I attached slides that explain an alternative method to infer stellar types taking into account extinction and distance uncertainties. 

This method is very similar to what is adopted by Green et al. 2014, when they infer a 3D dust extinction to individual stars. The advantage is that we can directly obtain a probability distribution of stellar intrinsic parameters (age, metallicity, mass, temperature, etc.) taking into account the uncertainties in distance and extinction, both of which are crucial for selecting F-stars from photometric information.  The major difficulty at the moment is a computational cost (~1 day, with multiprocessing with 50 CPUs ).  I will address this issue in the next week. 

I probably have discouraged you on a separate ticket, apologies.  I am very impressed by the slides; this is a very careful approach and looks really great.  My only concern is the compute time as you say; can we classify millions/billions of stars this way?  If my concern turns out not to be a problem, great, we should adopt this approach.  Otherwise, we might want to consider a little simpler algorithm...?

Thanks for your prompt reply! I will investigate whether we could reduce the computation time. 

The computation time for the MCMC analysis, mentioned in my previous post, has been reduced to 2-3 hours for one star with 50 CPUs. This may be still too long to process >100 million sources within a reasonable time scale. 

I think, therefore, we could take a hybrid approach; 

1. We first use the logistic regression algorithm, as we previously adopted. This method provides the probability of being an F star for all the Gaia-PS1 crossmatched sources with reliable parallax and griz photometry. To take into account the extinction correction/distance uncertainties, we flag objects with unreliable distance or reddening estimates. 
2. The MCMC analysis will be used as a supplementary information, if we want to prioritize among the Fstar candidates selected in the Step 1. 

As for the flagging of unreliable distance/reddening, stars with reddening uncertainty > 20% or distance uncertainty > 20 % are flagged at the moment. I attach a figure for the Gmag histogram of all Fstars and unflagged (reliable) Fstars for a small region of the sky.  

As for Step 2, I will continue trying to speed up the parameter estimates.  

Any comments or suggestions, especially on how we flag the F-star candidates, are appreciated.

With the new method using brutus code, the uncertainties in extinction correction are fully taken into account for the stellar temperature determination. The code outputs the posterior probability distribution of Teff given photometric data (PS1 griz) and the priors on Galactic stars. The validity of the new method should be tested by upcoming engineering observations. 

We will have to see how accurate the uncertainties from brutus are with real data, but that is the scope of a future ticket.