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We consider a new statistical model called the circulant correlation structure model, which is a multivariate Gaussian model with unknown covariance matrix and has a scale-invariance property. We construct shrinkage priors for the circulant…
Standard autoregressive language models generate text by repeatedly selecting a discrete next token, coupling prediction with irreversible commitment at every step. We show that token selection is not the only viable autoregressive…
We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$…
We discuss a Bayesian hierarchical copula model for clusters of financial time series. A similar approach has been developed in recent paper. However, the prior distributions proposed there do not always provide a proper posterior. In order…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…
Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…
Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that…
Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
Over the past two decades, shrinkage priors have become increasingly popular, and many proposals can be found in the literature. These priors aim to shrink small effects to zero while maintaining true large effects. Horseshoe-type priors…
We consider estimation of a normal mean matrix under the Frobenius loss. Motivated by the Efron--Morris estimator, a generalization of Stein's prior has been recently developed, which is superharmonic and shrinks the singular values towards…
The Bayesian Optimal Phase II (BOP2) framework is a flexible trial design that can naturally facilitate complex adaptations due to its Bayesian setting. BOP2 uses equal randomisation and equally placed interim analyses in its design, but it…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
Prediction-Powered Inference (PPI) is a powerful framework for enhancing statistical estimates by combining limited gold-standard data with machine learning (ML) predictions. While prior work has demonstrated PPI's benefits for individual…
Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…