Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory exploration of the sampling space become challenging. Adaptive MCMC methods employing a choice of proposal distribution can address this issue speeding up the convergence. In this paper we show an alternative way of performing adaptive MCMC, by using the outcome of Bayesian Neural Networks as the initial proposal for the Markov Chain. This combined approach increases the acceptance rate in the Metropolis-Hasting algorithm and accelerate the convergence of the MCMC while reaching the same final accuracy. Finally, we demonstrate the main advantages of this approach by constraining the cosmological parameters directly from Cosmic Microwave Background maps.
翻译:Markov链条蒙特卡洛(MCMC)算法通常用于从复杂概率分布中取样的多功能性,但是,随着分布范围的扩大,令人满意地探索取样空间的计算成本也变得具有挑战性。采用选择建议分布的适应性MCMC方法可以加速这一问题的趋同。在本文中,我们展示了另一种执行适应性MCMC的方法,即利用Bayesian神经网络的结果作为Markov链的初步建议。这种结合方法提高了Metropolis-Hasting算法的接受率,加快了MCMC的趋同,同时达到了同样的最终精确度。最后,我们通过直接限制科斯米微波背景地图的宇宙参数,展示了这一方法的主要优点。