Related papers: Bayesian Inversion of Stokes Profiles
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
First results of the inversion of Stokes I and V profiles from plage regions near disk center are presented. Both low and high spatial resolution spectra of FeI 6301.5 and FeI 6302.5 A obtained with the Advanced Stokes Polarimeter (ASP)…
We implemented the Bayesian analysis to the polarised neutron reflectivity data. Reflectivity data from a magnetic TbCo thin film structure was studied using the bundle of a Monte-Carlo Markov-chain algorithm, likelihood estimation, and…
Observations of the Sun in the visible spectral range belong to standard measurements obtained by instruments both on the ground and in the space. Nowadays, both nearly continuous full-disc observations with medium resolution and dedicated…
An inversion technique has been developed to recover LTE one-dimensional model photospheres for late-type stars from very high-resolution high signal-to-noise stellar line profiles. It is successfully applied to the Sun using a set of…
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…
Radio occultations are commonly used to assess remotely the thermodynamic properties of planets or satellites' atmospheres within the solar system. The data processing usually involves the so-called Abel inversion method or the numerical…
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…
With the advent of next generation high resolution telescopes, our understanding of how the magnetic field is organized in the internetwork (IN) photosphere is likely to advance.We aim to evaluate the extent to which we can retrieve…
Observations by the Interface Region Imaging Spectrograph (IRIS) in the Mg II h & k spectral lines have provided a new diagnostic window towards the knowledge of the complex physical conditions in the solar chromosphere. Theoretical efforts…
Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations…
The polarised spectrum of stellar radiation encodes valuable information on the conditions of stellar atmospheres and the magnetic fields that permeate them. In this paper, we give explicit expressions to estimate the magnetic field vector…
One of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way. Another challenge is that the number of true change…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…