On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
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DOI：
10.1214/21-aap1710
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Jianfeng Lu;Lihan Wang
中科院分区：
文献类型：
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作者：
Jianfeng Lu;Lihan Wang
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的变异框架，该框架结合了时间增强状态空间中的繁政型不平等和标准的$ 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 Poincare-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.