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《粒子滤波中的方差估计》勘误AI 解读

Biometrika (2018), 105, pp. 609–25. There are missing curly braces in (4), which should read The displays in Remark 1 should consequently be changed to and In addition the sentence immediately after (5) should be changed to: Observe the resemblance between the right-hand sides of (4) and (5): the role of |$X_{i}$| is played by |$\sum_{j:E_{n}^{j}=i}\varphi(\zeta_{n}^{j})$|⁠, the sum of |$\varphi$| evaluated at the descendants of |$\zeta_{0}^{i}$|⁠. The consequences of this…

期望乘积的无偏近似AI 解读

Summary We consider the problem of approximating the product of $n$ expectations with respect to a common probability distribution $\mu$. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated by pseudo-marginal Markov chain Monte Carlo schemes, we focus on unbiased estimators of such products. The standard approach is to sample $N$ particles from $\mu$ and assign each particle to one of the expectations; this is wasteful…

粒子滤波中的方差估计AI 解读

SummaryThis paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances of a number of Monte Carlo approximations that particle filters deliver. All our estimators can be computed from a single run of a particle filter. We establish that, as the number of particles grows, our estimators are weakly…