.1.2 The Shapes of RT Distributions

2.1.3 The Shapes of RT Distributions across Experimental Conditions

2.1.4 The Quantile-Probability Plot

2.2 Mathematical Complements: Probability Concepts for RT Models

3 Sequential-Sampling Models of Decision Making

3.1 Scope of This Chapter

3.2 The Variety of Model Types

3.3 A Taxonomy of Models Types

3.4 Random Walk Models

3.5 Simple and Continuous Random Walks and the SPRT model

3.6 From Random Walks to Diffusion Process Models

3.7 Diffusion Process Models of Decision Making

3.8 Mathematical Characterization of Diffusion Processes

3.9 The Theoretical Propriety of Across-Trial Variability

3.10 A Note on Terminology: "The Drift-Diffusion Model" and Evidence "Thresholds

3.11 Accumulator and Counter Models

3.12 Hybrid Accumulator-Diffusion Models

3.13 Mathematical Complements

3.13.1 The Log-Likelihood Ratio of Normal Random Variables

3.13.2 The Moment Generating Function of a Random Variable

4 Obtaining Predictions for Diffusion Models

4.1 Scope of This Chapter

4.2 The Infinite-Series Method

4.2.1 First-Passage Time Moment Generating Functions

4.2.2 Choice Probabilities for the Wiener Process

4.2.3 Inverting the Moment Generating Function

4.3 The Integral Equation Method

4.3.1 Integral Equation Representation of First-Passage Time Densities.

4.3.2 The Kernel of the Integral Equation

4.3.3 Examples of the Kernel Function

4.4 The Matrix Method

4.4.1 Markov Chain Representation of Evidence Accumulation

4.4.2 Diffusion Limit of a Markov Chain

4.4.3 Abrupt Versus Smooth Changes in Drift Rates

4.5 Across-Trial Variability in Drift Rates

4.6 Chapter Summary

4.7 Mathematical Complements: Second-Order Differential Equations and Numerical Methods for Partial Differential Equations

