Related papers: Objective Bayesian analysis for spatial Student-t …
The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via "standard"…
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors.…
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…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior…
Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…
The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian…
This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution…
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…
Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a…
We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
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…
Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…
Although spatial prediction is widely used for urban and environmental monitoring, its accuracy is often unsatisfactory if only a small number of samples are available in the study area. The objective of this study was to improve the…
Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for…
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,…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…