2025/03/14 by Sam Power, Chevallier, Augustin, Power, Sam +2 · 2 citations
Engineering · #62-08 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Microfluidic and Capillary Electrophoresis Applications #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2503.11479
openalex publication_date 2025/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.