Mathematical psychology
Encyclopedia
Mathematical psychology is an approach to psychological
research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. In practice "quantifiable behavior" is often constituted by "task performance".
As quantification of behavior is fundamental in this endeavor, the theory of measurement
is a central topic in mathematical psychology.
Mathematical psychology is therefore closely related to psychometrics
. However, where psychometrics is concerned with individual differences (or population structure) in mostly static variables, mathematical psychology focuses on process models of perceptual, cognitive and motor processes as inferred from the 'average individual'. Furthermore, where psychometrics investigates the stochastic dependence structure between variables as observed in the population, mathematical psychology almost exclusively focuses on the modeling of data obtained from experimental paradigms and is therefore even more closely related to experimental psychology
/cognitive psychology
/psychonomics
. Like computational neuroscience and econometrics, mathematical psychology theory often uses statistical optimality as a guiding principle, assuming that the human brain has evolved to solve problems in an optimized way. Central themes from cognitive psychology; limited vs. unlimited processing capacity, serial vs. parallel processing, etc., and their implications, are central in rigorous analysis in mathematical psychology.
Mathematical psychologists are active in many fields of psychology, especially in psychophysics
, sensation
and perception
, problem solving
, decision-making
, learning
, memory
, and language
, collectively known as cognitive psychology
, and the quantitative analysis of behavior
but also, e.g., in clinical psychology
, social psychology
, and psychology of music
.
Mathematical modeling has a long history in psychology starting in the 19th century with Ernst Weber
(1795–1878) and Gustav Fechner
(1801–1887) being among the first to apply successful mathematical technique of functional equations from physics to psychological processes. They thereby established the fields of experimental psychology
in general, and that of psychophysics
in particular.
Researchers in astronomy
in the 19th century were mapping distances between stars by denoting the exact time of a star's passing of a cross-hair on a telescope. For lack of the automatic registration instruments of the modern era, these time measurements relied entirely on human response speed. It had been noted that there were small systematic differences in the times measured by different astronomers, and these were first systematically studied by German astronomer Friedrich Bessel
(1782–1846). Bessel constructed personal equations from measurements of basic response speed that would cancel out individual differences from the astronomical calculations. Independently, physicist Hermann von Helmholtz
measured reaction times to determine nerve conduction speed.
These two lines of work came together in the research of Dutch physiologist F. C. Donders and his student J. J. de Jaager, who recognized the potential of reaction times for more or less objectively quantifying the amount of time elementary mental operations required. Donders envisioned the employment of his mental chronometry
to scientifically infer the elements of complex cognitive activity by measurement of simple reaction time
The first psychological laboratory was established in Germany by Wilhelm Wundt
, who amply used Donders' ideas. However, findings that came from the laboratory were hard to replicate and this was soon attributed to the method of introspection
that Wundt introduced. Part of the problems was due to the individual differences in response speed found by astronomers. Although Wundt did not seem to take interest in these individual variations and kept his focus on the study of the general human mind, Wundt's U.S. student James McKeen Cattell
was fascinated by these differences and started to work on them during his stay in England.
The failure of Wundt's method of introspection
led to the rise of different schools of thought. Wundt's laboratory was directed towards conscious human experience, in line with the work of Fechner and Weber on the intensity of stimuli. In the United Kingdom, under the influence of the anthropometric developments led by Francis Galton
, interest focussed on individual differences between humans on psychological variables, in line with the work of Bessel. Catell soon adopted the methods of Galton and helped laying the foundation of psychometrics
.
. Behaviorism dominated American psychology until the end of the Second World War, and largely refrained from inference on mental processes. Formal theories were mostly absent (except for vision
and audition
).
During the war, developments in engineering
, mathematical logic
and computability theory
, computer science
and mathematics
, and the military need to understand human performance and limitations
, brought together experimental psychologist, mathematicians, engineers, physicists, and economists. Out of this mix of different disciplines mathematical psychology arose. Especially the developments in signal processing
, information theory
, linear systems and filter theory, game theory
, stochastic processes and mathematical logic
gained a large influence on psychological thinking.
Two seminal papers on learning theory in Psychological Review
helped to establish the field in a world that was still dominated by behaviorists: A paper by Bush and Mosteller instigated the linear operator approach to learning, and a paper by Estes that started the stimulus sampling tradition in psychological theorizing. These two papers presented the first detailed formal accounts of data from learning experiments.
The 1950s saw a surge in mathematical theories of psychological processes, including Luce's theory of choice
, Tanner and Swets' introduction of signal detection theory for human stimulus detection, and Miller's approach to information processing. By the end of the 1950s, the number of mathematical psychologists had increased from a handful by more than a tenfold, not counting psychometricians. Most of these were concentrated at the University of Indiana, Michigan, Pennsylvania, and Stanford. Some of these were regularly invited by the U.S. Social Science Research Counsel to teach in summer workshops in mathematics for social scientists at Stanford University, promoting collaboration.
To better define field of mathematical psychology, the mathematical models of the 1950s were brought together in sequence of volumes edited by Luce, Bush, and Galanter: Two readings and three handbooks. This series of volumes turned out to be helpful in the development of the field. In the summer of 1963 the need was felt for a journal for theoretical and mathematical studies in all areas in psychology, excluding work that was mainly factor analytical. An initiative led by R. C. Atkinson
, R. R. Bush, W. K. Estes, R. D. Luce
, and P. Suppes resulted in the appearance of the first issue of the Journal of Mathematical Psychology in January, 1964.
Under the influence of developments in computer science, logic, and language theory, in the 1960s modeling became more in terms of computational mechanisms and devices. Examples of the latter constitute so called cognitive architectures (e.g., production rule systems, ACT-R
) as well connectionist systems or neural networks
.
Important mathematical expressions for relations between physical characteristics of stimuli and subjective perception are Weber's law (which is now sometimes called Weber-Fechner Law), Ekman's Law, Stevens' Power Law
, Thurstone's Law of Comparative Judgment
, the Theory of Signal Detection (borrowed from radar engineering), the Matching Law
, and Rescorla-Wagner rule
for classical conditioning. While the first three laws are all deterministic in nature, later established relations are more fundamentally stochastic. This has been a general theme in the evolution in mathematical modeling of psychological processes: From deterministic relations as found in classical physics to inherently stochastic models.
and the British Journal of Mathematical and Statistical Psychology
. There are three annual conferences in the field, the annual meeting of the Society for Mathematical Psychology in the U.S, the annual European Mathematical Psychology Group (EMPG) meeting in Europe, and the Australasian Mathematical Psychology conference.
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. In practice "quantifiable behavior" is often constituted by "task performance".
As quantification of behavior is fundamental in this endeavor, the theory of measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
is a central topic in mathematical psychology.
Mathematical psychology is therefore closely related to psychometrics
Psychometrics
Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...
. However, where psychometrics is concerned with individual differences (or population structure) in mostly static variables, mathematical psychology focuses on process models of perceptual, cognitive and motor processes as inferred from the 'average individual'. Furthermore, where psychometrics investigates the stochastic dependence structure between variables as observed in the population, mathematical psychology almost exclusively focuses on the modeling of data obtained from experimental paradigms and is therefore even more closely related to experimental psychology
Experimental psychology
Experimental psychology is a methodological approach, rather than a subject, and encompasses varied fields within psychology. Experimental psychologists have traditionally conducted research, published articles, and taught classes on neuroscience, developmental psychology, sensation, perception,...
/cognitive psychology
Cognitive psychology
Cognitive psychology is a subdiscipline of psychology exploring internal mental processes.It is the study of how people perceive, remember, think, speak, and solve problems.Cognitive psychology differs from previous psychological approaches in two key ways....
/psychonomics
Psychonomics
Psychonomics describes an approach to psychology that aims at discovering the laws that govern the workings of the mind . The field is directly related to experimental psychology. The word is used most prominently by the Psychonomic Society, a society of experimental psychologists in the United...
