论文标题
在MCMC算法中的分段确定性Markov流程的显式$ l^2 $ -Convergence速率估算
On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
论文作者
论文摘要
我们为三个流行的分段确定性马尔可夫工艺建立了$ l^2 $ - 指数收敛速率：随机的汉密尔顿蒙特卡洛法，锯齿形过程和弹力粒子采样器。我们的分析基于一个差异性框架，该框架结合了庞加莱型的不平等现象空间和标准的$ l^2 $能量估计。我们的分析提供了明确的收敛率估计值，比现有结果更定量。
We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process, and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard $L^2$ energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.