4.7.1 Solution of Second-Order Differential Equations

4.7.2 Numerical Solution of Partial Differential Equations for Diffusion Models

5 Empirical Assessment of Sequential-Sampling Models

5.1 Scope of This Chapter

5.2 Deriving Predictions for Counter and Accumulator Models

5.3 The Poisson Counter Model

5.4 The Vickers Accumulator Model

5.5 Response Time Distribution Predictions of Sequential-Sampling Models

5.6 Chapter Summary

5.7 Mathematical Complement: Incomplete Beta Representation of Choice Probabilities for the Poisson Counter Model

6 Time-Varying Diffusion Models, I. Time Pressure, Urgency, Collapsing Boundaries, and Optimality

6.1 Scope of This Chapter

6.2 Speed Stress Versus Deadlines

6.3 Urgency and Collapsing Decision Boundaries

6.4 Reward Rate Optimality and Collapsing Boundaries

6.5 Stochastic Dynamic Programming and the Bellman Equation

6.6 The Posterior Probability for the Wiener Diffusion Process

6.7 Evaluation of the Collapsing Bounds and Urgency Signal Models

6.7.1 Deadlines Are Not General Speed-Stress Manipulations

6.7.2 Reward Rate Maximization Is of Limited Generality

6.7.3 Model Tests at the Distribution Level Provide Limited Support

6.7.4 Collapsing Bounds May Be an Artifact of the DecisionTask

6.7.5 Perceptual and Neural Integration in the Random Dot Motion Task.

6.7.6 There Are Simpler Models for Time-Limited Processing

6.8 Chapter Summary

6.9 Mathematical Complements: Kernel Functions for the Urgency-Gating and Collapsing-Boundaries Models

6.9.1 Urgency-Gating Model

6.9.2 Collapsing-Boundaries Model

7 Diffusion Models for Time-Controlled Processing Tasks

7.1 Time-Controlled and Information-Controlled Processing

7.2 Mixture of Time-Controlled and Information-Controlled Processing

7.3 Time-Controlled Processing with Reflecting Boundaries

7.4 Evaluation of the Time-Controlled Processing Literature

7.5 Mathematical Complements: Decision Boundary Models for Time-Controlled Processing

7.5.1 The Forward Equation

7.5.2 Solution of the Forward Equation with Absorbing Boundaries

7.5.3 Solution of the Forward Equation with Reflecting Boundaries

8 Time-Varying Diffusion Models, II. Detection and Simple RT

8.1 Visual Psychophysics and the Time Course of Stimulus Encoding

8.2 Diffusion Processes with Time-Varying Drift Rates

8.3 Diffusion Processes Driven by Systems of Processes in Cascade

8.4 Diffusion Processes Driven by Sustained and Transient Channels

8.5 Bloch's Law Predictions from Diffusion Models of Detection

8.6 Peaked Hazard Functions from Drift Rate Variability

8.7 Chapter Summary

9 Diffusion Processes Driven by Time-Varying Stimulus Representations in Visual Working Memory

9.1 Response Times to Brief, Masked Stimuli

9.2 Attention, Visual Working Memory, and Drift Rate

9.3 The Integrated System Model

9.4 Decision Making in Dynamic Noise

9.5 The Overconstrained Estimation View

9.6 Modeling Attention in the No-Onset Paradigm

9.7 Remarks on Experimental Design and Model Testability

9.8 Chapter Summary

10 Neural Diffusion Models, I. Network and Dynamical System Models

10.1 Neural Foundations of Diffusion Decision Models.

10.2 Neural Architectures for Decision Making

10.2.1 Wang's Spiking Neural Network Model

10.2.2 Roxin and Ledberg's Nonlinear Diffusion Equation

10.2.3 Verdonck and Tuerlinckx's Ising Decision Maker

10.3 Chapter Summary

11 Neural Diffusion Models, II. Poisson Shot Noise and Related Models

11.1 Top-Down versus Bottom-Up Neural Diffusion Models

11.2 Poisson Shot Noise Models

11.2.1 Poisson Shot Noise and its Ornstein-Uhlenbeck Process Limit

11.2.2 The Integrated Ornstein

Uhlenbeck Process

11.2.3 The Leaky Integrated Threshold Model of MotorActivation

11.2.4 Recurrent Loop Poisson Shot Noise Model

11.2.5 Lévy Flight Models

11.3 The Linear Drift, Linear Infinitesimal Variance Diffusion Model

11.3.1 Three Principles of Theory Construction

11.3.2 Competition as a Fourth Principle?

11.4 Chapter Summary

11.5 Mathematical Complements: Analysis of Shot Noise Processes

11.5.1 The Moment Generating Function of the Exponential Shot Noise

11.5.2 Joint Generating Function of a Shot Noise Process

11.5.3 The Firing Rate Distribution of a Recurrent Loop

11.5.4 Overview of Shot Noise Process Results

12 Diffusion Models for Continuous-Outcome Decision Tasks

12.1 Continuous-Outcome Tasks in Perception and Memory

12.2 Diffusion Models for Continuous-Outcome Tasks

12.3 The Circular Diffusion Model

12.3.1 Obtaining Predictions for the CDM via the Girsanov Theorem

12.3.2 Properties of the CDM

12.3.3 Drift-Rate Variability

12.3.4 Decision Biases

12.4 The Spatially Continuous Diffusion Model

12.4.1 Applications of the Spatially Continuous DiffusionModel

12.4.2 Bimodal Distributions of Decision Outcomes

12.4.3 Relating the CDM and SCDM in RepresentationalSpace

12.5 Symmetrical Diffusion Models in Higher Dimensions

12.5.1 The Spherical Diffusion Model.

12.5.2 The Hyperspherical Diffusion Model of Visual Search

12.6 Chapter Summary

12.7 Mathematical Complements

12.7.1 Surface Area Scaling for Circularly Symmetrical Diffusion Models

12.7.2 Improving the Numerical Stability of the Circular Diffusion Model

13 Response Confidence

13.1 Peirce's Law, Random Walks, and Posterior Probabilities

13.2 Vickers' Balance of Evidence Hypothesis

13.3 Pleskac and Busemeyer's Postdecision Accumulation Model

13.4 Confidence in Higher-Dimensional Evidence Spaces

13.5 Perceptual Clarity and Evidence Accumulation in Spheres

13.6 Chapter Summary

14 EZ and Moment Models, Multialternative Decisions, and Expanded Judgment Tasks

14.1 Diffusion Process Models Based on Moments

14.2 The EZ-Diffusion Model of Wagenmakers et al. (2006)

14.3 The EZ-CDM of Qarehdaghi and Rad (2024)

14.4 Decision Field Theory

14.5 Multivariate Extensions

14.5.1 Busemeyer and Diederich's Three-Category Diffusion Model

14.5.2 Multialternative Decision Field Theory

14.5.3 Multivariate Optimality and Diffusion Models

14.5.4 The Boundaries Really Do Matter

14.6 Expanded Judgment Tasks

14.7 Chapter Summary

14.8 Mathematical Complements: Moments of Diffusion Process Models

14.8.1 Mean and Variance of the Wiener Process

14.8.2 Mean and Variance of the Circular Diffusion Model

14.9 Conclusion

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 28 Oct 2025).

Description based on publisher supplied metadata and other sources.

ISBN:

1-009-65270-2

1-009-65266-4

OCLC:

1574121936