Related papers: Properties of Nested Sampling
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…
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…
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…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
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…
Lifted samplers form a class of Markov chain Monte Carlo methods which has drawn a lot attention in recent years due to superior performance in challenging Bayesian applications. A canonical example of lifted samplers is the one that is…
We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs…
Nested stochastic modeling has been on the rise in many fields of the financial industry. Such modeling arises whenever certain components of a stochastic model are stochastically determined by other models. There are at least two main…
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…
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…
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.…
Estimating nested expectations is an important task in computational mathematics and statistics. In this paper we propose a new Monte Carlo method using post-stratification to estimate nested expectations efficiently without taking samples…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
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…
Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…
Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer…
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…