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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 geometric nested sampling algorithm I present here is based on the Metropolis Hastings method, but treats parameters as though they represent points on certain geometric objects, namely circles, tori and spheres. For parameters which represent points on a circle or torus, the trial distribution is wrapped around the domain of the posterior distribution such that samples cannot be rejected automatically when evaluating the Metropolis ratio due to being outside the sampling domain. Furthermore, this enhances the mobility of the sampler. For parameters which represent coordinates on the surface of a sphere, the algorithm transforms the parameters into a Cartesian coordinate system before sampling which again makes sure no samples are automatically rejected, and provides a physically intuitive way of the sampling the parameter space.
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
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
A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions. Often by construction, many target distributions ca