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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.
It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that that in the presence of plateaus in the likelihood function nested sampling (NS) produces faulty estimates of the evidence and posterior densities. After informally explain
Nested sampling (NS) computes parameter posterior distributions and makes Bayesian model comparison computationally feasible. Its strengths are the unsupervised navigation of complex, potentially multi-modal posteriors until a well-defined terminatio
We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of live points varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation accuracy comp
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions, particularly if
Metropolis nested sampling evolves a Markov chain from a current livepoint and accepts new points along the chain according to a version of the Metropolis acceptance ratio modified to satisfy the likelihood constraint, characteristic of nested sampli