Related papers: Inferring Evidence from Nested Sampling Data via I…
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 a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The…
We introduce a novel technique within the Nested Sampling framework to enhance efficiency of the computation of Bayesian evidence, a critical component in scientific data analysis. In higher dimensions, Nested Sampling relies on Markov…
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…
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…
Bayesian inference without the likelihood evaluation, or likelihood-free inference, has been a key research topic in simulation studies for gaining quantitatively validated simulation models on real-world datasets. As the likelihood…
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…
Reconstructing the electric field from the measured voltages in an antenna, unfolding the antenna response, comes with several problems. Due to the noisiness of the signal it is often necessary to disregard part of the bandwidth of the…
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,…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
The convex conjugate (i.e., the Legendre transform) of Type II error probability (volume) as a function of Type I error probability (volume) is determined for the hypothesis testing problem with randomized detectors. The derivation relies…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
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…
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…
We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…