Related papers: Nested sampling with any prior you like

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…

Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy and particle physics. We identify a previously unused property of NS related to order statistics: the insertion…

Inferring parameters and testing hypotheses from gravitational wave signals is a computationally intensive task central to modern astrophysics. Nested sampling, a Bayesian inference technique, has become an established standard for this in…

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…

Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation.…

Nested sampling is an increasingly popular technique for Bayesian computation, in particular for multimodal, degenerate problems of moderate to high dimensionality. Without appropriate settings, however, nested sampling software may fail to…

Nested sampling is a Bayesian sampling technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…

Bayesian inference methods rely on numerical algorithms for both model selection and parameter inference. In general, these algorithms require a high computational effort to yield reliable estimates. One of the major challenges in…

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…

Nested sampling is often used in Bayesian statistics problems in astronomy. It operates with a set of live points, iteratively replacing the point with the lowest likelihood with a new point of higher likelihood. Each iteration reduces the…

There is an ever-growing need in the gravitational wave community for fast and reliable inference methods, accompanied by an informative error bar. Nested sampling satisfies the last two requirements, but its computational cost can become…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to…

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…

In probabilistic (Bayesian) inferences, we typically want to compute properties of the posterior distribution, describing knowledge of unknown quantities in the context of a particular dataset and the assumed prior information. The marginal…

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…