A Note on E¢ cient Conditional Simulation of Gaussian Distributions
نویسنده
چکیده
Consider a multivariate Gaussian random vector which can be partitioned into observed and unobserved components.We review a technique proposed almost twenty years ago in the astrophysics literature to sample from the posterior Gaussian distribution of the unobserved components given the observed components [6]. This technique can be computationally cheaper than the standard approach which requires computing the Cholesky decomposition of the posterior covariance matrix. This useful method does not appear to be widely known and has been rediscovered independently in various publications. Keywords: forward ltering backward sampling, Gaussian processes, Kalman lter and smoother, multivariate normal distribution, state-space models Preliminary Remark. This note contains no original material and will never be submitted anywhere for publication. However it might be of interest to people working with Gaussian random elds/processes so I am making it publicly available. 1. Problem Statement Let Z be a R valued Gaussian random vector such that
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