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CRiSM Seminar - Pierre Jacob & Leonardo Bottolo

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Location: A1.01

Pierre Jacob
Estimation of the score vector and observed information matrix in intractable models
Ionides, King et al. (see Inference for nonlinear dynamical systems, PNAS 103) have introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to simulate the latent Markov model according its prior distribution. Their methodology bypasses the calculation of any derivative by expressing the score in the original model as an expectation under a modified model. Building upon this insightful work, we provide here a similar "derivative-free" estimator for the observed information matrix, expressed as a covariance matrix under a modified model. In principle the method is applicable for any latent variable model. We also discuss connections with Stein's method and proximal mappings.

Leonardo Bottolo
Mixture priors for subgroups classification
Technologies for the collection of genetic data, such as those based on RNA-Seq, are developing at a very fast rate. A crucial objective in these studies is gene clustering based on the similarity of their level of expression. A more important clustering task concerns samples themselves: this goes under the name of molecular profiling, and aims at identifying similarities across samples based on a few genes identified from the previous stage of the analysis.

In this talk we present a fully Bayesian hierarchical model for molecular profiling. A key ingredient of our approach is represented by the use of mixture distributions. First of all expression measurements are assumed to originate from a three-component mixture distribution, representing the underlying population classes (baseline, underexpression and overexpression) of samples relative to gene-expression. For each gene we assume a specific (random) probability of belonging to any of the three classes. Current Bayesian modelling assumes that the collection of gene-specific probabilities is exchangeable. Exchangeability assumption exhibits some drawbacks, the main one being its inability to capture heterogeneity in gene-behavior. This led us to model the gene-specific probabilities of under overexpression using a mixture of prior distributions with an unknown number of components: this represents the novelty of our approach which is meant to capture variation in gene behaviour and to identify clusters of genes in relation to their probability of under and overexpression.

The model is applied to gene expression levels from RNA-Seq analysis of left ventricular tissue derived from a cohort comprising 33 dilated cardiomyopathy patients with end-stage heart failure who underwent left ventricular assist device implant. Of these patients, 24 subsequently recovered their function whereas 9 did not. There is no obvious distinguishing features between them at the time the sample was taken. Molecular profiling is derived to predict recovery vs non-recovery patients. This is a joint work with Petros Dellaportas and Athanassios Petralias, Dept of Statistics, Athens University.

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