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We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as…

Completely random measures (CRMs) are fundamental to Bayesian nonparametric models, with applications in clustering, feature allocation, and network analysis. A key quantity of interest is the Laplace exponent, whose asymptotic behavior…

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Bayesian model-based spatial clustering methods are widely used for their flexibility in estimating latent clusters with an unknown number of clusters while accounting for spatial proximity. Many existing methods are designed for clustering…

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally-biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying…

We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…

The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant…

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…

The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Re-ranking the data sequence after each new observation can become too intensive computationally.…

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

The uncertainty of classification outcomes is of crucial importance for many safety critical applications including, for example, medical diagnostics. In such applications the uncertainty of classification can be reliably estimated within a…

Bayesian optimization is a powerful paradigm to optimize black-box functions based on scarce and noisy data. Its data efficiency can be further improved by transfer learning from related tasks. While recent transfer models meta-learn a…

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…