ﻻ يوجد ملخص باللغة العربية
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 termination point. A systematic literature review of nested sampling algorithms and variants is presented. We focus on complete algorithms, including solutions to likelihood-restricted prior sampling, parallelisation, termination and diagnostics. The relation between number of live points, dimensionality and computational cost is studied for two complete algorithms. A new formulation of NS is presented, which casts the parameter space exploration as a search on a tree. Previously published ways of obtaining robust error estimates and dynamic variations of the number of live points are presented as special cases of this formulation. A new on-line diagnostic test is presented based on previous insertion rank order work. The survey of nested sampling methods concludes with outlooks for future research.
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
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
Metropolis Hastings nested sampling evolves a Markov chain, accepting new points along the chain according to a version of the Metropolis Hastings acceptance ratio, which has been modified to satisfy the nested sampling likelihood constraint. The geo
The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with vari