论文标题
移动目标蒙特卡洛
Moving Target Monte Carlo
论文作者
论文摘要
在考虑从高维随机变量$ \ Mathbf {x} $中进行采样时，Markov Chain Monte Carlo（MCMC）方法可能会流行，并且可能是未均衡的概率密度$ p $并观察到的数据$ \ MATHBF {D} $。但是，MCMC需要在构造接受率时在每次迭代时评估建议的候选$ \ Mathbf {x} $的后验分布$ p（\ mathbf {x} | \ mathbf {d}）$。当此类评估棘手时，这是昂贵的。在本文中，我们引入了一种新的非马克维亚采样算法，称为移动目标蒙特卡洛（MTMC）。 $ n $ th迭代时的接受率是使用后验分布的迭代更新近似$ a_n（\ mathbf {x}）$而不是$ p（\ mathbf {x} | \ mathbf {d}）$的。仅当候选$ \ mathbf {x} $接受后，才能计算后$ p（\ mathbf {x} | \ mathbf {d}）$的真实值。近似$ a_n $使用这些评估，并将$ p $收敛为$ n \ rightarrow \ infty $。在不同情况下，给出了收敛和收敛速率估计的证明。
The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires evaluating the posterior distribution $p(\mathbf{x}|\mathbf{d})$ of the proposed candidate $\mathbf{x}$ at each iteration when constructing the acceptance rate. This is costly when such evaluations are intractable. In this paper, we introduce a new non-Markovian sampling algorithm called Moving Target Monte Carlo (MTMC). The acceptance rate at $n$-th iteration is constructed using an iteratively updated approximation of the posterior distribution $a_n(\mathbf{x})$ instead of $p(\mathbf{x}|\mathbf{d})$. The true value of the posterior $p(\mathbf{x}|\mathbf{d})$ is only calculated if the candidate $\mathbf{x}$ is accepted. The approximation $a_n$ utilises these evaluations and converges to $p$ as $n \rightarrow \infty$. A proof of convergence and estimation of convergence rate in different situations are given.
