Notes.txt

Notes
###############

spatial_BASCS.R code runs the fixed K (# sources) algorithm for disentangling sources.
### Please use the GitHub folder I set up. We can periodically save the code in Dropbox
but the main version should be in GitHub. 

Details:
1) The PSF is loaded in C++. The PSF should be checked against a bright source before
continuing. A visual step is built in to do this (inside a FALSE if statement). 
2) The number of iterations can be changed on lines 139 and 140.
3) Two runs that are performed. The first is a burnin period and is needed
to find the approximate locations of the sources. The second run is the main run used 
for inference. Importantly, the second run uses the locations found during burnin to 
deal with the label switching problem. See literature folder for more information
on label switching. Our approach is similar to an online version of Cron and West 
2011 which is a practical way to deal with the problem. Since the posteriors of 
source locations are typically well separated the label switching problem is not
something we need to spend too much effort on. 


Preliminary issues to address:
1) Mixing / sticking: in the example Chandra dataset 14 sources should be found, at least
for the full dataset. However, when we run the code often we do not find all the sources
but rather find two or more sources in some bright sources i.e. the MCMC sampler gets stuck
in some modes. I did not deal with this before because the RJMCMC aglorithm actually mitigates
it to a large degree because it can create and destroy unneeded sources including stuck
sources. However, I think that ideally we should make the MCMC work better and try to avoid
relying on the RJMCMC as much as possible, otherwise we may encounter unnecessary difficulties
down the line. There are two ways to address the problem: 

i) The first way is to use a simple approach to pick out the sources locations and then use these
to start the MCMC. This is not a complete solution but may be a worthwhile starting point to get 
to grips with things. You can use EM or if you are feeling more adventurous then try some 
nonparametric detection method (basically some form of binning andthresholding).
 
ii) The second way is to implement tempering as in Neal 1996. I think this is the real solution
and one of us should do it. Even if the eventual code skips the tempering part, we need it 
to be should of avoiding difficulties and for convincing ourselves andothers that the MCMC 
is working correctly. 


Main goal:
1) Build in model for the time data. The number of counts will be small since we are using 
X-ray data, so we should probably use the Poisson paradigm. Therefore Bayesian Blocks is a
good starting point.