Influência de funções de covariâncias sobre o modelo fatorial latente esparso com interações

Abstract

The factor analysis is an statistical tool widely used to identify a reduced number of factors supposed to explain the relationship between many variables in a data set. In this work, we explore this technique using the Bayesian approach in context of the analysis of gene expression. Initially, we study the simple latent factor model and verify its performance to t simulated data. Next, we evaluate the latent factor model withinteractions assuming sparse prior distributions to test whether the factors, dened for regions with copy number alterations, would aect genes located in other regions of the genome. The interaction was introduced in the model through a Gaussian process having in its structure a covariance function which is a key element in our study. The behavior and performance of the sparse latent factor model with interactions was evaluated through simulations using dierent covariances functions: quadratic exponential, as discussed inMayrink and Lucas (2013), power exponential and some functions options in the Matern class that dier in terms of the choice of the smoothing parameters. A sensitivity analysis is made considering these settings and the results indicate that some specications providea better model t than others. Finally, an application involving