A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments
Stephan Poppe, Philipp Benner, and Tobias Elze
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Submission date: 26. Apr. 2012
published in: Journal of mathematical psychology, 56 (2012) 3, p. 179-195
DOI number (of the published article): 10.1016/j.jmp.2012.04.002
Keywords and phrases: Adaptive Sequential Sampling, Optimal Design, Active Learning, Predictive Inference, Psychophysics, Efficient Statistical Computations
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 Pólya 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 theoretic quantities.
The actual computation of information theoretic 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.