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implicit Sampling,with Application to Data Assimilation

Chinese Annals of Mathematics,Series B 2013年第1期34卷 89-98页

作者： Alexandre J.CHORIN Matthias MORZFELD Xuemin TU Department of Mathematics University of California Lawrence Berkeley National Laboratory Department of Mathematics University of Kansas

There are many computational tasks, in which it is necessary to sample a given probability density function （or pdf for short）, i.e., to use a computer to construct a sequence of independent random vectors x~ （i ---- 1, 2, ~ ~ ~ ）, whose histogram converges to the given pdf. This can be difficult because the sample space can be huge, and more importantly, because the portion of the space, where the density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markov- chain Monte Carlo, the most widely used sampling scheme, can be thought of as a search algorithm, where one starts at an arbitrary point and one advances step-by-step towards the high probability region of the space. This can be expensive, in particular because one is typically interested in independent samples, while the chain has a memory. The authors present an alternative, in which samples are found by solving an algebraic equation with a random right-hand side rather than by following a chain; each sample is independent of the previous samples. The construction in the context of numerical integration is explained, and then it is applied to data assimilation.

关键词： Importance sampling Bayesian estimation Particle filter implicit filter Data assimilation

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An implicit Algorithm of Solving Nonlinear filtering Problems

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Communications in Computational Physics 2014年第7期16卷 382-402页

作者： Feng Bao Yanzhao Cao Xiaoying Han Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA School of Mathematics and Computational Sciences Sun Yat-sen UniversityChina

Nonlinear filter problems arise in many applications such as communications and signal *** used numerical simulation methods include Kalman filter method,particle filter method,*** this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation *** experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

关键词： Kalman filter particle filter implicit filter Monte Carlomethod stochastic differential equations.

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