Related papers: Spectral likelihood expansions for Bayesian infere…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

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…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…

This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the…

We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…

Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…