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The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification ('posterior credible sets'). We investigate Bayesian…
We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…
Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…
The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive…
We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…
A new class of functions, called the `Information sensitivity functions' (ISFs), which quantify the information gain about the parameters through the measurements/observables of a dynamical system are presented. These functions can be…
Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems…
Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
The information bottleneck (IB) method offers an attractive framework for understanding representation learning, however its applications are often limited by its computational intractability. Analytical characterization of the IB method is…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…