Browsing by Subject "statistics & probability"
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Item Open Access Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions(2009) Woodard, DB; Schmidler, SC; Huber, MWe give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.Item Open Access Incorporating Time-Dependent Source Profiles Using the Dirichlet Distribution in Multivariate Receptor Models(2010) Heaton, Matthew J; Reese, C Shane; Christensen, William FMultivariate receptor modeling is used to estimate profiles and contributions of pollution sources from concentrations of pollutants such as particulate matter in the air. The majority of previous approaches to multivariate receptor modeling assume pollution source profiles are constant through time. In an effort to relax this assumption, this article uses the Dirichlet distribution in a dynamic linear receptor model for pollution source profiles. The receptor model developed herein is evaluated using simulated datasets and then applied to a physical dataset of chemical species concentrations measured at the U.S. Environmental Protection Agency's St. Louis Midwest supersite. Supplemental materials to this articles are available online.