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.
翻译:我们建议采用新的Markov链条蒙特卡洛算法,对子磁带的概率分布进行抽样抽样,这些算法通过在MCMC算法的建议步骤中允许使用定值地图来概括以往的方法。这种概括化的动机是,用于预测拟议向利益下移的数值解算器可能会找到几种解决办法。我们表明,新算法确实正确地对目标概率计量进行了抽样,这得益于一些谨慎强制的可逆性属性。我们展示了新的MCMC算法对示例数字示例的兴趣。