Systematic Benchmark Compares Gradient-Free MCMC Samplers for Statistical Inference
Researchers benchmarked multiple gradient-free Markov Chain Monte Carlo (MCMC) samplers against the standard Metropolis-Hastings algorithm using controlled test functions and likelihood landscapes. The study found that the differential evolution algorithm, when tuned to a 25% acceptance fraction, outperformed other samplers in ergodicity, robustness, and likelihood performance. This work provides practical guidance for selecting appropriate sampling methods in computational statistics and Bayesian inference applications.
A new preprint presents a comprehensive evaluation framework for comparing modern gradient-free MCMC samplers, which are essential tools in Bayesian statistics and computational physics. The researchers tested multiple algorithms—including affine-invariant moves (stretch, walk), differential evolution, and snooker moves—alongside two novel variations: a PCA-modified stretch move and a hybrid blend move. Testing employed both unimodal benchmark functions (Rosenbrock, Neal's funnel) and multimodal Gaussian random likelihood landscapes in 3, 5, and 8 dimensions to ensure broad applicability. Beyond sampler comparison, the study demonstrated likelihood landscape reconstruction via quadtree algorithms and showed that post-sampling optimization consistently improved log-likelihood values, with gains becoming more pronounced in higher dimensions. The differential evolution algorithm emerged as the top performer across all tested metrics.
What's missing
The study does not discuss computational cost or wall-clock time comparisons between samplers, which would be relevant for practitioners choosing methods for large-scale problems. Additionally, the paper does not address how results generalize to non-smooth or discontinuous likelihood landscapes, which are common in some scientific applications.
What different sources said
- arXiv astro-phCenter
Choosing the right MCMC sampler: a systematic benchmark of gradient-free methods
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