RJMCMC Algorithm with Resampling Step: Implementation and Performance Analysis

In this article, we aim to explore the application of the RJMCMC (Reversible Jump Markov Chain Monte Carlo) algorithm enhanced with a resampling step to address specific computational challenges, demonstrating its performance through detailed case studies. To achieve this objective, we first introduce the fundamental working principles of the base RJMCMC algorithm, including key components like parameter space dimension jumping and acceptance probability calculation using Metropolis-Hastings ratio. Subsequently, we propose an improved algorithm integrating a systematic resampling mechanism, which involves importance weight recalculation and particle redistribution to mitigate sample degeneracy issues. This implementation typically requires: 1) Designing adaptive proposal distributions for trans-dimensional moves, 2) Implementing residual resampling with O(N) complexity, and 3) Balancing computational efficiency using annealing schedules. Through a series of benchmark experiments comparing effective sample sizes and convergence diagnostics (e.g., Gelman-Rubin statistic), we validate the algorithm's enhanced mixing properties and reduced autocorrelation. We further conduct critical analysis of the algorithm's advantages in handling model uncertainty and limitations in high-dimensional spaces, suggesting potential improvements such as incorporating parallel tempering or variational approximations for future research directions.