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Encyclopedia > Mathematical psychology
Psychology
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RESEARCH Ψ

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Transpersonal Psychology (from Greek: ψυχή, psukhē, spirit, soul; and λόγος, logos, knowledge) is both an academic and applied discipline involving the scientific study of mental processes and behavior. ... Image File history File links Psi2. ... The history of psychology as a scholarly study of the mind and behavior dates, in Europe, back to the Late Middle Ages. ... Experimental psychology is an approach to psychology that treats it as one of the natural sciences, and therefore assumes that it is susceptible to the experimental method. ... Abnormal psychology is the scientific study of abnormal behavior in order to describe, predict, explain, and change abnormal patterns of functioning. ... Biological psychology, sometimes referred to as psychobiology or biopsychology, is a subfield of psychology. ... Cognitive Psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ... Emotional redirects here. ... Experimental psychology is an approach to psychology that treats it as one of the natural sciences, and therefore assumes that it is susceptible to the experimental method. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ... Legal psychology involves the application of empirical psychological research to legal institutions and people who come into contact with the law. ... Neuropsychology is a branch of psychology and neurology that aims to understand how the structure and function of the brain relate to specific psychological processes and overt behaviors. ... Personality psychology is a branch of psychology which studies personality and individual differences. ... Positive psychology is a relatively young branch of psychology that studies the strengths and virtues that enable individuals and communities to thrive. ... Psychonomics describes an approach to psychology that aims at discovering the laws (Greek: nomos) that govern the workings of the mind (Greek: psyche). The field is directly related to experimental psychology. ... Psychophysics is the branch of cognitive psychology dealing with the relationship between physical stimuli and their perception. ... Social psychology is the scientific study of how peoples thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others (Allport, 1985). ... Transpersonal psychology is a school of psychology that studies the transpersonal, the transcendent or spiritual aspects of the human mind. ...

APPLIED Ψ

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Sport The basic premise of applied psychology is the use of psychological principles and theories to overcome practical problems in other fields, such as business management, product design, ergonomics, nutrition, law and clinical medicine. ... The Greek letter Psi is often used as a symbol of psychology. ... This article or section does not cite any references or sources. ... This article or section does not cite any references or sources. ...

LISTS

Publications
Topics
Therapies This is a list of important publications in psychology, organized by field. ... link title Headline text --Cknuth7 16:35, 3 April 2006 (UTC) This page aims to list articles related to psychology. ... This is an alphabetical List of Psychotherapies. ...

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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". Psychology (from Greek: ψυχή, psukhē, spirit, soul; and λόγος, logos, knowledge) is both an academic and applied discipline involving the scientific study of mental processes and behavior. ... Note: The term model is also given a formal meaning in model theory, a part of axiomatic set theory. ...


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, apparently 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. Various meters Measurement is an observation that reduces an uncertainty expressed as a quantity. ... Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, and personality traits. ... Experimental psychology is an approach to psychology that treats it as one of the natural sciences, and therefore assumes that it is susceptible to the experimental method. ... Cognitive Psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. ... Psychonomics describes an approach to psychology that aims at discovering the laws (Greek: nomos) that govern the workings of the mind (Greek: psyche). The field is directly related to experimental psychology. ...


Mathematical psychologists are active in many fields of psychology, especially in psychophysics, sensation and perception, problem solving, decision-making, learning, memory and language, and the quantitative analysis of behavior but also, e.g., in clinical psychology, social psychology, and psychology of music. Psychophysics is the branch of cognitive psychology dealing with the relationship between physical stimuli and their perception. ... It has been suggested that this article or section be merged with Sensation and perception psychology. ... In psychology and the cognitive sciences, perception is the process of acquiring, interpreting, selecting, and organizing sensory information. ... Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... In psychology, memory is an organisms ability to store, retain, and subsequently retrieve information. ... The Greek letter Psi is often used as a symbol of psychology. ... The scope of social psychological research. ... Music psychology, or the psychology of music, may be regarded either as a branch of psychology or as a branch of musicology. ...

Contents

History

Ernst Heinrich Weber
Ernst Heinrich Weber
Gustav Fechner
Gustav Fechner

Mathematical modeling has a long tradition in Psychology. Heinrich Weber (1795–1878) and Gustav Fechner (1801–1887) were among the first to apply successful mathematical techniques from physics to psychological processes, thereby establishing the fields of experimental psychology in general, and within that psychophysics in particular. Image File history File links Size of this preview: 458 × 599 pixelsFull resolution (515 × 674 pixel, file size: 63 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Size of this preview: 458 × 599 pixelsFull resolution (515 × 674 pixel, file size: 63 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Download high-resolution version (774x1100, 564 KB) Gustav Theodor Fechner (1801–1887), German experimental psychologist. ... Image File history File links Download high-resolution version (774x1100, 564 KB) Gustav Theodor Fechner (1801–1887), German experimental psychologist. ... Ernst Heinrich Weber, born on June 24, 1795 in Wittenberg, died on January 26, 1878 was a German physician. ... Gustav Theodor Fechner (April 19, 1801 - November 28, 1887), was a German experimental psychologist. ... Experimental psychology is an approach to psychology that treats it as one of the natural sciences, and therefore assumes that it is susceptible to the experimental method. ... Psychophysics is the branch of cognitive psychology dealing with the relationship between physical stimuli and their perception. ...


