Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the stepbystep 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.

Automatic Clustering by Detecting Significant Density Dips in Multiple Dimensions Clustering algorithms are used to find groups of similar items in a dataset. Automatic clustering algorithms achieve this task without requiring users to input critical parameters. A recent automatic clustering methodology uses Hartiganu0027s dip test to detect significant peaks in the distribution of a dataset. This test can detect peaks in the distribution of a onedimensional variable. To perform clustering in multiple dimensions, algorithms of this methodology rely on onedimensional transformations of the dataset, which limits their effectiveness. In this paper, we present MDip, an automatic clustering algorithm that works directly on multidimensional space. MDip also assumes that clusters correspond to different peaks in the distribution of the dataset. It separates clusters at the dips that form between neighboring peaks. Dips are detected directly in multidimensional space, using a graphbased method. Their statistical significance is evaluated through appropriate simulations. Our experimental evaluation indicates that MDip achieves significantly better results than existing algorithms based on Hartiganu0027s dip, as well as other stateoftheart automatic clustering algorithms.