Inhomogeneous evolutionary MCMC for Bayesian optimal sequential environmental monitoring
We develop a novel computational framework for Bayesian optimal sequential network design for environmental monitoring. This computational framework is based on inhomogeneous evolutionary Markov chain Monte Carlo, which combines ideas of genetic or evolutionary algorithms, Markov chain Monte Carlo, and inhomogenous Markov chains. Our framework allows optimality criteria with general utility functions that may include competing objectives, such as for example minimization of costs, minimization of the distance between true and estimated functions, and minimization of the prediction error. We illustrate our novel methodology with two applications to design of monitoring networks for ozone. The first application considers a one-time reduction of an existing network. The second application considers the design of a dynamic monitoring network where at each time point only a portion of the nodes of the network provide real time data.
KeywordsBayesian inference Evolutionary Monte Carlo Kernel function estimation Optimal experimental design
The work of Ferreira was supported in part by National Science Foundation Grant DMS-0907064. Part of this research was performed while Ferreira was visiting the Statistical and Applied Mathematical Sciences Institute (SAMSI). We gratefully acknowledge the constructive comments and suggestions made by two anonymous referees and the Associate Editor that led to a substantially improved article.
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