. Like computational neuroscience and econometrics, mathematical psychology theory often uses statistical optimality as a guiding principle, assuming that the human brain has evolved to solve problems in an optimized way. Central themes from cognitive psychology; limited vs. unlimited processing capacity, serial vs. parallel processing, etc., and their implications, are central in rigorous analysis in mathematical psychology.
Mathematical psychologists are active in many fields of psychology, especially in psychophysics
Psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they effect. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual...
, sensation
Sensation and perception psychology
In psychology, sensation and perception are stages of processing of the senses in human and animal systems, such as vision, auditory, vestibular, and pain senses. These topics are considered part of psychology, and not anatomy or physiology, because processes in the brain so greatly affect the...
and perception
Perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...
, problem solving
Problem solving
Problem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Consideredthe most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of...
, decision-making
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
, learning
Learning
Learning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information. The ability to learn is possessed by humans, animals and some machines. Progress over time tends to follow learning curves.Human learning...
, memory
Memory
In psychology, memory is an organism's ability to store, retain, and recall information and experiences. Traditional studies of memory began in the fields of philosophy, including techniques of artificially enhancing memory....
, and language
Psycholinguistics
Psycholinguistics or psychology of language is the study of the psychological and neurobiological factors that enable humans to acquire, use, comprehend and produce language. Initial forays into psycholinguistics were largely philosophical ventures, due mainly to a lack of cohesive data on how the...
, collectively known as cognitive psychology
Cognitive psychology
Cognitive psychology is a subdiscipline of psychology exploring internal mental processes.It is the study of how people perceive, remember, think, speak, and solve problems.Cognitive psychology differs from previous psychological approaches in two key ways....
, and the quantitative analysis of behavior
Society for Quantitative Analysis of Behavior
The Society for Quantitative Analysis of Behavior was founded in 1978 by Michael Lamport Commons and John Anthony Nevin. The first president was Richard J. Herrnstein. In the beginning it was called the Harvard Symposium on Quantitative Analysis of Behavior...
but also, e.g., in clinical psychology
Clinical psychology
Clinical psychology is an integration of science, theory and clinical knowledge for the purpose of understanding, preventing, and relieving psychologically-based distress or dysfunction and to promote subjective well-being and personal development...
, social psychology
Social psychology
Social psychology is the scientific study of how people's thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others. By this definition, scientific refers to the empirical method of investigation. The terms thoughts, feelings, and behaviors include all...
, and psychology of music
Music psychology
Music psychology,or the psychology of music, may be regarded as a branch of psychology or a branch of musicology. It aims to explain and understand musical behavior and musical experience...
.
History
Ernst Heinrich Weber
Ernst Heinrich Weber was a German physician who is considered one of the founders of experimental psychology.Weber studied medicine at Wittenberg University...
(1795–1878) and Gustav Fechner
Fechner
Fechner is a surname of:* Christian Fechner , a French film producer and screenwriter* Gustav Fechner , a German experimental psychologist* Harry Fechner , a German football defender...
(1801–1887) being among the first to apply successful mathematical technique of functional equations from physics to psychological processes. They thereby established the fields of experimental psychology
Experimental psychology
Experimental psychology is a methodological approach, rather than a subject, and encompasses varied fields within psychology. Experimental psychologists have traditionally conducted research, published articles, and taught classes on neuroscience, developmental psychology, sensation, perception,...
in general, and that of psychophysics
Psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they effect. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual...
in particular.
Researchers in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
in the 19th century were mapping distances between stars by denoting the exact time of a star's passing of a cross-hair on a telescope. For lack of the automatic registration instruments of the modern era, these time measurements relied entirely on human response speed. It had been noted that there were small systematic differences in the times measured by different astronomers, and these were first systematically studied by German astronomer Friedrich Bessel
Friedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
(1782–1846). Bessel constructed personal equations from measurements of basic response speed that would cancel out individual differences from the astronomical calculations. Independently, physicist Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
measured reaction times to determine nerve conduction speed.
