Related papers: When are Bayesian model probabilities overconfiden…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…

Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper, we argue that part of…

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)…

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…

Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal…

We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

We consider the problem of assessing goodness of fit of a single Bayesian model to the observed data in the inverse problem context. A novel procedure of goodness of fit test is proposed, based on construction of reference distributions…

For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…

Models are often misspecified in practice, making model criticism a key part of Bayesian analysis. It is important to detect not only when a model is wrong, but which aspects are wrong, and to do so in a computationally convenient and…

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…

The assessment of diversity and similarity is relevant in monitoring the status of ecosystems. The respective indicators are based on the taxonomic composition of biological communities of interest, currently estimated through the…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…

The counterfactual distribution models the effect of the treatment in the untreated group. While most of the work focuses on the expected values of the treatment effect, one may be interested in the whole counterfactual distribution or…

Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial data sets that are exchangeable with the real data under the null hypothesis (but not under the…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…