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 Judgement, 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. The Weber - Fechner law attempts to describe the relationship between the physical magnitudes of stimuli and human perception of the intensity of stimuli. ... Stevens power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. ... Signal detection theory, or SDT, is a means to quantify the ability to discern between signal and noise. ... 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. ... The Rescorla-Wagner model is a model of classical conditioning in which the animal is theorized to learn from the discrepancy between what it predicted would happen and what actually happened. ...


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. A cognitive architecture is a blueprint for intelligent agents. ... A production system (or production rule system) is a computer program typically used to provide some form of artificial intelligence, which consists primarily of a set of rules about behavior. ... ACT-R (pronounced act-ARE: Adaptive Control of Thought--Rational) is a cognitive architecture mainly developed by John R. Anderson at Carnegie Mellon University. ... Connectionism today generally refers to an approach in the fields of cognitive psychology, cognitive science and philosophy of mind which models mental or behavioral phenomena with neural networks, and is associated with a certain set of arguments for why this is a good idea. ... A neural network is an interconnected group of neurons. ...


Influential Mathematical Psychologists

Richard C. Atkinson (born March 1929) served as the president of the University of California from 1995 to 2003. ... William Kaye Estes is an American scientist. ... Daniel Kahneman Daniel Kahneman (born March 5, 1934 in Tel Aviv, in the then British Mandate of Palestine, now in Israel), is a key pioneer and theorist of behavioral finance, which integrates economics and cognitive science to explain seemingly irrational risk management behavior in human beings. ... R. Duncan Luce is the Distinguished Research Professor of Cognitive Science at the University of California, Irvine. ... There is also an Australian journalist and biographer named David Marr. ... James L. (Jay) McClelland (born December 1, 1948) is a Professor of Psychology and Cognitive Neuroscience at Carnegie Mellon University. ... Louis Narens is Professor in Department of Cognitive Sciences and Department of Logic and the Philosophy of Science at University of California, Irvine. ... Allen Newell (March 19, 1927 - July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND corporation and at Carnegie-Mellon’s School of Computer Science. ... David E. Rumelhart has made many contributions to the formal analysis of human cognition, working primarily within the frameworks of mathematical psychology, symbolic artificial intelligence, and parallel distributed processing. ... Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American political scientist whose research ranged across the fields of cognitive psychology, computer science, public administration, economics, management, and philosophy of science and a professor, most notably, at Carnegie Mellon University. ... Stanley Smith Stevens (1906-1973) was an American psychologist best known as the founder of Harvards Psycho-Acoustical Laboratory and credited with the introduction of Stevens power law. ... Patrick Colonel Suppes (b. ... Louis Leon Thurstone (29 May 1887–30 September 1955) was a U.S. pioneer in the fields of psychometrics and psychophysics. ... Amos Tversky (March 16, 1937 - June 2, 1996) was 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. ...

Important theories and models[1]

Sensation, Perception, and Psychophysics

  • Weber-Fechner Law
  • Stevens' Power Law

Simple detection

  • Signal Detection Theory

Stimulus identification

  • Accumulator models
  • Random Walk models
  • Diffusion models
  • Renewal models
  • Race models
  • Neural network/connectionist models

Simple decision

  • Recruitment model
  • Cascade model
  • Level and Change Race model
  • SPRT

Memory scanning, visual search

  • Serial exhaustive search (SES) model
  • Push-Down Stack

Error response times

  • Fast Guess model

Sequential Effects

  • Linear Operator model

Learning

  • Stochastic Learning theory

Journals and Organizations

Central journals are the Journal of Mathematical Psychology and the British Journal of Mathematical and Statistical Psychology. There are two annual conferences in the field, the annual meeting of the Society for Mathematical Psychology in the U.S, and the annual European Mathematical Psychology Group (EMPG) meeting.


External Links

  • Journal of Mathematical Psychology
  • British Journal of Mathematical and Statistical Psychology
  • Society for Mathematical Psychology
  • European Mathematical Psychology Group
  • Online tutorials on Mathematical Psychology from the Open Distance Learning initiative of the University of Bonn.

References

  1. ^ Luce, R. D. (1986) Response Times (Their Role in Inferring Elementary Mental Organization)". New York: Oxford University Press.

  Results from FactBites:
 
[Islam-Online- Psychology] (1052 words)
Many historians of psychology consider Fechner to be the founder of psychophysics and thus the founder of quantitative psychology.
Psychophysics, already related to psychology and physics by name, must on the one hand be based on psychology and on the other hand give psychology a mathematical foundation.
If mathematical psychology is possible, it must be founded on the basis of material phenomena that underlie the psychical, because they allow a direct mathematical approach and definite measurement, as is not true with respect to the psychical.
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Developmental Psychology - Developmental psychology is concerned with the behavioral, affective, and cognitive characteristics of the developing organism from conception to death.
Although developmental psychology utilizes theoretical and methodological contributions from many disciplines, the fundamental emphasis is upon the processes underlying growth and change in behavioral development across the life span.
Quantitative-Mathematical Psychology - The area of quantitative-mathematical psychology embraces all aspects of psychology that are of a mathematical or statistical nature, including the broad area of measurement.
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