#### [MADS] logistic regression

Although a bit of time has elapsed since my post space weather, saying that logistic regression is used for prediction, it looks like still true that logistic regression is rarely used in astronomy. Otherwise, it could have been used for the similar purpose not under the same statistical jargon but under the Bayesian modeling procedures.

Maybe, some astronomers want to check out this versatile statistical method, wiki:logistic regression to see whether they can fit their data to this statistical method in order to model/predict observation rates, unobserved rates, undetected rates, detected rates, absorbed rates, and so on in terms of what are observed and additional/external observations, knowledge, and theories. I wonder what would it be like if the following is fit using logistic regression: detection limits, Eddington bias, incompleteness, absorption, differential emission measures, opacity, etc plus brute force Monte Carlo simulations emulating likely data to be fit. Then, responses are the probability of observed vs not observed as a function of redshift, magnitudes, counts, flux, wavelength/frequency, and other measurable variables or latent variables.

My simple reasoning that astronomers observe partially and they will never have complete sample, has imposed a prejudice that logistic regression would appear in astronomical literature rather frequently. Against my bet, it was [MADS]. All stat softwares have packages and modules for logistic regression; therefore, you have a data set, application is very straight forward.

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Although logistic regression models are given in many good tutorials, literature, or websites, it might be useful to have a simple but intuitive form of logistic regression for sloggers.

When you have binary responses, metal poor star (Y=1) vs. metal rich star (Y=2), and predictors, such as colors, distance, parallax, precision, and other columns in catalogs (X is a matrix comprised of these variables), $logit(Pr(Y=1|X))=\log \frac{Pr(Y=1|X)}{1-Pr(Y=1|X)} = \beta_o+{\mathbf X^T \beta}$.
As astronomers fit a linear regression model to get the intercept and slope, the same approach is applied to get intercepts and coefficients of logistic regression models.