缓存和内插似然：加速宇宙学蒙特卡罗马尔可夫链
Caching and Interpolated Likelihoods: Accelerating Cosmological Monte Carlo Markov Chains
摘要：
我们描述了一种新的方法来加速蒙特卡罗马尔可夫链。我们的重点是宇宙学参数估计，但该算法适用于任何问题的可能性表面是一个光滑的函数的自由参数和计算昂贵的评估。我们使用马尔可夫链收集的第一个点作为训练集，生成一个高阶插值多项式的对数似然。然后，该多项式精确地计算链的后半部分所需的大部分似然。我们实现了一个简单的版本，这个算法作为一个补丁（InterpMC）的CosmoMC，并表明它加速参数估计的一个因素之间的两个和四个良好收敛的链。目前的代码主要是作为一个“概念证明”，我们认为，有相当大的空间，进一步提高性能。与其他加速参数拟合的方法不同，我们不使用预先计算的训练集或特殊的变量选择，InterpMC对用户几乎完全透明。
英文摘要：
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a "proof of concept", and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user.
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