Related papers: On Expectation Propagation and the Probabilistic E…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
Bayesian interpretations of neural processing require that biological mechanisms represent and operate upon probability distributions in accordance with Bayes' theorem. Many have speculated that synaptic failure constitutes a mechanism of…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…
The present paper considers modified extension of the exponential distribution with three parameters. We study the main properties of this new distribution, with special emphasis on its median, mode and moments function and some…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function.…
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is…
Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…
Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential…
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…