Related papers: Posterior Model Consistency in Variable Selection …
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…
Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…
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…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
We study Bayesian discriminative inference given a model family $p(c,\x, \theta)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and…
We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…