This paper introduces the boomerang sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. The methodology begins by representing the target density as a density, $e^{-U}$, with respect to a prescribed (usually) Gaussian measure and constructs a continuous trajectory consisting of a piecewise elliptical path. The method moves from one elliptical orbit to another according to a rate function which can be written in terms of $U$. We demonstrate that the method is easy to implement and demonstrate empirically that it can out-perform existing benchmark piecewise deterministic Markov processes such as the bouncy particle sampler and the Zig-Zag. In the Bayesian statistics context, these competitor algorithms are of substantial interest in the large data context due to the fact that they can adopt data subsampling techniques which are exact (ie induce no error in the stationary distribution). We demonstrate theoretically and empirically that we can also construct a control-variate subsampling boomerang sampler which is also exact, and which possesses remarkable scaling properties in the large data limit. We furthermore illustrate a factorised version on the simulation of diffusion bridges.

介绍Boomerang Sampler这一新颖的连续时间不可逆Markov Chain Monte Carlo算法类，该方法在高斯测度下构建了由分段椭圆形轨迹组成的连续轨迹，并通过该算法的速率函数在椭圆形轨迹中移动。此外，还演示了在大数据情况下，此算法可以采用数据子采样技术构建精确的控制变量子采样boomerang采样器，并展示了在扩散桥模拟中的应用。

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