Related papers: Distribution-Free Bayesian multivariate predictive…

We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, prediction sets can be constructed using the method of conformal prediction. The validity of…

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

We develop a non-parametric Bayesian prior for a family of random probability measures by extending the Polya tree ($PT$) prior to a joint prior for a set of probability measures $G_1,\dots,G_n$, suitable for meta-analysis with event time…

This paper proposes a hierarchical Bayesian multitask learning model that is applicable to the general multi-task binary classification learning problem where the model assumes a shared sparsity structure across different tasks. We derive a…

Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…

We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…

Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…

We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and…

Linear mixed models are widely used for analyzing hierarchically structured data involving missingness and unbalanced study designs. We consider a Bayesian clustering method that combines linear mixed models and predictive projections. For…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…

This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…