This dissertation studies a graphical processing unit (GPU) construction of Bayesian neural networks (BNNs) using large training data sets. The goal is to create a program for the mapping of phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameters to their predictions. This would allow for a more robust method of studying the Minimal Supersymmetric Standard Model,which is of much interest at the Large Hadron Collider (LHC) experiment CERN. A systematic study of the speedup achieved in the GPU application compared to a Central Processing Unit (CPU) implementation are presented.