Related papers: Computational statistics using the Bayesian Infere…

Despite the promise of Neural Posterior Estimation (NPE) methods in astronomy, the adaptation of NPE into the routine inference workflow has been slow. We identify three critical issues: the need for custom featurizer networks tailored to…

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…

Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave…

Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…

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…

A central challenge in many areas of science and engineering is to identify model parameters that are consistent with prior knowledge and empirical data. Bayesian inference offers a principled framework for this task, but can be…

This study proposes the novel Bayesian and inverse Bayesian (BIB) inference framework that incorporates symmetry bias into the Bayesian updating process to perform both conventional and inverse Bayesian updates concurrently. Conventional…

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…

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,…

Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…

We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…

Inference and decision making under uncertainty are key processes in every autonomous system and numerous robotic problems. In recent years, the similarities between inference and decision making triggered much work, from developing unified…

The formalism of Bayesian model selection provides a very elegant way of ranking different physical models in terms of how compatible they are with a given set of observed data. However, its practical application is often hampered by the…

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

1. Understanding the mechanisms underlying biological systems, and ultimately, predicting their behaviours in a changing environment requires overcoming the gap between mathematical models and experimental or observational data.…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…