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Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…

Statistical techniques are needed to analyse data structures with complex dependencies such that clinically useful information can be extracted. Individual-specific networks, which capture dependencies in complex biological systems, are…

A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain…

We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand supports a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities…

We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming…

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…

We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

We develop a novel full-Bayesian approach for multiple correlated precision matrices, called multiple Graphical Horseshoe (mGHS). The proposed approach relies on a novel multivariate shrinkage prior based on the Horseshoe prior that borrows…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

Convolutional neural network (CNN) has achieved unprecedented success in image super-resolution tasks in recent years. However, the network's performance depends on the distribution of the training sets and degrades on out-of-distribution…

The accurate assessment of neuroimaging specificity is critical for advancing our understanding of brain disorders. Current methodologies often rely on frequentist approaches and limited cross-pathology comparisons, leading to potential…

Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…

In this technical note, we address an unresolved challenge in neuroimaging statistics: how to determine which of several datasets is the best for inferring neuronal responses. Comparisons of this kind are important for experimenters when…

Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or credible intervals to inform data-driven decision making. We propose a framework for power curve approximation with such hypothesis tests. We present a fast…

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…

We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to…