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This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
Stars play a decisive role in our Universe, from its beginning throughout its complete evolution. For a thorough understanding of their properties, evolution, and physics of their outer envelopes, stellar spectra need to be analyzed by…
We review recent advances in our understanding of massive stars through the analysis of their spectra. Improvements in model atmospheres and analysis methods are briefly discussed. Results obtained for stars in the Local Group are compared…
One of the main goals of modern observational cosmology is to map the large scale structure of the Universe. A potentially powerful approach for doing this would be to exploit three-dimensional spectral maps, i.e. the specific intensity of…
Most gas in giant molecular clouds is relatively low-density and forms star inefficiently, converting only a small fraction of its mass to stars per dynamical time. However, star formation models generally predict the existence of a…
It is currently impossible to determine the abundances of stellar populations star-by-star in dense stellar systems more distant than a few megaparsecs. Therefore, methods to analyse the composite light of stellar systems are required. I…
The determination of chemical abundances from stellar spectra is considered a mature field of astrophysics. Digital spectra of stars are recorded and processed with standard techniques, much like samples in the biological sciences.…
(abridged) This thesis presents theoretical and statistical techniques broadly related to systems of dynamically-interacting particles composed of several different types of populations. They are applied to observations of dense star…
Over the last half-century quantitative stellar spectroscopy has made great progress. However, most stellar abundance analyses today still employ rather simplified models, which can introduce severe systematic errors swamping the…
Determining the mass of stars is crucial both to improving stellar evolution theory and to characterising exoplanetary systems. Asteroseismology offers a promising way to estimate stellar mean density. When combined with accurate radii…
Convection and turbulence in stellar atmospheres have a significant effect on the emergent flux from late-type stars. The theoretical advancements in convection modelling over recent years have proved challenging for the observers to obtain…
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
We present a review of the application of numerical methods to solve the problem of the stellar/solar wind with the local interstellar medium. Most of approaches described are developed by the authors. They include both purely gas dynamic…
Stellar models are calculated in the approximation of a uniform density distribution. Variational method was used for determination of the boundary of a stability loss, for stellar masses in the range from 2 up to $10^5$ $M_{\odot}$. The…
I describe recent progress in terms of 3D hydrodynamical model atmospheres and 3D line formation and their applications to stellar abundance analyses of late-type stars. Such 3D studies remove the free parameters inherent in classical 1D…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
Clustering is an effective tool for astronomical spectral analysis, to mine clustering patterns among data. With the implementation of large sky surveys, many clustering methods have been applied to tackle spectroscopic and photometric data…
A solid sphere is considered, with a uniformly distributed infinity of points. Two points being pseudorandomly chosen, the analytical probability density that their separation have a given value is computed, for three types of the…
We present a method to infer reddenings and distances to stars, based only on their broad-band photometry, and show how this method can be used to produce a three-dimensional dust map of the Galaxy. Our method samples from the full…
The stellar population synthesis in unresolved composite objects is a very tricky problem. Indeed, it is a degenerate problem since many parameters affect the observables. The stellar population synthesis issue thus deserves a deep and…