Continuing from where I left off last time, I tested out a three spot model today. Here’s the Maximum Likelihood solution for the two spot model in two dimensions:

where I used an Aitoff projection to show the spot locations and relative sizes. And here’s the three spot solution:

Note that the two rightmost spots in the three spot solution are very similar in size to the rightmost spot in the two spot solution. And the average latitude of those two rightmost spots in the three spot solution is approximately the latitude of the single rightmost spot in the two spot solution.

Including only three spots and we already see the degenerate dangers of spot modeling. On the two do list is to take a bayesian approach and use the emcee MCMC sampler to further explore parameter space and make sure the two rightmost spots in the two spot solution are not both getting caught in the same local minimum.

We also have a lot of prior information we know for this problem that we’ll be able to include when taking the Bayesian approach. More on that later…