These two lines of work came together in the research of Dutch physiologist F. C. Donders and his student J. J. de Jaager, who recognized the potential of reaction times for more or less objectively quantifying the amount of time elementary mental operations required. Donders envisioned the employment of his mental chronometry
Mental chronometry
Mental chronometry is the use of response time in perceptual-motor tasks to infer the content, duration, and temporal sequencing of cognitive operations....
to scientifically infer the elements of complex cognitive activity by measurement of simple reaction time
The first psychological laboratory was established in Germany by Wilhelm Wundt
Wilhelm Wundt
Wilhelm Maximilian Wundt was a German physician, psychologist, physiologist, philosopher, and professor, known today as one of the founding figures of modern psychology. He is widely regarded as the "father of experimental psychology"...
, who amply used Donders' ideas. However, findings that came from the laboratory were hard to replicate and this was soon attributed to the method of introspection
Introspection
Introspection is the self-observation and reporting of conscious inner thoughts, desires and sensations. It is a conscious and purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul...
that Wundt introduced. Part of the problems was due to the individual differences in response speed found by astronomers. Although Wundt did not seem to take interest in these individual variations and kept his focus on the study of the general human mind, Wundt's U.S. student James McKeen Cattell
James McKeen Cattell
James McKeen Cattell , American psychologist, was the first professor of psychology in the United States at the University of Pennsylvania and long-time editor and publisher of scientific journals and publications, most notably the journal Science...
was fascinated by these differences and started to work on them during his stay in England.
The failure of Wundt's method of introspection
Introspection
Introspection is the self-observation and reporting of conscious inner thoughts, desires and sensations. It is a conscious and purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul...
led to the rise of different schools of thought. Wundt's laboratory was directed towards conscious human experience, in line with the work of Fechner and Weber on the intensity of stimuli. In the United Kingdom, under the influence of the anthropometric developments led by Francis Galton
Francis Galton
Sir Francis Galton /ˈfrɑːnsɪs ˈgɔːltn̩/ FRS , cousin of Douglas Strutt Galton, half-cousin of Charles Darwin, was an English Victorian polymath: anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician...
, interest focussed on individual differences between humans on psychological variables, in line with the work of Bessel. Catell soon adopted the methods of Galton and helped laying the foundation of psychometrics
Psychometrics
Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...
.
20th century
In the United States, behaviorism arose in opposition to introspectionism and associated reaction-time research, and turned the focus of psychological research entirely to learning theory. In Europe introspection survived in Gestalt psychologyGestalt psychology
Gestalt psychology or gestaltism is a theory of mind and brain of the Berlin School; the operational principle of gestalt psychology is that the brain is holistic, parallel, and analog, with self-organizing tendencies...
. Behaviorism dominated American psychology until the end of the Second World War, and largely refrained from inference on mental processes. Formal theories were mostly absent (except for vision
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...
and audition
Audition
An audition is a sample performance by an actor, singer, musician, dancer or other performing artist.Audition may also refer to:* The sense of hearing* Adobe Audition, audio editing software...
).
During the war, developments in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and computability theory
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, and the military need to understand human performance and limitations
Human factors
Human factors science or human factors technologies is a multidisciplinary field incorporating contributions from psychology, engineering, industrial design, statistics, operations research and anthropometry...
, brought together experimental psychologist, mathematicians, engineers, physicists, and economists. Out of this mix of different disciplines mathematical psychology arose. Especially the developments in signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
, information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, linear systems and filter theory, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, stochastic processes and mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
gained a large influence on psychological thinking.
Two seminal papers on learning theory in Psychological Review
Psychological Review
Psychological Review is a scientific journal that publishes articles on psychological theory. It was founded by Princeton psychologist James Mark Baldwin and Columbia psychologist James McKeen Cattell in 1894 as a publication vehicle for psychologists not connected with the Clark laboratory of G....
helped to establish the field in a world that was still dominated by behaviorists: A paper by Bush and Mosteller instigated the linear operator approach to learning, and a paper by Estes that started the stimulus sampling tradition in psychological theorizing. These two papers presented the first detailed formal accounts of data from learning experiments.
The 1950s saw a surge in mathematical theories of psychological processes, including Luce's theory of choice
Luce's choice axiom
In probability theory, Luce's choice axiom, formulated by R. Duncan Luce , states that the probability of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool...
