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Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive…

The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…

The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…

Scientists and engineers use simulators to model empirically observed phenomena. However, tuning the parameters of a simulator to ensure its outputs match observed data presents a significant challenge. Simulation-based inference (SBI)…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and…

Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…

Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…

Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…

Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…

The structure of a protein is crucial in determining its functionality, and is much more conserved than sequence during evolution. A key task in structural biology is to compare protein structures in order to determine evolutionary…

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that…

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…

Many contemporary machine learning models require extensive tuning of hyperparameters to perform well. A variety of methods, such as Bayesian optimization, have been developed to automate and expedite this process. However, tuning remains…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…

Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naive Bayes classifier from the machine…

Machine learning classification problems are widespread in bioinformatics, but the technical knowledge required to perform model training, optimization, and inference can prevent researchers from utilizing this technology. This article…