论文标题
子曼属上的多个投影MCMC算法
Multiple projection MCMC algorithms on submanifolds
论文作者
论文摘要
我们提出了新的马尔可夫链蒙特卡洛算法来采样子序列上的概率分布，这些概率分布通过在MCMC算法的建议步骤中允许使用设置值映射来概括先前的方法。这种概括的动机是，用于将提议的移动投射到感兴趣的子手机的数值求解器可能会找到几种解决方案。我们表明，由于一些精心执行的可逆性属性，新算法确实正确采样了目标概率度量。我们证明了新的MCMC算法对说明性数值示例的兴趣。
We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.
