Using the Z-Order Curve for Bayesian Model Comparison

Abstract

BayeSys is an MCMC-based program that can be used to perform Bayesian model comparison for problems with atomic models. To sample distributions with more than one parameter, BayeSys uses the Hilbert curve to index the multidimensional parameter space using one very large integer. While the Hilbert curve maintains locality well, computations to translate back and forth between parameter coordinates and Hilbert curve indexes are time-consuming. The Z-order curve is an alternative SFC with faster transformation algorithms. This work presents an efficient bitmask-based algorithm for performing the Z-order curve transformations for an arbitrary number of parameter space dimensions and integer bit-lengths. We compare results for an exponential decay separation problem evaluated using BayeSys with both the Hilbert and Z-order curves. We demonstrate that no appreciable precision penalty is incurred by using the Z-order curve, and there is a significant increase in time efficiency.