Related papers: Bayesian Magnetohydrodynamic Seismology of Coronal…
The analysis of quickly damped transverse oscillations of solar coronal loops using magneto-hydrodynamic seismology allow us to infer physical parameters that are difficult to measure otherwise. Under the assumption that such damped…
We present an analytic approximate seismic inversion scheme for damped transverse coronal loop oscillations based on the thin tube and thin boundary approximation for computing the period and the damping time. Asymptotic expressions for the…
Seismology of coronal loops using observations of damped transverse oscillations in combination with results from theoretical models is a tool to indirectly infer physical parameters in the solar atmospheric plasma. Existing seismology…
We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic (MHD) transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink waves in the…
High resolution observations have permitted to resolve the solar prominences/filaments as sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. We use…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…
Time and spatial damping of transverse magnetohydrodynamic (MHD) kink oscillations is a source of information on the cross-field variation of the plasma density in coronal waveguides. We show that a probabilistic approach to the problem of…
This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
One of the proposed damping mechanisms of coronal (transverse) loop oscillations in the kink-mode is resonant absorption as a result of the Alfven speed variation at the outer boundary of coronal loops. Analytical expressions for the period…
The spatial variation of physical quantities, such as the mass density, across solar atmospheric waveguides governs the timescales and spatial scales for wave damping and energy dissipation. The direct measurement of the spatial…
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical…
The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the…
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…