Related papers: Adaptive Bayesian density regression for high-dime…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…

Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

While deep learning-based classification is generally tackled using standardized approaches, a wide variety of techniques are employed for regression. In computer vision, one particularly popular such technique is that of confidence-based…

We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data…

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…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…