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Bayesian multiresolution dynamic models

Kim, Yong Ku

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Statistics.
Dynamic process models such as state space models or diffusion process models are widely used for many natural dynamic phenomena. Statistical modelling has been essential tool for performing inference and prediction for processes in the various application areas including physics, economics, engineering, environment and biological sciences, climatology, etc. However, nonstationary and/or nonGaussian process models remain challenging. I consider a class of nonstationary dynamic process models with time-varying coefficients. The key to the approach is the development of a hierarchical model for the main process of interest conditional upon coefficients which are themselves modeled via state space models. These parameter models are allowed to have different time scales. Bayesian inference for such a multi-resolution dynamic process model is applied to various examples such as surface temperature data. Bayesian model selection and model uncertainty problems are also discussed. Spatiotemporal processes in the physical, environmental, and biological sciences often exhibit complicated and diverse patterns across different space-time scales. Both scientific understanding and observed data also vary in form and content across these scales. I develop a Bayesian hierarchical framework by which the combination of information sources accross spatiotemporal scale can be accomplished. The approach restricts a few essential scales when such a restriction justify the trade-off between comparatively simple modeling and analysis strategy with the task of forming models valid at all scales. Instead of combining the information directly, I also consider change of spatiotemporal scale issues through multiresolution tree structures. Various approximations useful in computations are suggested and explored. Specific results involve the treatment of nuisance parameters. I also provide some theoretical results regarding the Bayesian sensitivity. I explore the effects on the target posterior distribution by approximations to the posterior distribution of nuisance parameters and studied the approximate sensitivity of the posterior distribution of interest to the approximation to the marginal posterior distribution of nuisance parameters in terms of the Kullback-Leibler divergence. This result can be directly applied to the sensitivity of posterior distribution to the predictive distribution or the sensitivity of prior distribution to the marginal density for Bayesian model selection.
L. Berliner (Advisor)
118 p.

Recommended Citations

Citations

  • Kim, Y. K. (2007). Bayesian multiresolution dynamic models [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1180465799

    APA Style (7th edition)

  • Kim, Yong Ku. Bayesian multiresolution dynamic models. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1180465799.

    MLA Style (8th edition)

  • Kim, Yong Ku. "Bayesian multiresolution dynamic models." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1180465799

    Chicago Manual of Style (17th edition)