Progress in European Mathematical Psychology

It is commonplace, when discussing the subject of psychological theory, to write articles from the assumption that psychology differs from the physical sciences in that we have no theories that would support cumulative, incremental science. In this brief article I discuss one counterexample: Shepard’s law of generalization and the various Bayesian extensions that it inspired over the past 3 decades. Using Shepard’s law as a running example, I argue that psychological theory building is not a statistical problem, mathematical formalism is beneficial to theory, measurement and theory have a complex relationship, rewriting old theory can yield new insights, and theory growth can drive empirical work. Although I generally suggest that the tools of mathematical psychology are valuable to psychological theorists, I also comment on some limitations to this approach.

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Mathematical psychology and psychophysiology

Journal of Mathematical Psychology ◽

10.1016/0022-2496(83)90032-9 ◽

1983 ◽

Vol 27 (1) ◽

pp. 118-119

Author(s):

Alwyn C. Scott

Keyword(s):

Mathematical Psychology

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A historical and contemporary perspective on random scale representations of choice probabilities and reaction times in the context of , Journal of Mathematical Psychology, 34) results

Journal of Mathematical Psychology ◽

10.1016/0022-2496(90)90013-y ◽

1990 ◽

Vol 34 (1) ◽

pp. 81-87 ◽

Cited By ~ 22

Author(s):

A.A.J. Marley

Keyword(s):

Reaction Times ◽

Mathematical Psychology ◽

Contemporary Perspective ◽

Random Scale ◽

Choice Probabilities

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Ising formulations of some graph-theoretic problems in psychological research: models and methods

10.31234/osf.io/4udfw ◽

2020 ◽

Author(s):

Michael Brusco ◽

Clintin Davis-Stober ◽

Douglas Steinley

Keyword(s):

Paired Comparison ◽

Psychological Research ◽

Directed Acyclic Graphs ◽

Spin Model ◽

Mathematical Psychology ◽

Linear Ordering ◽

Spin Models ◽

Graph Theoretic ◽

Algorithm Efficiency ◽

Ising Spin

It is well known that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a particular history in mathematical psychology, most notably max-cut clustering, graph coloring, a linear ordering problem related to paired comparison ranking and directed acyclic graphs, and the problem of finding a minimum subset of points necessary to contain another point within a convex hull. New Ising spin models are presented for the latter two problems. In addition, we provide MATLAB software programs for obtaining solutions via enumeration of all spin ensembles (when computationally feasible) and simulated annealing. Although we are not advocating that the Ising spin model is the preferred approach for formulation and solution of graph-theoretic problems on conventional digital computers, it does provide a unifying framework for these problems. Moreover, recent progress in the development of quantum computing architecture has shown that Ising spin models can afford enormous improvements in algorithm efficiency when implemented on these platforms, which may ultimately lead to widespread use of the methodology in the future.

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