A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments

Citation:

Poppe S, Benner P, Elze T. A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments. Journal of Mathematical Psychology. 2012;56:179–195.

Abstract:

We present a predictive account on adaptive sequential sampling of stimulus-response relations in psychophysical experiments. Our discussion applies to experimental situations with ordinal stimuli when there is only weak structural knowledge available such that parametric modeling is no option. By introducing a certain form of partial exchangeability, we successively develop a hierarchical Bayesian model based on a mixture of Polya urn processes. Suitable utility measures permit us to optimize the overall experimental sampling process. We provide several measures that are either based on simple count statistics or more elaborate information theoretical quantities. The actual computation of information theoretical utilities often turns out to be infeasible. This is not the case with our sampling method, which relies on an efficient algorithm to compute exact solutions of our posterior predictions and utility measures. Finally, we demonstrate the advantages of our framework on a hypothetical sampling problem. (C) 2012 Elsevier Inc. All rights reserved.