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This paper explores Bayesian inference for a biased sampling model in situations where the population of interest cannot be sampled directly, but rather through an indirect and inherently biased method. Observations are viewed as being the…

The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct…

The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…

We propose an objective Bayesian approach to the selection of covariates and their penalised splines transformations in generalised additive models. Specification of a reasonable default prior for the model parameters and combination with a…

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

Macroeconomists using large datasets often face the choice of working with either a large Vector Autoregression (VAR) or a factor model. In this paper, we develop methods for combining the two using a subspace shrinkage prior. Subspace…

Fine-tuning pre-trained models is a popular approach in machine learning for solving complex tasks with moderate data. However, fine-tuning the entire pre-trained model is ineffective in federated data scenarios where local data…

We theoretically justify the recent empirical finding of [Teh et al., 2025] that a transformer pretrained on synthetically generated data achieves strong performance on empirical Bayes (EB) problems. We take an indirect approach to this…

Pattern recognition applications often suffer from skewed data distributions between classes, which may vary during operations w.r.t. the design data. Two-class classification systems designed using skewed data tend to recognize the…

In this work, we propose a novel prior learning method for advancing generalization and uncertainty estimation in deep neural networks. The key idea is to exploit scalable and structured posteriors of neural networks as informative priors…

Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…

The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo & Johnson and the Dual…

Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…

This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment…

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…

Inferring the means in the multivariate normal model $X \sim N_n(\theta, I)$ with unknown mean vector $\theta=(\theta_1,...,\theta_n)' \in \mathbb{R}^n$ and observed data $X=(X_1,...,X_n)'\in {\mathbb R}^n$ is a challenging task, known as…

Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…