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Related papers: Nested Sampling Methods

200 papers

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…

Computation · Statistics 2019-01-23 Edward Higson , Will Handley , Mike Hobson , Anthony Lasenby

We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested…

Machine Learning · Computer Science 2023-12-08 Pablo Lemos , Nikolay Malkin , Will Handley , Yoshua Bengio , Yashar Hezaveh , Laurence Perreault-Levasseur

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…

Computation · Statistics 2023-04-19 Johannes Buchner

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…

Computation · Statistics 2021-03-24 Sara Pérez-Vieites , Joaquín Míguez

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…

Computation · Statistics 2021-03-05 Andrew Fowlie , Will Handley , Liangliang Su

The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…

Statistics Theory · Mathematics 2021-04-29 Doris Schittenhelm , Philipp Wacker

Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…

Computation · Statistics 2015-01-15 Brendon J. Brewer

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

Computation · Statistics 2015-09-14 Christian A. Naesseth , Fredrik Lindsten , Thomas B. Schön

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

Computation · Statistics 2025-01-03 Omiros Papaspiliopoulos , Timothée Stumpf-Fétizon , Giacomo Zanella

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…

High Energy Physics - Phenomenology · Physics 2022-08-09 David Yallup , Timo Janßen , Steffen Schumann , Will Handley

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…

Computation · Statistics 2020-08-25 Andrew Fowlie , Will Handley , Liangliang Su

Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…

Computation · Statistics 2014-12-03 Johannes Buchner

Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems.…

Methodology · Statistics 2022-08-23 Yan Wang , Meng Wang , Areej AlBahar , Xiaowei Yue

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison.…

Instrumentation and Methods for Astrophysics · Physics 2021-06-30 Justin Alsing , Will Handley

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…

Instrumentation and Methods for Astrophysics · Physics 2024-10-17 Isidro Gómez-Vargas , J. Alberto Vázquez

We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS…

Data Analysis, Statistics and Probability · Physics 2022-01-17 Andrew Fowlie , Sebastian Hoof , Will Handley

Recently, neural architecture search (NAS) has been applied to automate the design of neural networks in real-world applications. A large number of algorithms have been developed to improve the search cost or the performance of the final…

Machine Learning · Computer Science 2022-06-20 Yao Shu , Yizhou Chen , Zhongxiang Dai , Bryan Kian Hsiang Low

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…

Computation · Statistics 2020-02-11 Kamran Javid

Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…

Computation · Statistics 2010-10-11 Nicolas Chopin , Christian Robert

In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…

Machine Learning · Computer Science 2012-12-27 Miguel Á. Carreira-Perpiñán , Weiran Wang