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.

Surface Chemistry of Gold Nanoparticles Produced by Laser Ablation in Pure and Saline Water

“…A quantitative evaluation of the probability p 1 of a fitting model (1) compared to a second one (2) can thus be evaluated using p 1 = ev 1 /(ev 1 + ev 2 ). This analysis is performed using the code Nested_Fit, described in refs − . In the following, it is assumed that the counts in each channel follow a Poisson distribution function which gives access to the associated uncertainty.…”

Nested Sampling Methods

“…In practice, the computational cost is specific to the model structure as well. Thus requiring numerical testing (see for example Figure 15 in Pitkin et al (2017) and Figure 6 in Trassinelli and Ciccodicola, 2020). Finally, the discovery of likelihood peaks is also regulated by N (see §4.4).…”

“…This work does not verify the correctness of their implementation. A later publication by the same author includes MCMC proposals that do not preserve detailed balance (Trassinelli, 2019, their first high-failure recovery procedure).…”

“…Different to MultiNest's x-means, Trassinelli (2019) explores Gaussian mixture method and the mean-shift clustering method with MCMC, but lacks numerical comparisons to judge any improvements over previous publications, both for the proposal and clustering method.…”

Hybrid nested sampling method for identifying the uncertainty of the high-dimensional updating parameters in Bayesian structural model updating

“…Higson et al (2019) introduced the dynamic NS algorithm, which varies the number of live samples to increase efficiency. Trassinelli and Ciccodicola (2020) presented a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm to search the new samples. Wang et al (2021) proposed a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions, and a delayed rejection adaptive Metropolis algorithm is adopted to generate numerical samples.…”