Unbiased approximations of products of expectations
Unbiased approximations of products of expectations
复制标题
期望乘积的无偏近似
作者：
Anthony Lee;S. Tiberi;Giacomo Zanella
我们考虑的问题，近似产品的$n$期望关于一个共同的概率分布$\mu$。在统计学中，这种乘积通常作为潜在变量模型中的可能性值出现。出于伪边际马尔可夫链蒙特卡罗计划，我们专注于无偏估计的产品。标准的方法是从$\mu$中采样$N$个粒子，并将每个粒子分配给一个期望值;这是浪费的，通常需要粒子数量随着期望值的数量二次增长。我们提出了一种替代估计器，它使用大多数粒子来逼近每个期望，同时保持无偏性，当模拟成本大大超过似然评估成本时，它在计算上更有效。我们仔细研究了我们提出的估计器的性质，表明在潜变量背景下，它只需要${O}（n）$粒子就可以匹配具有${O}（n^{2}）$粒子的标准方法的性能。我们展示了两个潜在变量的例子，从近似贝叶斯计算和单细胞基因表达分析，观察计算增益的因素约25和450，分别的程序。
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 and typically requires the number of particles to grow quadratically with the number of expectations. We propose an alternative estimator that approximates each expectation using most of the particles while preserving unbiasedness, which is computationally more efficient when the cost of simulations greatly exceeds the cost of likelihood evaluations. We carefully study the properties of our proposed estimator, showing that in latent variable contexts it needs only ${O} (n)$ particles to match the performance of the standard approach with ${O}(n^{2})$ particles. We demonstrate the procedure on two latent variable examples from approximate Bayesian computation and single-cell gene expression analysis, observing computational gains by factors of about 25 and 450, respectively.
影响因子：
1.8
作者：
C. Andrieu;M. Vihola
通讯作者：
C. Andrieu;M. Vihola