具有抽样偏差模型的MCMC推断：使用SAGE数据的说明
MCMC Inference for a Model with Sampling Bias: An Illustration using SAGE data
摘要：
本文探讨了有偏抽样模型的贝叶斯推断的情况下，感兴趣的人口不能直接抽样，而是通过一个间接的和固有的偏见的方法。观察结果被视为从标记的总体中进行多项抽样过程的结果，而标记的总体又是来自原始感兴趣总体的有偏样本。本文提出了几种吉布斯抽样技术，根据标记种群的观测计数估计原始种群的联合后验分布。这些算法有效地从一个非常大的多项式参数向量的联合后验分布中采样。该方法的样本可用于生成联合和边缘后验推理。我们还提出了一个迭代优化过程的基础上的条件分布的吉布斯采样直接计算的模式的后验分布。为了说明我们的方法，我们将其应用于使用常见的高通量技术，基因表达系列分析（SAGE）生成的信使RNA（mRNA）的标记群体。在酵母酿酒酵母的mRNA表达水平的推断报告。
英文摘要：
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.
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