Sampling vs. Metasampling Based on Straightforward Hilbert Representation of Isolation Kernel

This study presents a novel metasampling scheme for Approximate Bayesian Computation (ABC) that leverages a metasampling algorithm based on a straightforward Hilbert representation of an isolation kernel constructed from Voronoi diagrams. The mapping to Hilbert space utilized identification of Voronoi sites to evaluate the similarity between observation and generated points, and the metasampling algorithm selects the points to maximize similarity to observation one in Hilbert space. To evaluate performance, a method competition was conducted using a high-dimensional stochastic Gaussian model with sparse data in the region of interest, and compared to several state-of-the-art methods including K2-ABC with Gaussian, Laplacian and isolation kernels, adaptive sequential Monte Carlo, and Markov chain Monte Carlo. Our method has demonstrated superiority over existing methods, as shown on a 6-dimensional model where, after 4000 simulations, the mean square error of our approach outperformed adaptive sequential Monte Carlo by two orders of magnitude and K2-ABC by four orders of magnitude. However, it should be noted that the metasampling method requires significantly more computational time per simulation step compared to kernel-based methods. The results obtained show the high accuracy of our proposed method, especially in scenarios with non-uniformly distributed datasets and models of this kind, indicating that it can be applied in genetic data analysis, which is a challenging area for future research. In the context of the current study, we applied the method to one example of a branching process model simulating personalized cancer cell evolution, where the posterior distribution of the personalized genetic parameters is located around the observation, contrasting with the kernel approach.