Probabilistic Description of Stellar Ensembles

Abstract

I describe the modeling of stellar ensembles in terms of probability distributions. This modeling is primary characterized by the number of stars included in the considered resolution element, whatever its physical (stellar cluster) or artificial (pixel/IFU) nature. It provides a solution of the direct problem of characterizing probabilistically the observables of stellar ensembles as a function of their physical properties. In addition, this characterization implies that intensive properties (like color indices) are intrinsically biased observables, although the bias decreases when the number of stars in the resolution element increases. In the case of a low number of stars in the resolution element (N<10⁵), the distributions of intensive and extensive observables follow nontrivial probability distributions. Such a situation ​​​ can be computed by means of Monte Carlo simulations where data mining techniques would be applied. Regarding the inverse problem of obtaining physical parameters from observational data, I show how some of the scatter in the data provides valuable physical information since it is related to the system size (and the number of stars in the resolution element). However, making use of such ​​​ information requires following iterative procedures in the data analysis.