Bayesian Conditional Density Filtering. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Guhaniyogi, Rajarshi; Qamar, Shaan; Dunson, David B.
• Is Part Of: Journal of computational and graphical statistics. Volume 27:Issue 3(2018)
• Page Start: 657
• Page End: 672
• Publication Date: 2018-07-03
• Subjects: Approximate MCMC -- Density filtering -- Dimension reduction -- Sequential Monte Carlo -- Streaming data; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1422431
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: We propose a conditional density filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. In the cases where dimension of the model parameter does not grow with time, we also establish sufficient conditions under which C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrive. Supplementary materials of C-DF are available online.