Stumbled upon

I stumbled upon a result today that verifies that my theory works! This idea came at just the right time. I had just gotten out of a meeting with my adviser in which we were discussing strategies on how to test the theory, some of the ideas were to run simulations that could take weeks, because all of my preliminary results suggested I needed a ridiculously large sample size.

The filtering technique definitely improved the time of my results but still the tests were going to consume alot of precious time without even knowing if the theory was correct. As I was going back to my office thinking about how much work I would have to do just to test the theory, I thought "what if I just decrease the jump size"?

I had done this before in some early tests but I didn't think to do it in the parameter estimation, however the logic suggest a smaller jump size would imply smaller particle size. Woila it works! The likelihood increases at each iteration which is consistent with the theory, my parameter estimates are not the same, but the theory doesnt guarantee that; only an increase in the likelihood. But this means at the very least that the theory works.

I cannot overestimate how much a sigh of relief this was, I have found dry ground. I barely know where I am, how I got here, or what this means, but I know I have dry ground. Right now I am running the algorithm from different initial conditions. This should be the beginning of the end.