How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS
How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS
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DOI：
10.1002/sim.2112
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发表时间：
2005-08-15
影响因子：
2
通讯作者：
Jones, DR
中科院分区：
文献类型：
--
作者：
Lambert, PC;Sutton, AJ;Jones, DR
最近，贝叶斯方法在医学研究中的使用有所增长。其主要原因是基于计算机密集型仿真的方法（例如马尔可夫链蒙特卡罗（MCMC））的发展、计算能力的提高以及WinBUGS等功能强大的软件的引入。这使得能够拟合越来越复杂的模型。拟合这些复杂模型的能力使得 MCMC 方法被常客们用作一种方便的工具，他们可能不希望完全成为贝叶斯模型。研究人员通常希望在没有先验信息的情况下“数据占主导地位”，因此尝试使用模糊的先验分布。然而，对于少量数据，使用模糊先验可能会出现问题。结果可能对先验分布的选择敏感。一般来说，位置参数的问题较少。主要问题是尺度参数。有了尺度参数，不仅要决定先验分布的分布形式，还要决定是否将先验分布放在方差、标准差或精度上。我们进行了一项模拟研究，比较了13种不同的尺度参数先验分布对模拟随机效应荟萃分析数据的影响。我们改变了研究数量（5、10 和 30），并比较了三种不同的研究间方差，给出了九种不同的模拟场景。为每个场景生成了 1000 个数据集，并且使用 13 种不同的先验分布对每个数据集进行了分析。研究了偏倚和覆盖率的频率特性，以了解研究间方差和效应大小。当只有五项研究时，先验分布的选择至关重要。 13 种不同先验分布的研究间方差估计存在很大差异。随着大量研究的进行，先验分布的选择不再那么重要。估计的效应大小没有偏差，但估计的精度随着先验分布的选择而变化，导致覆盖区间不同，并可能导致不同的统计推论。同样，研究数量越多，问题就越小。如果研究间方差接近零边界，则会出现一个特殊问题，因为 MCMC 结果往往会产生研究间方差的向上偏差估计，特别是如果推论基于后验均值。“模糊”先验分布的选择可能会导致结果显着变化，特别是在小型研究中。应始终评估对先验分布选择的敏感性。版权所有 (c) 2005 John Wiley & Sons, Ltd.
There has been a recent growth in the use of Bayesian methods in medical research. The main reasons for this are the development of computer intensive simulation based methods such as Markov chain Monte Carlo (MCMC), increases in computing power and the introduction of powerful software such as WinBUGS. This has enabled increasingly complex models to be fitted. The ability to fit these complex models has led to MCMC methods being used as a convenient tool by frequentists, who may have no desire to be fully Bayesian.Often researchers want 'the data to dominate' when there is no prior information and thus attempt to use vague prior distributions. However, with small amounts of data the use of vague priors can be problematic. The results are potentially sensitive to the choice of prior distribution. In general there are fewer problems with location parameters. The main problem is with scale parameters. With scale parameters, not only does one have to decide the distributional form of the prior distribution, but also whether to put the prior distribution on the variance, standard deviation or precision.We have conducted a simulation study comparing the effects of 13 different prior distributions for the scale parameter on simulated random effects meta-analysis data. We varied the number of studies (5, 10 and 30) and compared three different between-study variances to give nine different simulation scenarios. One thousand data sets were generated for each scenario and each data set was analysed using the 13 different prior distributions. The frequentist properties of bias and coverage were investigated for the between-study variance and the effect size.The choice of prior distribution was crucial when there were just five studies. There was a large variation in the estimates of the between-study variance for the 13 different prior distributions. With a large number of studies the choice of prior distribution was less important. The effect size estimated was not biased, but the precision with which it was estimated varied with the choice of prior distribution leading to varying coverage intervals and, potentially, to different statistical inferences. Again there was less of a problem with a larger number of studies. There is a particular problem if the between-study variance is close to the boundary at zero, as MCMC results tend to produce upwardly biased estimates of the between-study variance, particularly if inferences are based on the posterior mean.The choice of 'vague' prior distribution can lead to a marked variation in results, particularly in small studies. Sensitivity to the choice of prior distribution should always be assessed. Copyright (c) 2005 John Wiley & Sons, Ltd.