# Bayesian hierarchical estimation of visual change detection using Gaussian Markov Random Field priors

In the visual change detection paradigm, observers are shown two stimuli in succession, labeled x and y, and are asked to report whether they are the same or different. The goal in such studies is to determine the probability that an observer will detect a difference as a function of the stimuli, represented by f(x, y). However, when the number of possible stimuli is large, it is infeasible to sample all (x, y) combinations. Bayesian hierarchical models offer a solution to this problem by introducing statistical dependencies between variables (e.g., different observers or different stimuli). In this work, we utilize a Gaussian Markov Random Field (GMRF) prior to estimate visual sensitivity. GMRFs are a technique from spatial statistics that introduces dependencies between variables based on their proximity. As applied to the change detection paradigm, such a prior assumes that f(x, y) should be similar to f(x + delta, y). Our approach allows for the estimation of the complete function f(x, y) even when the stimulus space is sparsely sampled. Posterior inference for the model is performed using MCMC, implemented via the Stan software package. We apply our approach to a change detection experiment in which stimuli were visually complex animations of geologic faults varying in their structural features. Research participants were novices to the domain of geology, who first underwent one of two training sessions that introduced knowledge of different geologic fault categories. Our analysis reveals a significant effect of category knowledge on visual working memory performance.

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