Related papers: Power-Conditional-Expected Priors: Using g-priors …

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…

We examine necessary and sufficient conditions for posterior consistency under $g$-priors, including extensions to hierarchical and empirical Bayesian models. The key features of this article are that we allow the number of regressors to…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification ('posterior credible sets'). We investigate Bayesian…

We revisit widely used preferential Gaussian processes by Chu et al.(2005) and challenge their modelling assumption that imposes rankability of data items via latent utility function values. We propose a generalisation of pgp which can…

Bayesian model selection procedures based on nonlocal alternative prior densities are extended to ultrahigh dimensional settings and compared to other variable selection procedures using precision-recall curves. Variable selection…

Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…

There has been increased interest in using prior information in statistical analyses. For example, in rare diseases, it can be difficult to establish treatment efficacy based solely on data from a prospective study due to low sample sizes.…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in…

In this work, we show that under specific choices of the copula, the lasso, elastic net, and $g$-prior are particular cases of `copula prior,' for regularization and variable selection method. We present `lasso with Gauss copula prior' and…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

We introduce a joint posterior $p$-value, an extension of the posterior predictive $p$-value for multiple test statistics, designed to address limitations of existing Bayesian $p$-values in the setting of continuous model expansion. In…

To improve word representation learning, we propose a probabilistic prior which can be seamlessly integrated with word embedding models. Different from previous methods, word embedding is taken as a probabilistic generative model, and it…

Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…

In data sets with many predictors, algorithms for identifying a good subset of predictors are often used. Most such algorithms do not account for any relationships between predictors. For example, stepwise regression might select a model…

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model…