The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics, motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the first title in this field to be published, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. This first volume focuses on select mathematical ideas, theories, and modeling approaches to form a foundational treatment of mathematical psychology.

The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the original Handbook, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. The second volume focuses on areas of mathematics that are used in constructing models of cognitive phenomena and decision making, and on the role of measurement in psychology.

Measurement and Representation of Sensations offers a glimpse into the most sophisticated current mathematical approaches to psychophysical problems. In this book, editors Hans Colonius and Ehtibar N. Dzhafarov, top scholars in the field, present a broad spectrum of innovative approaches and techniques to classical problems in psychophysics at different levels of stimulus complexity. The chapters emphasize rigorous mathematical constructions to define psychophysical concepts and relate them to observable phenomena. The techniques presented, both deterministic and probabilistic, are all original and recent. Subjects addressed throughout the six chapters of this volume include: *computing subjective distances from discriminability; *a new psychophysical theory of intensity judgments; *computing subjective distances from two discriminability functions; *an alternative to the model-building approach based on observable probabilities; and *possible forms of perceptual separability developed within a generalization of General Recognition Theory. Measurement and Representation of Sensations is a valuable text for both behavioral scientists and applied mathematicians.

"Measurement and Representation of Sensations "offers a glimpse into the most sophisticated current mathematical approaches to psychophysical problems. In this book, editors Hans Colonius and Ehtibar N. Dzhafarov, top scholars in the field, present a broad spectrum of innovative approaches and techniques to classical problems in psychophysics at different levels of stimulus complexity. The chapters emphasize rigorous mathematical constructions to define psychophysical concepts and relate them to observable phenomena. The techniques presented, both deterministic and probabilistic, are all original and recent.
 
Subjects addressed throughout the six chapters of this volume include:
*computing subjective distances from discriminability;
*a new psychophysical theory of intensity judgments;
*computing subjective distances from two discriminability functions;
*an alternative to the model-building approach based on observable probabilities; and
*possible forms of perceptual separability developed within a generalization of General Recognition Theory.
 
"Measurement and Representation of Sensations" is a valuable text for both behavioral scientists and applied mathematicians.

The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made both in traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the original Handbook, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. The third volume provides up-to-date, foundational chapters on early vision, psychophysics and scaling, multisensory integration, learning and memory, cognitive control, approximate Bayesian computation, and encoding models in neuroimaging.

The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the original Handbook, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. The second volume focuses on areas of mathematics that are used in constructing models of cognitive phenomena and decision making, and on the role of measurement in psychology.

The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics, motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the first title in this field to be published, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. This first volume focuses on select mathematical ideas, theories, and modeling approaches to form a foundational treatment of mathematical psychology.

In der vor1iegenden Arbeit wird versucht, stochasti- sche Theorien des mensch1ichen Wah1verha1tens aus der Perspektive der MeBtheorie darzuste11en. Das BemUhen urn eine einheit1iche Formu1ierung der Mode11e hat eine lange Tradition (vg1. den Oberb1icksartike1 von LUCE & SUPPES,1965). Ein vorrangiges Zie1 dieser Form der Analyse ist die Her1eitung von Eigenschaften, die die Mode11e identifizierbar und empirisch UberprUfbar machen. Dies ist bis heute nur tei1weise ge1ungen. Eine wesent1iche Ursache hierfUr dUrfte in der stochastischen FQrmu1ierung der Theorien 1iegen, die jedoch fUr eine angemessene Beschreibung der Verha1tensdaten unabding- bar ist. In den fo1genden Kapite1n soll zumindest exem- p1arisch gezeigt werden, daB die Heranziehung bzw. Ent- wick1ung geeigneter wahrschein1ichkeitstheoretischer Hi1fsmitte1 zur Losung der offenen Prob1eme beitragen kann. Die Darste11ung erhebt keinen Anspruch auf Vo11standig- keit. FUr einen Oberb1ick sei auf LUCE & SUPPES (1965) sowie HOLMAN & MARLEY (1974) verwiesen. Empirische Er- gebnisse wurden nur in dem MaBe herangezogen, in we1chem sie direkten Einf1u6 auf die Mode11bi1dung genommen haben. Auch die wichtigen Prob1eme der Parameterschatzung und der statistischen OberprUfung der Mode11e wurden weitgehend auBer acht ge1assen.