论文标题
嵌套采样算法中的平均移位群集识别方法实现
Mean shift cluster recognition method implementation in the nested sampling algorithm
论文作者
论文摘要
嵌套采样是用于计算贝叶斯证据和后参数概率分布的有效算法。它基于通过蒙特卡洛采样对参数空间进行分步探索，其一系列值集称为Live点，这些值朝向感兴趣的区域，即可能性函数最大。在几个局部可能性最大值的情况下，该算法很难收敛。一些系统的错误也可以通过未探索的参数卷区域引入。为了避免这种情况，文献中提出了不同的方法，即使在存在局部最大值的情况下，也有效地搜索了新的实时点。在这里，我们基于在随机步行搜索算法中实现的平均移位群集识别方法提出了一个新解决方案。聚类识别集成在贝叶斯分析程序NestedFit中。通过对一些困难案例的分析进行了测试。与没有集群识别的分析结果相比，计算时间大大减少了。同时，有效地探索了整个参数空间，这转化为贝叶斯证据提取值的较小不确定性。
Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e. where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.
