In this work we present a non-reversible, tuning- and rejection-free Markov
chain Monte Carlo which naturally fits in the framework of hit-and-run. The
sampler only requires access to the gradient of the log-density function, hence
the normalizing constant is not needed. We prove the proposed Markov chain is
invariant for the target distribution and illustrate its applicability through
a wide range of examples. We show that the sampler introduced in the present
paper is intimately related to the continuous sampler of Peters and de With
(2012), Bouchard-Cote et al. (2017). In particular, the computation is quite
similar in the sense that both are centered around simulating an inhomogenuous
Poisson process. The computation can be simplified when the gradient of the
log-density admits a computationally efficient directional decomposition into a
sum of two monotone functions. We apply our sampler in selective inference,
gaining significant improvement over the formerly used sampler (Tian et al.
2016).

本文提出了一种非可逆、无需调整和拒绝的 Markov 链 Monte Carlo，它自然地适应于 hit-and-run 框架中。该取样器只需要访问 log-density 函数的梯度，因此不需要归一化常数。我们证明了所提出的马尔科夫链不变于目标分布，并通过广泛的例子说明了它的适用性。我们证明，本文中介绍的取样器与 Peters and de With (2012)，Bouchard-Cote 等人 (2017) 的连续取样器密切相关。特别是，在梯度的 log-density 存在计算有效的方向分解成两个单调函数之和时，计算可以被简化。我们将取样器应用于选择推理，在 Tian 等人 (2016) 以前使用的取样器上获得了显着的改进。

通过迭代随机函数实现无需调整和拒绝的非可逆马尔科夫链蒙特卡罗

Non-reversible, tuning- and rejection-free Markov chain Monte Carlo via  iterated random functions

Hit-and-Run is known to be one of the best random sampling algorithms, its
mixing time is polynomial in dimension. Nevertheless, in practice the number of
steps required to achieve uniformly distributed samples is rather high. We
propose new random walk algorithm based on billiard trajectories. Numerical
experiments demonstrate much faster convergence to uniform distribution.

本文介绍了基于撞球轨迹的新型随机游走算法，与 Hit-and-Run 随机采样算法相比，本算法在实践中需要的步骤数更少，能更快地达到均匀分布。