Sampling designs via a multivariate hypergeometric-Dirichlet process model for a multi-species assemblage with unknown heterogeneity

In a sample of mRNA species counts, sequences without duplicates or with small numbers of copies are likely to carry information related to mutations or diseases and can be of great interest. However, in some situations, sequence abundance is unknown and sequencing the whole sample to find the rare sequences is not practically possible. To collect mRNA sequences of interest, or more generally, species of interest, we propose a two-phase Bayesian sampling method that addresses these concerns. The first phase of the design is used to infer sequence (species) abundance levels through a cluster analysis applied to a pilot data set. The clustering method is built upon a multivariate hypergeometric model with a Dirichlet process prior for species relative frequencies. The second phase, through Monte Carlo simulations, infers the sample size necessary to collect a certain number of species of particular interest. Efficient posterior computing schemes are proposed. The developed approach is demonstrated and evaluated via simulations. An mRNA segment data set is used to illustrate and motivate the proposed sampling method.