Abstract
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.
Highlights
Bayesian methods are routinely used in many fields: astrophysics and cosmology [1,2,3,4,5,6,7,8], particle physics [9], plasma physics [10,11], machine learning [12] and many others [13,14]
In the more recent Polycord program [29], where the search of new live points is based on the slice sampling, the cluster recognition is obtained by the k-nearest neighbor algorithm
We present a new application of cluster recognition to a nested sampling algorithm for the evaluation of the Bayesian evidence and posterior parameter probability distributions
Summary
Bayesian methods are routinely used in many fields: astrophysics and cosmology [1,2,3,4,5,6,7,8], particle physics [9], plasma physics [10,11], machine learning [12] and many others [13,14]. Because of its high-efficiency and relatively moderate calculation power requirement compared to other approaches, the nested sampling method is implemented in several data analysis codes such Multinest [3,27], Diamonds [28], Polycord [29], UltraNest, DNest4 [30] and Dynesty [31] for the computation of the Bayesian evidence and posterior probability distributions. We present an original approach based on cluster recognition with the mean shift method, one of the classic clustering algorithm widely used and included in the major machine learning libraries This method is implemented in the program NestedFit, a code developed by one of the authors and described in details in [39,40]. The article will end with a conclusive section (Section 4)
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