相关论文: On the Posterior Computation Under the Dirichlet-L…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost…

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Exemplar-based clustering methods have been shown to produce state-of-the-art results on a number of synthetic and real-world clustering problems. They are appealing because they offer computational benefits over latent-mean models and can…

Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a…

In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…