Related papers: A statistical test for Nested Sampling algorithms
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…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
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…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
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…
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissection, sparsification and low-rank compression. After…
We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice…
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…
We study the problem of sampling from a target distribution in $\mathbb{R}^d$ whose potential is not smooth. Compared with the sampling problem with smooth potentials, this problem is much less well-understood due to the lack of smoothness.…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
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…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…
Streaming computation plays an important role in large-scale data analysis. The sliding window model is a model of streaming computation which also captures the recency of the data. In this model, data arrives one item at a time, but only…
Sampling from multi-modal distributions and estimating marginal likelihoods, also known as evidences and normalizing constants, are well-known challenges in statistical computation. They can be overcome by nested sampling, which evolves a…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…