Journal of Mathematical Psychology最新文献

Think about a thought. Easy to do but where does the thought come from? How is it created? Can it be measured? If so what in the mind is measured? This presentation describes a method for answering these basic questions. The answers derive from a new experimental method called Directly Measured Stimulus Differences (DMSD) and a new theory of mental measurement, a cybernetic process, for the creation of thought. The ideas of Prime Thought and Prime Mind are introduced.

A sequence of visual or auditory events may be perceived as a single continuing sequence or as two or more separate sequences occurring in parallel. The latter percept occurs when the perceived distance between events is large, and the timing is fast, and is referred to as “streaming.” Several researchers have previously argued that streaming indicates a velocity constraint on the movement of attention. To test this hypothesis the present experiment measured tradeoffs between distance and timing for the onset or loss of streaming in a rectangular pattern of displayed lights. Two linear tradeoffs were found, one corresponding to the loss of streaming when the light pattern was slowed down, and one corresponding to the onset of streaming when the light pattern was sped up. The slopes of these linear relations are interpreted as integer multiples of the velocity of spatio-temporal attention waves. A process model postulates that participants adjust the wavelength of their spatio-temporal attentional traveling wave to match the height of the displayed rectangle. Streaming is assumed to occur when peaks in the attentional traveling wave coincide with the onsets of lights at the top and bottom of the displayed rectangle. Additional supporting evidence for temporal and spatial attention waves is reviewed. This model may be useful for understanding some forms of attentional deficits as well as expert attentional skills arising in musical performance, sports, meditation, and other tasks.

The human’s capacity to perceptually entrain to an auditory rhythm has been repeatedly modeled as a dynamical system consisting of one or more forced oscillators. However, a more recent perspective, closely related to the popular theory of Predictive Processing, treats auditory entrainment as an inference process in which the observer infers the phase, tempo, and/or metrical structure of an auditory stimulus based on event timing. Here, we propose a close relationship between these two perspectives. We show for the first time that a system performing variational Bayesian inference about the circular phase underlying a rhythmic stimulus takes the form of a forced, damped oscillator with a specific nonlinear phase response function corresponding to the internal metrical model of the underlying rhythm. This algorithm can be extended to simultaneous inference on both phase and tempo using one of two possible approximations that closely align with the two most prominent models of auditory entrainment: one yields a single oscillator with an adapting period, and the other yields a networked bank of oscillators. We conclude that an inference perspective on rhythm perception can offer similar descriptive power and flexibility to a dynamical systems perspective while also plugging into the fertile unifying framework of Bayesian Predictive Processing.

The APA encourages authors to thoroughly report their results, including confidence intervals. However, considerable debate exists regarding the computation of confidence intervals in within-subject designs. Nathoo et al.’s (2018) recently proposed a Bayesian within-subject credible interval, which has faced criticism for not accounting for the uncertainty associated with estimating subject-specific effects. In this article, we show how Nathoo et al.’s within-subject credible interval can be easily corrected by utilizing the theory of degrees of freedom. This correction obviates the necessity for estimates of subject-specific effects that offer shrinkage. Instead, it involves a straightforward adjustment in degrees of freedom in both the interaction mean squares and the $t$-distribution used to compute the interval. Therefore, our proposed interval, being easily computable through a simple formula, eliminates the need for fully Bayesian approaches. It accurately represents uncertainty and offers the interpretational benefit of Bayesian intervals.

Two intriguing papers of the late 1990’s and early 2000s by J. Tanaka and colleagues put forth the hypothesis that a repository of face memories can be viewed as a vector space where points in the space represent faces and each of these is surrounded by an attractor field. This hypothesis broadens the thesis of T. Valentine that face space is constituted of feature vectors in a finite dimensional vector space (e.g., Valentine, 2001). The attractor fields in the atypical part of face space are broader and stronger than those in typical face regions. This notion makes the substantiated prediction that a morphed midway face between a typical and atypical parent will be perceptually more similar to the atypical face. We propose an alternative interpretation that takes a more standard geometrical approach but also departs from the popular types of metrics assumed in almost all multidimensional scaling studies. Rather we propose a theoretical structure based on our earlier investigations of non-Euclidean and especially, Riemannian Face Manifolds (e.g., Townsend, Solomon, & Spencer-Smith, 2001). We assert that this approach avoids some of the issues involved in the gradient theme by working directly with the type of metric inherently associated with the face space. Our approach emphasizes a shift towards a greater emphasis on non-Euclidean geometries, especially Riemannian manifolds, integrating these geometric concepts with processing-oriented modeling. We note that while fields like probability theory, stochastic process theory, and mathematical statistics are commonly studied in mathematical psychology, there is less focus on areas like topology, non-Euclidean geometry, and functional analysis. Therefore, both to elevate comprehension as well as to propagate the latter topics as critical for our present and future enterprises, our exposition moves forward in a highly tutorial fashion, and we embed the material in its proper historical context.

In the past years, several theories for assessment have been developed within the overlapping fields of Psychometrics and Mathematical Psychology. The most notable are Item Response Theory (IRT), Cognitive Diagnostic Assessment (CDA), and Knowledge Structure Theory (KST). In spite of their common goals, these frameworks have been developed largely independently, focusing on slightly different aspects. Yet various connections between them can be found in literature. In this contribution, Part I of a three-part work, a unified perspective is suggested that uses two primitives (structure and process) and two operations (factorization and reparametrization) to derive IRT, CDA, and KST models. A Taxonomy of models is built using a two-processes sequential approach that captures the similarities between the conditional probabilities featured in these models and separates them into a first process modeling the effects of individual ability on item mastering, and a second process representing the effects of pure chance on item solving.

This paper explores a relationship between lexicographic and majority preferences as a novel explanation of preference cycles in choice. Already May (1954) notes that, among subjects in his experiment who did not display a (majority) preference cycle, a vast majority ordered alternatives according to an attribute that they found overridingly important, suggesting that a lexicographic heuristic was used. Our model, Lexicographic Majority, reconciles these findings by providing a unified framework for lexicographic and simple majority preferences. We justify lexicographic majority preferences by providing an axiomatization in terms of behavioral properties.

The multiplicative inequality (MI) introduced by Sattath and Tversky (1976) is a rare example of a simple and intuitively appealing condition relating choice probabilities across choice sets of different sizes. It is also a testable implication of two models of stochastic discrete choice: the Elimination by Aspects model of Tversky (1972b) and the independent random utility model. We prove several results on the multiplicative inequality and its relationship to the regularity condition. One major result illustrates how little the MI constrains binary choice probabilities: it implies that every system of binary choice probabilities on a universe of choice objects can be extended to a complete system of choice probabilities satisfying the MI. In this sense, the MI is complementary to axioms for binary choice probabilities, of which many have been proposed. We also discuss choice environments where the multiplicative inequality is implausible.

Action-feedback delay during operation reduces sense of agency (SoA). In this study, using information-theoretic free energy, we formalized a novel mathematical model for explaining the influence of delay on SoA in continuous operations. Based on the mathematical model, we propose that visualization of predicted future outcomes prevents SoA degradation resulting from response delays. Model-based simulations and operational experiments with participants confirmed that operational delay considerably reduces SoA. Furthermore, the proposed visualization mitigates these problems. Our findings support the model-based interface design for continuous operations with delay to prevent SoA degradation.