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

TL;DR

This paper develops Gibbs Sampling methods for Bayesian inference in biased sampling models, enabling estimation of original population parameters from biased tagged samples, demonstrated on SAGE mRNA data.

Contribution

It introduces efficient Gibbs Sampling algorithms and an iterative optimization procedure for biased sampling models, with application to gene expression data.

Findings

Successfully estimated mRNA expression levels in yeast.

Demonstrated Gibbs Sampling effectiveness for large multinomial parameters.

Provided a practical approach for biased sampling inference.

Abstract

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.