, Tanner and Swets' introduction of signal detection theory for human stimulus detection, and Miller's approach to information processing. By the end of the 1950s, the number of mathematical psychologists had increased from a handful by more than a tenfold, not counting psychometricians. Most of these were concentrated at the University of Indiana, Michigan, Pennsylvania, and Stanford. Some of these were regularly invited by the U.S. Social Science Research Counsel to teach in summer workshops in mathematics for social scientists at Stanford University, promoting collaboration.
To better define field of mathematical psychology, the mathematical models of the 1950s were brought together in sequence of volumes edited by Luce, Bush, and Galanter: Two readings and three handbooks. This series of volumes turned out to be helpful in the development of the field. In the summer of 1963 the need was felt for a journal for theoretical and mathematical studies in all areas in psychology, excluding work that was mainly factor analytical. An initiative led by R. C. Atkinson
Richard C. Atkinson
Richard Chatham Atkinson is an American professor of psychology and academic administrator. He is the former president and regent of the University of California system, and former chancellor of U.C...
, R. R. Bush, W. K. Estes, R. D. Luce
R. Duncan Luce
Robert Duncan Luce is the Distinguished Research Professor of Cognitive Science at the University of California, Irvine.Luce received a B.S. in Aeronautical Engineering from the Massachusetts Institute of Technology in 1945, and PhD in Mathematics from the same university in 1950...
, and P. Suppes resulted in the appearance of the first issue of the Journal of Mathematical Psychology in January, 1964.
Under the influence of developments in computer science, logic, and language theory, in the 1960s modeling became more in terms of computational mechanisms and devices. Examples of the latter constitute so called cognitive architectures (e.g., production rule systems, ACT-R
ACT-R
ACT-R is a cognitive architecture mainly developed by John Robert Anderson at Carnegie Mellon University. Like any cognitive architecture, ACT-R aims to define the basic and irreducible cognitive and perceptual operations that enable the human mind....
) as well connectionist systems or neural networks
Neural Networks
Neural Networks is the official journal of the three oldest societies dedicated to research in neural networks: International Neural Network Society, European Neural Network Society and Japanese Neural Network Society, published by Elsevier...
.
Important mathematical expressions for relations between physical characteristics of stimuli and subjective perception are Weber's law (which is now sometimes called Weber-Fechner Law), Ekman's Law, Stevens' Power Law
Stevens' power law
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...
, Thurstone's Law of Comparative Judgment
Law of comparative judgment
The law of comparative judgment was conceived by L. L. Thurstone. In modern day terminology, it is more aptly described as a model that is used to obtain measurements from any process of pairwise comparison...
, the Theory of Signal Detection (borrowed from radar engineering), the Matching Law
Matching law
In operant conditioning, the matching law is a quantitative relationship that holds between the relative rates of response and the relative rates of reinforcement in concurrent schedules of reinforcement...
, and Rescorla-Wagner rule
Rescorla-Wagner model
The Rescorla–Wagner model is a model of classical conditioning in which the animal is theorized to learn from the discrepancy between what is expected to happen and what actually happens. This is a trial-level model in which each stimulus is either present or not present at some point in the trial...
for classical conditioning. While the first three laws are all deterministic in nature, later established relations are more fundamentally stochastic. This has been a general theme in the evolution in mathematical modeling of psychological processes: From deterministic relations as found in classical physics to inherently stochastic models.
Influential mathematical psychologists
- John Anderson
- Richard C. AtkinsonRichard C. AtkinsonRichard Chatham Atkinson is an American professor of psychology and academic administrator. He is the former president and regent of the University of California system, and former chancellor of U.C...
- C. H. CoombsClyde CoombsClyde Hamilton Coombs was an American psychologist specializing in the field of mathematical psychology. He devised a voting system, that was hence named Coombs' method....
- Robyn DawesRobyn DawesRobyn Mason Dawes was an American psychologist who specialized in the field of human judgment. His research interests included human irrationality, human cooperation, intuitive expertise, and the United States AIDS policy...
