Bayesian Posterior Distributions Without Markov Chains
Bayesian Posterior Distributions Without Markov Chains
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DOI：
10.1093/aje/kwr433
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发表时间：
2012-03-01
影响因子：
5
通讯作者：
Richardson, David B.
中科院分区：
文献类型：
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作者：
Cole, Stephen R.;Chu, Haitao;Richardson, David B.
贝叶斯后验参数分布通常使用马尔可夫链蒙特卡罗（MCMC）方法进行模拟。然而，MCMC方法并不总是必需的，也不能帮助外行理解贝叶斯推理。作为理解贝叶斯推理的桥梁，作者举例说明了一种透明拒绝抽样方法。在例1中，他们用一项病例对照研究（1976-1983）中的36个病例和198个对照来说明排斥抽样，该研究评估了住宅暴露于磁场与儿童癌症发展之间的关系。拒绝抽样的结果（比值比（OR） 1.69, 95%后验区间（PI）： 0.57, 5.00）与MCMC结果（OR 1.69, 95% PI: 0.58, 4.95）和数据增强先验的近似（OR 1.74, 95% PI: 0.60, 5.06）相似。在例2中，作者将排斥抽样应用于315名人类免疫缺陷病毒血清转化者（1984-1998）的队列研究，以评估感染后病毒载量与5年获得性免疫缺陷综合征发病率之间的关系，调整（连续）血清转化时的年龄和种族。在这个更复杂的例子中，拒绝抽样比MCMC抽样需要更长的运行时间，但仍然是可行的，并且再次产生类似的结果。拟议方法的透明度是以不如MCMC适用范围广泛为代价的。
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.