Accelerating Posterior sampling for Scalable Gaussian Process model

This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian computation in spatial analysis. The focus is on the application of symbolic decomposition and preconditioners, which are essential for the computational efficiency of conjugate gradient. The findings reveal notable differences in the effectiveness of these acceleration methods. Specific preconditioners, such as the Diagonal Preconditioner, consistently delivered improvements in computational speed. However, in settings involving high-dimensional matrices, traditional solvers were less effective, underscoring the importance of specialized acceleration techniques like the diagonal preconditioner and cgsparse. These methods demonstrated robust performance across a variety of scenarios. The results of this study not only enhance our understanding of the algorithmic dynamics within spatial statistics but also offer valuable guidance for practitioners in choosing the most appropriate computational techniques for their specific needs.