相关论文: Power-Expected-Posterior Priors as Mixtures of g-P…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…

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 statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…

Extrapolating treatment effects from related studies is a promising strategy for designing and analyzing clinical trials in situations where achieving an adequate sample size is challenging. Bayesian methods are well-suited for this…

The mixture extension of exponential family principal component analysis (EPCA) was designed to encode much more structural information about data distribution than the traditional EPCA does. For example, due to the linearity of EPCA's…

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…

Gaussian stochastic process (GaSP) has been widely used in two fundamental problems in uncertainty quantification, namely the emulation and calibration of mathematical models. Some objective priors, such as the reference prior, are studied…

Although by now the ensemble-based probabilistic forecasting is the most advanced approach to weather prediction, ensemble forecasts still might suffer from lack of calibration and/or display systematic bias, thus require some…

Bayesian inference in generalized linear models requires a prior on the coefficient vector $\beta$. Practitioners naturally reason about response probabilities at specific covariate values, not about abstract log-odds parameters. We develop…

Bayesian modeling helps applied researchers articulate assumptions about their data and develop models tailored for specific applications. Thanks to good methods for approximate posterior inference, researchers can now easily build, use,…

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate…

In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the mixture. The posterior distributions of the…

Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian…

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…