## ABCD: Approximate Bayesian Computing Design

**Werner Mueller (Johannes Kepler Universitat Linz, Austria)**

We are concerned with improving data collecting schemes via methods of optimum experimental design, which can be applied in cases where the experimenter has at least partial control over the experimental conditions. Furthermore we focus on cases where a probability model for the investigated phenomenon is not easily available and the situation lends itself naturally to simulation-based approaches in conjunction with a recently popularized simulation technique called approximate Bayesian computing (ABC).

The objective of optimum experimental design is to find the best possible configuration of factor settings with respect to a well-defined criterion or measure of information for a specific statistical model. In Bayesian experimental design, a prior distribution is attached to the parameters of the statistical model. This prior distribution reflects prior knowledge about the parameters of the model. In the Bayesian setting it is natural to average a criterion over the parameter values with respect to the prior distribution. In a decision-theoretic approach to experimental design the criterion of interest is computed for the posterior distribution of the parameters and then averaged over the marginal distribution of the data. The information criterion on the posterior distribution reflects some notion of learning from the observations.

The computation of the expected criterion value can be a challenging task. Usually this involves the evaluation of integrals or sums. If the integrals are analytically intractable and numerical integration routines do not work, Monte Carlo simulation strategies can be applied in a framework of stochastic optimization. Some of our proposed methods will be based on simulation-based optimal design algorithms which utilize Markov chain Monte Carlo (MCMC) methods, but we intend to go beyond that class. Simulation-based methods make it possible to efficiently solve a wider range of problems for which standard methods cannot provide tractable solutions. In this presentation we outline potentials and limitations of ABC for design purposes. Furthermore we will report details on an application for dealing with spatial extremes.

References:

Hainy, M., Müller, W. G., Wynn, H. P., 2013. Approximate Bayesian computation design (ABCD), an introduction. In: Ucinski, D., Atkinson, A. C., Patan, M. (Eds.), mODa 10 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Springer International Publishing, pp. 135-143.

Hainy, M., Müller, W., Wagner, H., 2015. Likelihood-free simulation-based optimal design with an application to spatial extremes. Stochastic Environmental Research and Risk Assessment, 1-12.