Likelihood-free simulation-based optimal design with an application to spatial extremes

Abstract

In this paper we employ a novel method to find the optimal design for problems where the likelihood is not available analytically, but simulation from the likelihood is feasible. To approximate the expected utility we make use of approximate Bayesian computation methods. We detail the approach for a model on spatial extremes, where the goal is to find the optimal design for efficiently estimating the parameters determining the dependence structure. The method is applied to determine the optimal design of weather stations for modeling maximum annual summer temperatures.Electronic supplementary materialThe online version of this article (doi:10.1007/s00477-015-1067-8) contains supplementary material, which is available to authorized users.

SSNdesign—An R package for pseudo-Bayesian optimal and adaptive sampling designs on stream networks

“…We refer to the optimal configuration of sites as d � . Inside SSNdesign, the quality of a design and its suitability for a stated goal is measured using a function called the expected utility U(d) [13]. Larger values of U(d) indicate better designs and the calculation of U(d) is linked to the utility function, U (d, θ, y).…”

“…The theoretical properties of geostatistical models can also be exploited in optimal and adaptive experimental designs [13][14][15][16], which are used to select sampling locations that maximize information gain and minimize costs. However, the exact locations included in an optimal design will depend on the objectives of the monitoring program.…”

“…Bayesian and pseudo-Bayesian methods can enhance optimal and adaptive designs. Utility functions often depend on the parameters of the geostatistical model that one intends to fit over the design; however, the utility function can only be evaluated when these parameter values are fixed [13]. If the values change, for example, through random variations in field conditions, then the design may no longer be optimal.…”

“…To our knowledge, SSNdesign is the first software package that allows users to optimise experimental designs on stream networks using geostatistical models and covariance functions that account for unique stream characteristics within a robust design framework. It combines the statistical modelling functionality found in the SSNpackage [20] with principles of pseudo-Bayesian design [13] into a generalised toolkit for solving optimal and adaptive design problems on stream networks. In Section 2, we discuss the mathematical principles underpinning these tools and outline the structure of the core functions in SSNdesign package along with a summary of the package's speed and performance.…”

Spectral density regression for bivariate extremes

“…Extreme values play a key role in environmental research and risk assessment (see for instance Wang et al, 2014;Fernández-Ponce and Rodríguez-Griñolo, 2015;Hainy et al, 2016). Modeling nonstationarity in marginal distributions has been the focus of much recent literature in applied extreme value modelling.…”