Enriching Brownian motion with regenerations from a fixed regeneration distribution $\mu$ at a particular regeneration rate $\kappa$ results in a Markov process that has a target distribution $\pi$ as its invariant distribution. For the purpose of Monte Carlo inference, implementing such a scheme requires firstly selection of regeneration distribution $\mu$, and secondly computation of a specific constant $C$. Both of these tasks can be very difficult in practice for good performance. We introduce a method for adapting the regeneration distribution, by adding point masses to it. This allows the process to be simulated with as few regenerations as possible and obviates the need to find said constant $C$. Moreover, the choice of fixed $\mu$ is replaced with the choice of the initial regeneration distribution, which is considerably less difficult. We establish convergence of this resulting self-reinforcing process and explore its effectiveness at sampling from a number of target distributions. The examples show that adapting the regeneration distribution guards against poor choices of fixed regeneration distribution and can reduce the error of Monte Carlo estimates of expectations of interest, especially when $\pi$ is skewed.

翻译：通过以固定的再生分布$\mu$和特定的再生速率$\kappa$丰富布朗运动中的再生过程，可得到一个以目标分布$\pi$为不变分布的马尔可夫过程。为进行蒙特卡洛推断，实施此类方案首先需要选择再生分布$\mu$，其次需要计算特定的常数$C$。在实际应用中，这两项任务往往因难以实现良好的性能而极具挑战性。我们提出了一种通过向再生分布添加点质量来自适应调整该分布的方法。该方法能以尽可能少的再生次数模拟过程，并省去了寻找常数$C$的需求。此外，固定$\mu$的选择被替换为初始再生分布的选择，这大大降低了难度。我们证明了这种自增强过程的收敛性，并探讨了其从多个目标分布中采样的有效性。实验表明，自适应调整再生分布能够防范固定再生分布的不良选择，并降低蒙特卡洛期望估计的误差——尤其是在$\pi$呈偏态分布时。