Related papers: Progressive Gaussian Filtering
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Gaussian processes are one of the dominant approaches in Bayesian learning. Although the approach has been applied to numerous problems with great success, it has a few fundamental limitations. Multiple methods in literature have addressed…
We consider the statistical nonlinear inverse problem of recovering the absorption term $f>0$ in the heat equation $$ \partial_tu-\frac{1}{2}\Delta u+fu=0 \quad \text{on $\mathcal{O}\times(0,\textbf{T})$}\quad u = g \quad \text{on…
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…
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…
We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally…
In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…
We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence with limited…
Gaussian processes (GPs) offer a flexible, uncertainty-aware framework for modeling complex signals, but scale cubically with data, assume static targets, and are brittle to outliers, limiting their applicability in large-scale problems…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…