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Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II) pp 59–87Cite as

Markov Chain Monte Carlo Methods: Theory and Applications

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Abstract

Markov chain Monte Carlo algorithms constitute flexible and powerful solutions to Bayesian inverse problems. They return a sample of the unapproximated posterior probability density, and make no assumptions as to linearity or the form of the prior or likelihood. MCMC algorithms are in principle easy to construct, however, they can prove difficult to implement in practice. This chapter describes the theory that underlies MCMC simulation, provides guidance for its practical implementation, and presents examples of applications of MCMC to satellite retrievals and model uncertainty characterization. Though the high dimensionality of Earth system datasets and the complexity of atmospheric, oceanic, and hydrologic models present significant challenges, continued advances in theory and practice are making application of MCMC algorithms increasingly feasible.

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Acknowledgements

The author gratefully acknowledges the support of the NASA Modeling, Analysis, and Prediction program under grants NNX09AJ43G and NNX09AJ46G, the Office of Naval Research Broad Agency Announcement program under grant N00173-10-1-G035, and the National Science Foundation Physical and Dynamic Meteorology Program under grant AGS 1005454. Tomislava Vukicevic (NOAA-AOML), Craig Bishop (NRL-Monterey), Marcus van Lier-Walqui (U. Miami-RSMAS), Tristan L’Ecuyer (U. Wisconsin), Steve Cooper (U. Utah), and Graeme Stephens (NASA-JPL) all contributed to this research. Luca Della Monache (NCAR), Dan Hodyss (NRL-Monterey), Peter Norris (NASA Goddard Space Flight Center), and an anonymous reviewer all contributed valuable feedback on this manuscript.

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  1. Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, 2455 Hayward Street, Ann Arbor, MI, 48103, USA

    Derek J. Posselt

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  1. Derek J. Posselt
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Correspondence to Derek J. Posselt .

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  1. , Environmental Science and Engineering, Ewha Womans University, Ewhayeodae-gil, Seodaemun-gu 52, Seoul, 120-750, Korea, Republic of (South Korea)

    Seon Ki Park

  2. Naval Research Laboratory, Grace Hopper Ave. 7, Monterey, 93943-5502, California, USA

    Liang Xu

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Posselt, D.J. (2013). Markov Chain Monte Carlo Methods: Theory and Applications. In: Park, S., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35088-7_3

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