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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. The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. Quantifiable behavior is in practice 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. ==History== 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. Some of the problems resulted from 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mathematical psychology」の詳細全文を読む スポンサード リンク
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