标题： 具有抽样偏差的模型的MCMC推理：使用SAGE数据的说明 显示英文标题

标题： MCMC Inference for a Model with Sampling Bias: An Illustration using SAGE data

摘要： 本文探讨了贝叶斯推断在一种有偏抽样模型中的应用，该模型适用于无法直接抽取感兴趣总体的情况，而是通过一种间接的、本质上有偏的方法来抽取样本。 观察值被视为是从一个标记群体中通过多项式抽样过程得到的结果，而这个标记群体本身又是从原始感兴趣的总体中抽取的一个有偏样本。 本文提出了几种Gibbs采样技术，用于根据标记群体的观测计数估计原始总体的联合后验分布。 这些算法能够高效地从非常大的多项式参数向量的联合后验分布中抽取样本。 这种方法产生的样本可以用来生成联合和边缘后验推断。 我们还提出了一种基于Gibbs采样条件分布的迭代优化程序，该程序可以直接计算后验分布的众数。 为了说明我们的方法，我们将它应用于使用一种常见的高通量技术——基因表达的序列分析（SAGE）——生成的信使RNA（mRNA）标记群体。 报告了酵母（Saccharomyces cerevisiae）中mRNA表达水平的推断结果。 显示英文摘要

摘要： This paper explores Bayesian inference for a biased sampling model in situations where the population of interest cannot be sampled directly, but rather through an indirect and inherently biased method. Observations are viewed as being the result of a multinomial sampling process from a tagged population which is, in turn, a biased sample from the original population of interest. This paper presents several Gibbs Sampling techniques to estimate the joint posterior distribution of the original population based on the observed counts of the tagged population. These algorithms efficiently sample from the joint posterior distribution of a very large multinomial parameter vector. Samples from this method can be used to generate both joint and marginal posterior inferences. We also present an iterative optimization procedure based upon the conditional distributions of the Gibbs Sampler which directly computes the mode of the posterior distribution. To illustrate our approach, we apply it to a tagged population of messanger RNAs (mRNA) generated using a common high-throughput technique, Serial Analysis of Gene Expression (SAGE). Inferences for the mRNA expression levels in the yeast Saccharomyces cerevisiae are reported.