Mean shift cluster recognition method implementation in the nested sampling algorithm

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.

References in corpus (8)

• Bayes in the sky: Bayesian inference and model selection in cosmology
• A statistical test for Nested Sampling algorithms
• DIAMONDS: a new Bayesian Nested Sampling tool. Application to Peak Bagging of solar-like oscillations
• Direct comparison between Bayesian and frequentist uncertainty quantification for nuclear reactions
• Bayesian Calibrated Significance Levels Applied to the Spectral Tilt and Hemispherical Asymmetry
• Constant-pressure nested sampling with atomistic dynamics
• Bayesian inference of a negative quantity from positive measurement results
• Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

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