Closing the evidence gap: reddemcee, a fast adaptive parallel tempering sampler

Context. Markov chain Monte Carlo (MCMC) excels at sampling complex posteriors, but traditionally lags behind nested sampling in accurate evidence estimation, which is crucial for model comparison in astrophysical problems. Aims. We introduce <ns0:monospace>reddemcee</ns0:monospace>, an adaptive parallel tempering ensemble sampler, aiming to close this gap by simultaneously presenting next-generation automated temperature-ladder adaptation techniques and robust, low-bias evidence estimators. Methods. <ns0:monospace>reddemcee</ns0:monospace> couples an affine-invariant stretch move with five interchangeable ladder-adaptation objectives – a uniform swap-acceptance rate, swap mean distance, Gaussian area overlap, a small Gaussian gap, and equalised thermodynamic length – implemented through a common differential update rule. Three evidence estimators are provided: curvature-aware thermodynamic integration (TI+), geometric-bridge stepping stones (SS+), and a novel hybrid algorithm that blends both approaches (H+). The performance and accuracy of the sampler are benchmarked on n-dimensional Gaussian shells, Gaussian egg-box, Rosenbrock functions, and the real exoplanet radial-velocity time-series dataset of HD 20794. Results. Across shells up to 15 dimensions, <ns0:monospace>reddemcee</ns0:monospace> achieves roughly 7 times the effective sampling speed of the best dynamic nested sampling configuration. The TI+, SS+, and H+ estimators recover estimates to within |∆ ln 𝒵|≲3% and supply realistic error bars with as few as six temperatures. In the HD 20794 case study, <ns0:monospace>reddemcee</ns0:monospace> reproduces literature model rankings and yields tighter yet consistent planetary parameters compared with <ns0:monospace>dynesty</ns0:monospace>, with evidence errors that track run-to-run dispersion. Conclusions. By unifying fast ladder adaptation with reliable evidence estimators, <ns0:monospace>reddemcee</ns0:monospace> delivers strong throughput and accurate evidence estimates, often matching, and occasionally surpassing, dynamic nested sampling, while preserving the rich posterior information that makes MCMC indispensable for modern Bayesian inference.