- Ehtibar Dzhafarov
- William EstesWilliam EstesWilliam Estes may refer to:*William Kaye Estes , American scientist*William Lee Estes , U.S. federal judge...
- B. F. Green
- Daniel KahnemanDaniel KahnemanDaniel Kahneman is an Israeli-American psychologist and Nobel laureate. He is notable for his work on the psychology of judgment and decision-making, behavioral economics and hedonic psychology....
- D. H. Krantz
- D. R. J. Laming
- R. Duncan LuceR. Duncan LuceRobert Duncan Luce is the Distinguished Research Professor of Cognitive Science at the University of California, Irvine.Luce received a B.S. in Aeronautical Engineering from the Massachusetts Institute of Technology in 1945, and PhD in Mathematics from the same university in 1950...
- David Marr
- James L. McClelland
- Louis NarensLouis NarensLouis Narens is Professor in the Department of Cognitive Sciences and the Department of Logic and the Philosophy of Science at the University of California, Irvine.He is one of the major exponents of measurement theory in mathematical psychology...
- Allen NewellAllen NewellAllen Newell was a researcher in computer science and cognitive psychology at the RAND corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology...
- David E. Rumelhart
- Herbert A. SimonHerbert SimonHerbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...
- Roger ShepardRoger ShepardRoger Newland Shepard is a cognitive scientist and author of Toward a Universal Law of Generalization for Psychological Science. He is seen as a father of research on spatial relations....
- Stanley S. StevensStanley Smith StevensStanley Smith Stevens was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory and is credited with the introduction of Stevens' power law. Stevens authored a milestone textbook, the 1400+ page "Handbook of Experimental Psychology" . He was also one of the founding organizers...
- Saul SternbergSaul SternbergSaul Sternberg is a Professor Emeritus of Psychology and former Paul C. Williams Term Professor at the University of Pennsylvania. He is a pioneer in the field of cognitive psychology in the development of experimental techniques to study human information processing...
- Patrick Suppes
- John A. SwetsJohn A. SwetsJohn A. Swets is a psychologist. He has played a key role in adaptation of signal detection theory to first the psychology of perception and later as a central tool in medical diagnostics.- Further reading :...
- Joshua TenenbaumJoshua TenenbaumJoshua Tenenbaum is Associate Professor of Cognitive Science and Computation at the Massachusetts Institute of Technology. He is known for contributions to mathematical psychology. Tenenbaum previously taught at Stanford University, where he is presently the Wasow Visiting Fellow.-Life:Tenenbaum...
- Louis L. Thurstone
- Amos TverskyAmos TverskyAmos Nathan Tversky, was a cognitive and mathematical psychologist, a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his early work concerned the foundations of measurement...
- Thomas D. Wickens
Stimulus identification
- Accumulator models
- Diffusion models
- Neural networkNeural networkThe term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...
/connectionist models - Race models
- Random walk models
- Renewal models
Simple decision
- Cascade model
- Level and change race model
- Recruitment model
- SPRT
- Decision field theoryDecision field theoryDecision Field Theory , is a dynamic - cognitive approach to human decision making. It is a cognitive model that describes how people make decisions rather than a rational model that prescribes what people should do...
Journals and organizations
Central journals are the Journal of Mathematical PsychologyJournal of Mathematical Psychology
The Journal of Mathematical Psychology is a peer-reviewed scientific journal established in 1964. It covers all areas of mathematical and theoretical psychology, including sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation...
and the British Journal of Mathematical and Statistical Psychology
British journal of mathematical and statistical psychology
The British Journal of Mathematical and Statistical Psychology is a British scientific journal founded in 1965. It covers the fields of psychology, statistics, and mathematical psychology...
. There are three annual conferences in the field, the annual meeting of the Society for Mathematical Psychology in the U.S, the annual European Mathematical Psychology Group (EMPG) meeting in Europe, and the Australasian Mathematical Psychology conference.
External links
- British Journal of Mathematical and Statistical Psychology
- European Mathematical Psychology Group
- Journal of Mathematical Psychology
- Online tutorials on Mathematical Psychology from the Open Distance Learning initiative of the University of Bonn.
- Society for Mathematical Psychology