Related papers: Model selection for spectro-polarimetric inversion…
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…
Our knowledge of the lower solar atmosphere is mainly obtained from spectropolarimetric observations, which are often carried out in the red or infrared spectral range and almost always cover only a single or a few spectral lines. Here we…
Accurate measurement of polarization in spectral lines is important for the reliable inference of magnetic fields on the Sun. For ground based observations, polarimetric precision is severely limited by the presence of Earth's atmosphere.…
The weak-field approximation is one of the simplest models that allows us to relate the observed polarization induced by the Zeeman effect with the magnetic field vector present on the plasma of interest. It is usually applied for…
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…
Comparison of appropriate models to describe observational data is a fundamental task of science. The Bayesian model evidence, or marginal likelihood, is a computationally challenging, yet crucial, quantity to estimate to perform Bayesian…
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
[abridged] Inversion techniques are the most powerful methods to obtain information about the thermodynamical and magnetic properties of solar and stellar atmospheres. In the last years, we have witnessed the development of highly…
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…
We derive a generalization of forward fitting for X-ray spectroscopy to include linear polarization of X-ray sources, appropriate for the anticipated next generation of space-based photoelectric polarimeters. We show that the inclusion of…
Models of coupled human-environment systems often face a tradeoff between realism and tractability. Spectrum opinion models, where social preferences vary continuously, offer descriptive richness but are computationally demanding and…
A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and…
Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…
We present a new approach for correcting instrumental polarization by modeling the non-depolarizing effects of a complex series of optical elements to determine physically realizable Mueller matrices. Provided that the Mueller matrix of the…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model…
Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…