先验样本选择育种法估计后验分布
Evaluating Posterior Distributions by Selectively Breeding Prior Samples
摘要：
使用马尔可夫链蒙特卡罗从后验分布中进行抽样是使贝叶斯数据分析实用化的关键创新。然而，众所周知，MCMC很难调优、诊断和并行化。本教学笔记探讨了通用{ \em non}-马尔可夫链蒙特卡罗方案的变体，用于从后验分布进行采样。基本思想是从先验分布中提取参数值，评估每次提取的可能性，然后复制与其可能性成比例的多次提取。复制后的分布是对后验的近似，当初始样本的数量达到无穷大时，后验变得精确;近似的收敛性很容易分析，并且在Glivenko-Cantelli类上是一致的。虽然不{ \em完全}实用，但该方案易于实现（几行R），易于并行化，并且不需要拒绝，老化，收敛诊断或任何控制设置的调整。我提供了对现有技术的参考，该现有技术以计算和分析的简单性为代价来处理一些实际障碍。
英文摘要：
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This pedagogical note explores variants on a universal {\em non}-Markov-chain Monte Carlo scheme for sampling from posterior distributions. The basic idea is to draw parameter values from the prior distributions, evaluate the likelihood of each draw, and then copy that draw a number of times proportional to its likelihood. The distribution after copying is an approximation to the posterior which becomes exact as the number of initial samples goes to infinity; the convergence of the approximation is easily analyzed, and is uniform over Glivenko-Cantelli classes. While not {\em entirely} practical, the schemes are straightforward to implement (a few lines of R), easily parallelized, and require no rejection, burn-in, convergence diagnostics, or tuning of any control settings. I provide references to the prior art which deals with some of the practical obstacles, at some cost in computational and analytical simplicity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
