Bayesian Method for Repeated Threshold Estimation

Abstract:

We propose a method for estimating perceptual learning curves from long sequences of low-quality 2AFC data. Perceptual learning experiments require naive observers and very long schedules. Motivation is low and lapse rates are high. The good news is that there are thousands of observations. Our objective is to track the threshold of interest with as fine temporal resolution as possible. The method uses long, overlapping data sequences to obtain a joint posterior distribution of the lapse rate and other "nuisance" parameters of the psychometric function. With this information, the threshold can be estimated reliably from short data segments. A MATLAB routine approximates the Bayesian distributions on a 3-dimensional grid, assuming a Weibull psychometric function. Monte Carlo simulations validate the method and compare it with standard methods that treat each data block independently. The mode of the posterior threshold distribution is a nearly unbiased estimator of the true threshold. The posterior mean and median are unbiased too, but have slightly higher variance than the mode. The posterior threshold distribution tends to underestimate the sampling variance of the true threshold. It is advantageous to include a few high-intensity presentations in each block to stabilize the estimate of the lapse rate. Concurrent estimation of the psychometric slope is possible but less reliable than the threshold estimation. The method is applied on behavioral data from a perceptual learning study of orientation discrimination of Gabor patches embedded in visual noise. MATLAB software available at http://alexpetrov.com/softw/

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