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In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…

Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…

Mislabeled, duplicated, or biased data in real-world scenarios can lead to prolonged training and even hinder model convergence. Traditional solutions prioritizing easy or hard samples lack the flexibility to handle such a variety…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…

The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

We propose a probabilistic framework to directly insert prior knowledge in reinforcement learning (RL) algorithms by defining the behaviour policy as a Bayesian posterior distribution. Such a posterior combines task specific information…

Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise…

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP)…

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. In principle, prior elicitation transforms domain knowledge…

A comparison of structural features of quantum and classical physical theories, such as the information capacity of systems subject to these theories, requires a common formal framework for the presentation of corresponding concepts (such…

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…