A Poisson random walk model of response times.

Abstract

Based on the simple what first comes to mind rule, the theory of visual attention (TVA; Bundesen, 1990) provides a comprehensive account of visual attention that has been successful in explaining performance in visual categorization for a variety of attention tasks. If the stimuli to be categorized are mutually confusable, a response rule based on the amount of evidence collected over a longer time seems more appropriate. In this paper, we extend the idea of a simple race to continuous sampling of evidence in favor of a certain response category. The resulting Poisson random walk model is a TVA-based response time model in which categories are reported based on the amount of evidence obtained. We demonstrate that the model provides an excellent account for response time distributions obtained in speeded visual categorization tasks. The model is mathematically tractable and its parameters are well founded and easily interpretable. We also provide an extension of the Poisson random walk to any number of response alternatives. We tested the model in experiments with speeded and non-speeded binary responses and a speeded response task with multiple report categories. The Poisson random walk model agreed very well with the data. A thorough investigation of processing rates revealed that the perceptual categorizations described by the Poisson random walk were the same as those obtained from TVA. The Poisson random walk model could therefore provide a unifying account of attention and response times.

Extending systems factorial technology to errored responses.

“…Diffusion models assume a kind of random walk back and forth on continuous evidence regarding the two choices (Ratcliff, 1978). Although discrete state-space random walks are possible (e.g., Link & Heath, 1975) and random walk models based on Poisson distributions have now appeared (Blurton et al, 2020), we focus on the continuous state-space models here with the usual underlying Wiener process noise system.…”

The Autocorrelated Bayesian Sampler: A Rational Process for Probability Judgments, Estimates, Confidence Intervals, Choices, Confidence Judgments, and Response Times

“…SPRT accumulates log-likelihood ratios of the observed evidence sequence and guarantees the smallest number of sampled pieces of evidence to reach a prescribed level of accuracy (Wald, 2004). This rule has been implemented in, for instance, the drift diffusion model and the Poisson random walk model (Ratcliff & Rouder, 1998;Blurton et al, 2020;Nosofsky & Palmeri, 1997). Similarly, here, the sampling algorithm of ABS is terminated when one choice has accumulated some criterion amount of evidence, ∆N, more than the other alternative (see Figure 1 for an illustration when ∆N = 2).…”

“…Regardless of whether the sampling algorithm operates in physical or biological machinery, producing a new sample takes times. One classical approach to model response times for sequential arrival of samples is the Poisson process (Blurton et al, 2020;Nosofsky & Palmeri, 1997). In this approach, the inter-sample interval is exponentially distributed and the average number of samples for a fixed amount of time is constant (λ).…”

“…The RT distribution for a fixed N samples will follow a positively skewed distribution. Combined with a random walk model of the decision process, the Poisson process provides a good fit with response time distributions (Blurton et al, 2020). As we here focus on qualitative model predictions, we somewhat arbitrarily set the average sampling rate at 0.1 per second.…”

“…Despite strong empirical evidence of, and a computational rationale for, autocorrelation in behaviours both between-and within-trial, models of choice, confidence, and response time quite often assume that each piece of evidence is independent of the last, even if the evidence accumulation process is not (Blurton, Kyllingsbaek, Nielsen, & Bundesen, 2020;Ratcliff & Rouder, 1998;Pleskac & Busemeyer, 2010;Usher & McClelland, 2001;Nosofsky & Palmeri, 1997). We instead assume that people use computationally cheaper, local sampling algorithms in the hypothesis space.…”