MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Stephan Poppe, Philipp Benner and Tobias Elze


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.

Adaptive Sequential Sampling, Optimal Design, Active Learning, Predictive Inference, Psychophysics, Efficient Statistical Computations

Related publications

2012 Repository Open Access
Stephan Poppe, Philipp Benner and Tobias Elze

A predictive approach to nonparametric inference for adaptive sequential sampling of psychophysical experiments

In: Journal of mathematical psychology, 56 (2012) 3, pp. 179-195