Greenland Sander
Departments of Epidemiology and Statistics, University of California, Los Angeles, CA 90095-1772, USA.
Int J Epidemiol. 2006 Jun;35(3):765-75. doi: 10.1093/ije/dyi312. Epub 2006 Jan 30.
One misconception (of many) about Bayesian analyses is that prior distributions introduce assumptions that are more questionable than assumptions made by frequentist methods; yet the assumptions in priors can be more reasonable than the assumptions implicit in standard frequentist models. Another misconception is that Bayesian methods are computationally difficult and require special software. But perfectly adequate Bayesian analyses can be carried out with common software for frequentist analysis. Under a wide range of priors, the accuracy of these approximations is just as good as the frequentist accuracy of the software--and more than adequate for the inaccurate observational studies found in health and social sciences. An easy way to do Bayesian analyses is via inverse-variance (information) weighted averaging of the prior with the frequentist estimate. A more general method expresses the prior distributions in the form of prior data or 'data equivalents', which are then entered in the analysis as a new data stratum. That form reveals the strength of the prior judgements being introduced and may lead to tempering of those judgements. It is argued that a criterion for scientific acceptability of a prior distribution is that it be expressible as prior data, so that the strength of prior assumptions can be gauged by how much data they represent.
关于贝叶斯分析（众多误解之一）是，先验分布引入的假设比频率论方法所做的假设更值得怀疑；然而，先验中的假设可能比标准频率论模型中隐含的假设更合理。另一个误解是，贝叶斯方法计算困难且需要特殊软件。但使用常见的频率论分析软件就可以进行完全足够的贝叶斯分析。在广泛的先验条件下，这些近似的准确性与软件的频率论准确性一样好——对于健康和社会科学中不准确的观察性研究来说绰绰有余。进行贝叶斯分析的一种简单方法是通过先验与频率论估计的逆方差（信息）加权平均。一种更通用的方法是以先验数据或“数据等效物”的形式表达先验分布，然后将其作为一个新的数据层输入到分析中。这种形式揭示了所引入的先验判断的强度，可能会导致对这些判断进行调整。有人认为，先验分布科学可接受性的一个标准是它可以表示为先验数据，这样先验假设的强度就可以通过它们所代表的数据量来衡量。
