Hunt E. The Mathematics of Behavior

Cambridge: Cambridge University Press, 2007. — 346 p. — ISBN 978-0-521-85012-4.Книга посвящена использованию математических методов в психологии, охватывая широкий спектр тем, включая применение теории вероятностей, психофизику, теорию динамических систем, включая хаотическую динамику, теорию полезности, статистическую проверку гипотез, многомерное шкалирование, факторный анализ и другие статистические методы, построение тестов, модели сложных систем на основе клеточных автоматов и нейросетей и другие вопросы.
Для студентов, аспирантов и преподавателей в области математической психологии.What's in the Book?
Some Examples of Formal and Informal Thinking
A Bit of History
How Big Is the Earth? Eratosthenes' Solution
A Critique of Eratosthenes
Applications of Mathematics to Social and Behavioral Lssues
Statistics
Applying Probality Theory to Problems in Sociology and PsychologyDefining Probability and Probability Measures 23. How Closely Connected Are We?
Conscious and Unconscious Memories
Some Final Comments
Appendix A. The Basis for Kolmogorov's Axioms
Appendix B. Some Important Properties of Probability Measures
From Physics to Perception
The Psychophysical Problem
Weber's Law
Fechner's Law
Stevens's Scaling Technique: Deriving the Psychophysical Function from Magnitude Estimation
Judging Complex Objects
A Comment on Measurement
When Systems Evolve Over Time
Systems of Variables
Differences and Differentiation
Exponential Growth and Decay
Numerical Analysis: The Transmission of Jokes and Colds
Questions about Modeling
Graphical Analysis: The Evolution of War and Peace
Making Love, Not War: The Gottman-Murray Model of Marital Interactions
Concluding Comments on Modeling Simple Systems
Appendix A. A Proof of the Exponential Growth Equation
Non-Linear and Chaotic Systems
Continuous Change and Sudden Jumps
The Lotka-Volterra Model of Predator and Prey Interactions
The Logistic Equation: Introduction and Behavior When k<1
Non-zero Asvmptotes and Cycles as k Increases
Chaos
Chaos and Network Models
Closing Comments on Chaos
Defining Rationality
Axiomatic Reasoning
Decision Making under Risk
The Concept of Utility
Von Neumann and Morgenstern's Axiomatic Approach to Decision Making
The Utility of Money
A Summary of the Argument
Psychological Research on Decision Making
The Problem of Voting
Definition and Notation
Arrow's Axioms: The Restrictions on Social Welfare Functions
Illustration of the Definitions and Concepts for the Three-Person Society
A Proof of Arrow's Theorem
Commentary on the Implications of Arrow's Theorem
Summary Comments and Questions About Axiomatic Reasoning
How to Evaluate Evidence
The Legacy of Reverend Bayes
Bayes' Theorem
Some Numerical Examples
Calculating the Odds
Some Examples of Signal Detection
A Mathematical Formulation of the Signal Detection Problem
The Decision Analyst’s Problem
A Numerical Example of ROC Analysis
Establishing a Criterion
Examples
Four Challenge Problems
Multidimensional Scaling
The Basic Idea
Steps and Technique
Extensions to Non-geometric Data
Extending the Idea to Conceptual Classes
Generalizations of Semantic Space Models
Qualifications on the Semantic Space Model
The Mathematical Models behind Psychological TestingA Brief Review of Correlation and Covariance
Predicting One Variable from Another: Linear Regression
The Single Factor Model: The Case of General Intelligence
Multifactor Theories of Intelligence and Personality
Geometric and Graphic Interpretations
What Sort of Results Are Obtained?
Appendix A. A Matrix Algebra Presentation of Factor Analysts
How to Know You Asked a Good Question
The Problem
An Illustrative Case: Vocabulary Testing
The Basics of Item Response Theory
Standardization: Estimating Item and Person Parameters Simultaneously
The Application Phase: Adaptive Testing
More Complicated IRT Models
Mathematics Meets the Social World: Mathematical Issues and Social Relevance
Appendix A. The Adaptive Testing Algorithm
Appendix B. An Exercise in Adaptive Testing
The Construction of Complexity
Some Grand Themes
The Problem of Complexity
Cellular Automata Can Create Complicated Constructions
Is Capitalism Inherently Unfair? Reconstructing a Simple Market Economy
Residential Segregation, Genocide, and the Usefulness of the Police
Is This a New Kind of Science?
Connectionism
The Brain and the Mind
Computation at the Neural Level
Computations at the Network Level
A Philosophical Aside
Connection is t Architectures
Simulating a Phenomenon in Visual Recognition: The Interactive Activation Model
An Artificial Intelligence Approach to Learning
A Biological Approach to Learning: The Hebbian Algorithm
The Auto-associator
A Final Word
L'Envoi