Simulation-based Evaluation of the Reliability of Bayesian Hierarchical Models for sc-RNAseq Data

A Bayesian hierarchical model (BHM) is typically formulated specifying the data model, the parameters model and the prior distributions. The posterior inference of a BHM depends both on the model specification and on the computation algorithm used. The most straightforward way to test the reliability of a BHM inference is to compare the posterior distributions with the ground truth value of the model parameters, when available. However, when dealing with experimental data, the true value of the underlying parameters is typically unknown. In these situations, numerical experiments based on synthetic datasets generated from the model itself offer a natural approach to check model performance and posterior estimates. Surprisingly, validation of BHMs with high-dimensional parameter spaces and non-Gaussian distributions, is unexplored. In this paper, we show how to test the reliability of a BHM. We introduce a change in the model assumptions to allow for prior contamination, and develop a simulation-based evaluation framework to assess the reliability of the inference of a given BHM. We illustrate our approach on a specific BHM used for the analysis of Single-cell Sequencing Data (BASiCS).