Validating Bayesian Inference Algorithms with Simulation-Based Calibration

Verifying the correctness of Bayesian computation is challenging. This is
especially true for complex models that are common in practice, as these
require sophisticated model implementations and algor ...

Philosophy and the practice of Bayesian statistics

A substantial school in the philosophy of science identifies Bayesian
inference with inductive inference and even rationality as such, and seems to
be strengthened by the rise and practical success of ...

Bayes and Frequentism: a Particle Physicist's perspective

In almost every scientific field, an experiment involves collecting data and
then analysing it. The analysis stage will often consist in trying to extract
some physical parameter and estimating its un ...

Calibrating Model-Based Inferences and Decisions

As the frontiers of applied statistics progress through increasingly complex
experiments we must exploit increasingly sophisticated inferential models to
analyze the observations we make. In order to ...

A Parsimonious Tour of Bayesian Model Uncertainty

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 a ...

A Conceptual Introduction to Markov Chain Monte Carlo Methods

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many
modern scientific analyses by providing a straightforward approach to
numerically estimate uncertainties in the parameters of ...

Generalized Posteriors in Approximate Bayesian Computation

Complex simulators have become a ubiquitous tool in many scientific
disciplines, providing high-fidelity, implicit probabilistic models of natural
and social phenomena. Unfortunately, they typically l ...

Computing Bayes: Bayesian Computation from 1763 to the 21st Century

The Bayesian statistical paradigm uses the language of probability to express
uncertainty about the phenomena that generate observed data. Probability
distributions thus characterize Bayesian inferenc ...

Bayesian Methods in Cosmology

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 ...