Inhomogeneous evolutionary MCMC for Bayesian optimal sequential environmental monitoring
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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.
- Caselton WF, Husain T (1980) Hydrologic networks: information transmission. J Water Resour Plan Manag Div 106(2):503–520Google Scholar
- DeGroot M (1970) Optimal statistical decisions. McGraw Hill, New YorkGoogle Scholar
- Drugan M, Thierens D (2004) Evolutionary Markov chain Monte Carlo. In: Liardet P, Collet P, Fonlupt C, Luton E, Shoenauer M (eds) Artificial evolution: 6th international conference, evolution artificielle, EA, 2003, Lecture Notes in Computer Science. Springer, Berlin, pp 63–76Google Scholar
- Gamerman D, Lopes HF (2006) Markov chain Monte Carlo: stochastic simulation for Bayesian inference, 2nd edn. Chapman and Hall/CRC, Boca RatonGoogle Scholar
- Li W, Han J (2010) Dynamic wireless sensor network parameters optimization adapting different node mobility. In: Proceedings of the IEEE aerospace conference, 2010, paper # 1170. IEEEGoogle Scholar
- Ruiz-Cárdenas R, Ferreira MAR, Schmidt AM (2010) Stochastic search algorithms for optimal monitoring network designs. Environmetrics 21:102–112Google Scholar
- Song W-Z, Huang R, Xu M, Ma A, Shirazi B, LaHusen R (2009) Air-dropped sensor network for real-time high-fidelity volcano monitoring. In: Proceedings of the 7th international conference on mobile systems, applications, and services. ACM, pp 305–318Google Scholar
- West M, Harrison J (1997) Bayesian forecasting and dynamic models, 2nd edn. Springer, New YorkGoogle Scholar