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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 variable errors, and deriving parameter uncertainties is often an after-thought. Classic forward-folding analyses with Markov Chain Monte Carlo or Nested Sampling enable parameter estimation and model comparison, even for complex and slow-to-evaluate physical models. However, these approaches require independent runs for each data set, implying an unfeasible number of model evaluations in the Big Data regime. Here I present a new algorithm, collaborative nested sampling, for deriving parameter probability distributions for each observation. Importantly, the number of physical model evaluations scales sub-linearly with the number of data sets, and no assumptions about homogeneous errors, Gaussianity, the form of the model or heterogeneity/completeness of the observations need to be made. Collaborative nested sampling has immediate application in speeding up analyses of large surveys, integral-field-unit observations, and Monte Carlo simulations.
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
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
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
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