Mathematical psychology can be defined as “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 observing the "quantifiable behavior" is habitually constituted by "task performance".
As quantification of behavior is essential in this venture, the theory of measurement is a vital theme in mathematical psychology. There is a close relation to psychometrics in regard to mathematical psychology. On the other hand, wherever psychometrics is apprehensive with individual differences (or population structure) in typically static variables, mathematical psychology has its focus on progression models of perceptual, cognitive and motor processes as contingent from the 'average individual'.
Mathematical psychology more or less utterly has its focus on the modeling of data obtained by means of experimental paradigms and is consequently still more very much related to experimental psychology/cognitive psychology/psychonomics. Moreover, everywhere the psychometrics investigates the stochastic dependence structure among variables that are pragmatic in the population.
Similar to computational neuroscience and econometrics, mathematical psychology theory regularly uses statistical optimality as a guiding principle, presumptuous that the human brain has evolved to work out the troubles in an optimized way.
Mathematical psychologists are full of life i.e. energetic in numerous fields of psychology, particularly in psychophysics, problem solving, sensation and perception, memory, learning, decision-making, and language, together known as cognitive psychology, and the quantitative investigation of behavior.
To get an enhanced definition for the mathematical psychology, it can be termed this way: “the mathematical models during the year 1950s were brought collectively in series of volumes edited by Luce, Bush, and Galanter: Two readings and three handbooks. This series of volumes were of a great help in the development of the field of mathematical psychology.
The vital journals are the Journal of Mathematical Psychology and the British Journal of Mathematical and Statistical Psychology. Presently 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.”