Related papers: Inferring Evidence from Nested Sampling Data via I…

When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…

Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal…

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.…

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

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…

We present Nested Sampling with Slice-within-Gibbs (NS-SwiG), an algorithm for Bayesian inference and evidence estimation in high-dimensional models whose likelihood admits a factorization, such as hierarchical Bayesian models. We construct…

To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior:…

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…

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…

This paper proposes an extension to the classical 3D variational data assimilation approach by explicitly incorporating as a prior information, the transform-domain sparsity observed in a large class of geophysical signals. In particular,…

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…

We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

Improving our understanding of how information is encoded in vector space can yield valuable interpretability insights. Alongside vector dimensions, we argue that it is possible for the vector norm to also carry linguistic information. We…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested…

Pre-trained contextual representations have led to dramatic performance improvements on a range of downstream tasks. Such performance improvements have motivated researchers to quantify and understand the linguistic information encoded in…

We present mathematical and conceptual foundations for the task of robust amplitude estimation using engineered likelihood functions (ELFs), a framework introduced in Wang et al. [PRX Quantum 2, 010346 (2021)] that uses Bayesian inference…