| Gene-gene interactions, or epistasis, are widely believed to be fundamental to the genetic etiology of many complex phenotypes. However, accounting for these interactions in genetic association studies containing millions of markers is computationally very difficult. Consideration of all possible interactions is intractable, as a typical genetic association study may have billions or trillions of possible interactions. This dissertation describes a flexible Bayesian neural network method designed to address many of these challenges. First, some of the necessary computational infrastructure required by the Bayesian neural network model is developed. This model relies on the Hamiltonian Monte Carlo (HMC) algorithm, which can be very slow for large datasets. By using graphics processing units (GPUs) to evaluate certain portions of the HMC algorithm, the time needed to perform the simulation is reduced by several orders of magnitude. This work demonstrates some of the largest fully Bayesian analyses to date.;The GPU framework is leveraged to enable the use of Bayesian neural networks on large genetic datasets. It is shown that this method is capable of accurately identifying causal genetic loci in a variety of simulated scenarios. In addition, a novel Bayesian test of variable relevance is derived and implemented. It is demonstrated that this test achieves high sensitivity and specificity and allows for precise discrimination between causal and non-causal genetic markers. In comparison to existing methods, this approach shows good power to detect genetic markers associated with disease status. The Bayesian neural network model is extended to analyze cell-based, dose-response genetic association studies. The method is compared to an existing approach where it again performs very well. The methods developed as part of this dissertation show a promising ability to analyze large, complex genetic data in a variety of scenarios. |
