STATISTICAL MODELLING OF RNA-SEQ DATA AND DENSITY ESTIMATION IN FINITE MIXTURE MODELS

Abstract

In this thesis, we study two statistical research topics. We propose a zero-inflated mixture Poisson linear model for RNA-Seq data; it integrates zero-inflation and mixture pattern commonly observed for the read counts, together with multiple sequencing preferences to capture non-uniformity of the read counts arising from sequencing bias into a unified framework. We also propose a modified kernel density estimator for unknown component densities in finite mixture models with known mixture proportions. Observations determine points where Gaussian kernels are placed at, as well as point-specific bandwidths and weights associated with the kernels. Our proposed estimator inherits all properties of a probability density function and can handle observations with discrete or continuous mixture proportions. We derive algorithms based on expectation-maximisation algorithm to fit both proposed methods and procedures based on Bayesian information criterion to choose their number of mixture components. Results from simulation studies and real data analysis show promising performances.