Related papers: Bayesian calculus and predictive characterizations…

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…

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…

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…

We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…

A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. Here we extend this idea by…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

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…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…

Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse…

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models…