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. We introduce reddemcee, 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. reddemcee couples an affine-invariant stretch move with five interchangeable ladder-adaptation objectives, Uniform Swap Acceptance Rate, Swap Mean Distance, Gaussian-Area Overlap, 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+). Performance and accuracy are benchmarked on n-dimensional Gaussian Shells, Gaussian Egg-box, Rosenbrock Functions, and exoplanet radial-velocity time-series of HD 20794. Across Shells up to 15 dimensions, reddemcee presents roughly 7 times the effective sampling speed of the best dynamic nested sampling configuration. The TI+, SS+ and H+ estimators recover estimates under 3 percent error and supply realistic uncertainties with as few as six temperatures. In the HD 20794 case study, reddemcee reproduces literature model rankings and yields tighter yet consistent planetary parameters compared with dynesty, with evidence errors that track run-to-run dispersion. By unifying fast ladder adaptation with reliable evidence estimators, reddemcee delivers strong throughput and accurate evidence estimates, often matching, and occasionally surpassing, dynamic nested sampling, while preserving the rich posterior information which makes MCMC indispensable for modern Bayesian inference.

翻译：马尔可夫链蒙特卡罗（MCMC）在采样复杂后验分布方面表现出色，但在精确估计证据（这对于天体物理问题中的模型比较至关重要）方面，传统上落后于嵌套采样。我们推出了reddemcee，一种自适应并行回火集成采样器，旨在通过同时提供下一代自动化温度阶梯自适应技术和稳健、低偏差的证据估计器来弥合这一差距。reddemcee将仿射不变拉伸移动与五种可互换的阶梯自适应目标——均匀交换接受率、交换平均距离、高斯区域重叠、小高斯间隙和均衡热力学长度——相结合，并通过一个通用的微分更新规则实现。该工具提供了三种证据估计器：曲率感知热力学积分（TI+）、几何桥接踏脚石（SS+）以及一种融合了两种方法的新型混合算法（H+）。我们在n维高斯壳、高斯蛋盒函数、Rosenbrock函数以及HD 20794的系外行星径向速度时间序列上对性能和准确性进行了基准测试。在高达15维的壳模型中，reddemcee的有效采样速度大约是最佳动态嵌套采样配置的7倍。TI+、SS+和H+估计器恢复的估计值误差低于3%，并且仅用六个温度即可提供真实的误差估计。在HD 20794的案例研究中，reddemcee重现了文献中的模型排序，并产生了比dynesty更紧凑但仍一致的系外行星参数，其证据误差与多次运行间的离散度相符。通过将快速阶梯自适应与可靠的证据估计器相统一，reddemcee实现了强大的吞吐量和精确的证据估计，其性能通常与动态嵌套采样相当，有时甚至更优，同时保留了丰富的后验信息，这使得MCMC对于现代贝叶斯推断不可或缺。