Researchers, including scientists from CHASC, working on color magnitude diagrams to infer ages, metalicities, temperatures, and other physical quantities of stars and stellar clusters may find this paper useful.

Methodologies for temperature calibration (fairly accurate estimation from V-K and a new calibration from b-y), metallicity calibration, absolute magnitude/distance calibration, interstellar reddening, and stellar ages were presented with reviews on stellar models and their parameters, astrophysical calibration errors, metalicity distribution function, age-metallicity diagram, age-velocity relation, and thin disk vs thick disk. It seems like that the previous methodologies for F and G stars need to be revised.

Despite my incapability of full understanding the theory of star formation history and the uncertainties of calibrations (looks like that all go toward regression problems to me), this paper fully manifests the complexity of the stellar models and their calibration process. From a statistical perspective, the complexity of the stellar models and calibrations comes from many predictors and only a few response variables with uncertainties (even more they are heteroskedastic). Furthermore, the relationship between predictors and response variables is sparsely known, which makes fitting the model to a star or a stellar cluster or inferencing physical information from them difficult. The mapping is considered to be highly structured black box and its required careful investigations.

I’d rather end this very technical preprint by citing a sentence:

The question of interest is therefore how well these relations and their intrinsic scatter can be determined from the observations

[hlee: Instead of determining, modeling seems to reflect the flexibilities and uncertainties.]

I rather skip all technical details on ultracool dwarfs and binary stars, reviews on star formation studies, like initial mass function (IMF), astronomical survey studies, which Allen gave a fair explanation in arxiv/astro-ph:0707.2064v1 but want to emphasize that based on simple Bayes’ rule and careful set-ups for likelihoods and priors according to data (ultracool dwarfs), quite informative conclusions were drawn:

1. the peak at q~1 is significant,
2. lack of companions with a distance greater than 15-20 A.U. (a unit indicates the distance between the Sun and the Earth),
3. less binary stars with later spectral types,
4. inconsistency of undetected low mass ratio systems to the current data, and
5. 30% spectroscopic binaries are from ultracool binaries.

Before, asking for observational efforts for improvements, it is commented 75% as the the upper limit of the ultracool binary population.