摘要翻译：
本文探讨了当感兴趣的总体不能直接采样，而是通过一种间接的、固有的有偏的方法采样时，有偏采样模型的贝叶斯推理。观察被看作是从一个带标签的群体中的多项式抽样过程的结果，这个群体反过来又是来自原始感兴趣的群体的有偏见的样本。本文提出了几种Gibbs抽样技术来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。该方法的样本可以用来产生联合和边缘后验推断。我们还提出了一个基于Gibbs采样器条件分布的迭代优化过程，该过程直接计算后验分布的模式。为了说明我们的方法，我们将其应用于一个标记的信使RNA（mRNA）群体，使用一种常见的高通量技术，基因表达序列分析(SAGE)产生。本文报道了酵母中mRNA表达水平的推论。
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英文标题：
《MCMC Inference for a Model with Sampling Bias: An Illustration using
  SAGE data》
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作者：
Russell Zaretzki and Michael A. Gilchrist and William M. Briggs and
  Artin Armagan
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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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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PDF链接：
https://arxiv.org/pdf/711.3765