samsara: A Continuous-Time Markov Chain Monte Carlo Sampler for Trans-Dimensional Bayesian Analysis

TL;DR

samsara introduces a novel continuous-time MCMC framework for efficient Bayesian inference in high-dimensional and trans-dimensional problems, outperforming traditional methods like RJMCMC in accuracy and convergence.

Contribution

The paper presents samsara, a CTMCMC method that models parameter changes via Poisson processes, enabling automatic trans-dimensional moves and improved efficiency in Bayesian analysis.

Findings

Validated on benchmark problems with excellent agreement to analytical results.

Achieved high sampling efficiency and automatic acceptance of trans-dimensional moves.

Demonstrated superiority over RJMCMC in large- and variable-dimensional Bayesian inference.

Abstract

Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as Mixture Models (MM) with an unknown number of components or the inference of overlapping signals in noisy data, as in the Laser Interferometer Space Antenna (LISA) Global Fit problem. Traditional approaches, such as product-space methods or Reversible-Jump Markov Chain Monte Carlo (RJMCMC), often face efficiency and convergence limitations. This paper presents samsara, a Continuous-Time Markov Chain Monte Carlo (CTMCMC) framework that models parameter evolution through Poisson-driven birth, death, and mutation processes. samsara is designed to sample models of unknown dimensionality. By requiring detailed balance through adaptive rate definitions, CTMCMC achieves automatic acceptance of trans-dimensional moves and high sampling efficiency. The code features waiting time weighted estimators, optimized memory storage, and a modular design for easy customization. We validate samsara on three benchmark problems: an analytic trans-dimensional distribution, joint inference of sine waves and Lorentzians in time series, and a Gaussian MM with an unknown number of components. In all cases, the code shows excellent agreement with analytical and Nested Sampling results. All these features push samsara as a powerful alternative to RJMCMC for large- and variable-dimensional Bayesian inference problems.