Related papers: Bayesian inference of solar and stellar magnetic f…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a…
The inverse problem which consists of determining the flow at the Earth's Core Mantle Boundary according to an outer core magnetic field and secular variation model, has been investigated through a Bayesian formalism. To circumvent the…
Vacuum polarization, a key prediction of quantum theory, can cause a variety of intriguing phenomena that can be triggered by high-intensity laser pulses. The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of…
We present a Bayesian method for inferring axisymmetric plasma equilibria from the magnetic field and plasma pressure measurements. The method calculates all possible solutions for plasma current and pressure distributions consistent with…
The analysis of high spectral resolution spectroscopic and spectropolarimetric observations constitute a very powerful way of inferring the dynamical, thermodynamical, and magnetic properties of distant objects. However, these techniques…
We examine whether or not it is possible to derive the field strength distribution of quiet Sun internetwork regions from very high spatial resolution polarimetric observations in the visible. In particular, we consider the case of the…
A Bayesian probability based approach is applied to the problem of detecting and parameterizing oscillations in the upper solar atmosphere for the first time. Due to its statistical origin, this method provides a mechanism for determining…
The behavior of the observed polarization amplitudes with spatial resolution is a strong constraint on the nature and organization of solar magnetic fields below the resolution limit. We study the polarization of the very quiet Sun at…
Magnetic fields on the surface of the Sun and stars in general imprint or modify the polarization state of the electromagnetic radiation that is leaving from the star. The inference of solar/stellar magnetic fields is performed by…
We employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line. The synthetic Stokes profiles have properties in common with those observed in the quiet Sun. The…
Bayesian model selection provides a powerful and mathematically transparent framework to tackle hypothesis testing, such as detection tests of gravitational waves emitted during the coalescence of binary systems using ground-based laser…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…
Basic aspects of the relationship between the magnetic field and polarized maser radiation are described with the emphasis on interpreting the observed spectra. Special attention is given to three issues--the limitations on the…
The linear polarization that is observed, together with likely changes in the orientation of the magnetic field along the line of sight and hence of the optical axes of the medium, can lead to the circular polarization that is observed in…
Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources.…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
The next generation of weak lensing probes can place strong constraints on cosmological parameters by measuring the mass distribution and geometry of the low redshift universe. We show that a future all-sky tomographic cosmic shear survey…
The magnetic fields in the solar polar region are important to our understanding of the internal dynamo process, the global coronal structure, and the origin of the solar wind. The inference of polar fields based on spectropolarimetric…