CA6: MCMC results for linear response function

Here are the marginalized posterior pdfs for the linear coefficients describing response function in linear.txt:

It took me about a 1.5 hours to write the code to first do a grid search (red line, peak set to unity), and then write the MCMC algorithm (black histogram). I imagine the Gaussian line profile fit due Monday should take you about 3 hours, most of it debugging. Such is research.

Some tips for writing MCMC code:

1. For the linear fit, do a grid analysis first. This will help you get a sense for the probability space. If you have a handy amoeba or downhill simplex code, you can do a maximum likelihood search for the best-fitting line profile parameters for problem 3, and then use those pars as the initial guesses for your MCMC code.
   
2. Work with logarithmic probabilities!
3. Make sure each step of your code makes logical sense. Did log(L) increase when you moved closer to the best values?
4. You will start each chain link from some set of parameters with some starting value of log(L). If you do not accept the step, make sure you go back to the starting values of the parameters and log(L). Otherwise you random-walk yourself into oblivion (this is what had me stuck for 30 minutes this morning).
5. 10^7 chain links required only 2 minutes on a 2.9 GHz Intel CPU for the linear problem. Vectorize your code!
6. In IDL, use a WHILE or REPEAT-UNTIL loop. FOR loop control variables can't go high enough for most MCMC applications. UPDATE: Prof. Fitzgerald noted that you can use Long variable types as loop control variables: FOR i = 0L, long(N-1) DO ...