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| Implicit Sampling, with Application to Data Assimilation |
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Citation： |
Alexandre J. CHORIN,Matthias MORZFELD,Xuemin TU.Implicit Sampling, with Application to Data Assimilation[J].Chinese Annals of Mathematics B,2013,34(1):89~98 |
| Page view： 2324
Net amount： 1720 |
Authors： |
Alexandre J. CHORIN; Matthias MORZFELD; Xuemin TU; |
Foundation： |
Director, Office of Science, Computational and Technology Research, U. S. Department of Energy (No.DE-AC02-05CH11231) and the National Science Foundation (Nos.DMS-0705910, OCE-0934298). |
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| Abstract： |
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 $x_i\ (i=1,2,\cdots )$, 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, wherethe density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markov-chain MonteCarlo, 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. |
Keywords： |
Importance sampling, Bayesian estimation, Particle filter, Implicit filter,Data assimilation |
Classification： |
11K45, 34K60, 62M20, 65C50, 93E11 |
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