samsara: a continuous-time Markov chain Monte Carlo sampler for trans-dimensional Bayesian analysis

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 , a continuous-time Markov chain Monte Carlo (CTMCMC) framework that models parameter evolution through Poisson-driven birth, death, and mutation processes. 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 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 as a powerful alternative to RJMCMC for large- and variable-dimensional Bayesian inference problems.