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

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.

[1]  P. Müller.  Simulation Based Optimal Design , 2005 .

[2]  Jürgen Pilz,et al.  Spatial sampling design and covariance-robust minimax prediction based on convex design ideas , 2010 .

[3]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[4]  H. Bayraktar,et al.  A Kriging-based approach for locating a sampling site—in the assessment of air quality , 2005 .

[5]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[6]  Arnaud Doucet,et al.  An adaptive sequential Monte Carlo method for approximate Bayesian computation , 2011, Statistics and Computing.

[7]  P. Müller,et al.  Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation , 2004 .

[8]  L. de Haan,et al.  A Spectral Representation for Max-stable Processes , 1984 .

[9]  S. Coles,et al.  Inference for Stereological Extremes , 2007 .

[10]  Markus Hainy,et al.  Approximate Bayesian Computation Design (ABCD), an Introduction , 2013 .

[11]  James V. Zidek,et al.  Designing environmental monitoring networks to measure extremes , 2007, Environmental and Ecological Statistics.

[12]  S. Sisson,et al.  Likelihood-free Markov chain Monte Carlo , 2010, 1001.2058.

[13]  Helga Wagner,et al.  Likelihood-free Simulation-based Optimal Design , 2013 .

[14]  A. Davison,et al.  Statistical Modeling of Spatial Extremes , 2012, 1208.3378.

[15]  Paul Fearnhead,et al.  Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC , 2010, 1004.1112.

[16]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[17]  H. Joe.  Multivariate extreme value distributions , 1997 .

[18]  David Welch,et al.  Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems , 2009, Journal of The Royal Society Interface.

[19]  Xun Huan,et al.  Simulation-based optimal Bayesian experimental design for nonlinear systems , 2011, J. Comput. Phys..

[20]  Anthony C. Davison,et al.  Statistical Modelling of Spatial Extremes , 2012 .

[21]  Anthony N Pettitt,et al.  Bayesian Experimental Design for Models with Intractable Likelihoods , 2013, Biometrics.

[22]  Léo R. Belzile,et al.  Multivariate Extreme Value Distributions , 2015 .

[23]  Richard L. Smith,et al.  Approximate Bayesian computing for spatial extremes , 2011, Comput. Stat. Data Anal..

[24]  Jesús López Fidalgo,et al.  Moda 8 - Advances in Model-Oriented Design and Analysis , 2007 .

[25]  Robert J. Erhardt,et al.  Weather Derivative Risk Measures for Extreme Events , 2014 .

[26]  Scott M. Lesch,et al.  Sensor-directed response surface sampling designs for characterizing spatial variation in soil properties , 2005 .

[27]  Michael P. H. Stumpf,et al.  Maximizing the Information Content of Experiments in Systems Biology , 2013, PLoS Comput. Biol..

[28]  Gerard B. M. Heuvelink,et al.  Optimizing the spatial pattern of networks for monitoring radioactive releases , 2011, Comput. Geosci..

[29]  Martin Schlather,et al.  Models for Stationary Max-Stable Random Fields , 2002 .

[30]  Alfred Stein,et al.  An overview of spatial sampling procedures and experimental design of spatial studies for ecosystem comparisons , 2003 .

[31]  Werner G. Müller,et al.  Collecting Spatial Data: Optimum Design of Experiments for Random Fields , 1998 .

[32]  Richard L. Smith,et al.  MAX-STABLE PROCESSES AND SPATIAL EXTREMES , 2005 .

[33]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[34]  Martin Charlton,et al.  Geographically weighted methods and their use in network re-designs for environmental monitoring , 2014, Stochastic Environmental Research and Risk Assessment.

[35]  Markus Hainy,et al.  Learning Functions and Approximate Bayesian Computation Design: ABCD , 2014, Entropy.

[36]  Hana Sevcikova,et al.  R Interface to RNG with Multiple Streams , 2015 .

[37]  Ali M. Mosammam.  Spatio-temporal design: advances in efficient data acquisition , 2014 .

[38]  Don L. Stevens,et al.  Sparse sampling: Spatial design for monitoring stream networks , 2008, 0808.4057.

[39]  Markus Hainy,et al.  Likelihood-Free Simulation-Based Optimal Design: An Introduction , 2014 .

[40]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[41]  J. Møller.  Discussion on the paper by Feranhead and Prangle , 2012 .

[42]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .