Related papers: Posterior propriety and admissibility of hyperprio…

Modern neural network libraries all take as a hyperparameter a random seed, typically used to determine the initial state of the model parameters. This opinion piece argues that there are some safe uses for random seeds: as part of the…

High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…

Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…

Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure)…

For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the…

Bayesian variable selection often assumes normality, but the effects of model misspecification are not sufficiently understood. There are sound reasons behind this assumption, particularly for large $p$: ease of interpretation, analytical…

We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class…

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…

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…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

Meta-analytic-predictive (MAP) priors have been proposed as a generic approach to deriving informative prior distributions, where external empirical data are processed to learn about certain parameter distributions. The use of MAP priors is…

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…

Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…