Related papers: Bayesian Magnetohydrodynamic Seismology of Coronal…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
We simulate transverse oscillations in radiatively cooling coronal loops and forward-model their spectroscopic and imaging signatures, paying attention to the influence of background emission. The transverse oscillations are driven at one…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Kink oscillations in coronal loops have been extensively studied for their potential contributions to coronal heating and their role in plasma diagnostics through coronal seismology. A key focus is the strong damping of large-amplitude kink…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is based on a quasi-linear approach with prescribed inner and outer boundary conditions. The 1-d diffusion…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation given noisy observation data on its solution at a set of spatial points. We study approximation of the posterior probability…
We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in…
Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
The quantification of myocardial perfusion MRI has the potential to provide a fast, automated and user-independent assessment of myocardial ischaemia. However, due to the relatively high noise level and low temporal resolution of the…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…
The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference…
Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the…
We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the…