Evaluate the effect of initial theta estimates

[ericbair-sciome]

The current initial theta estimates are arbitrary and probably suboptimal. I have noticed that the estimates for the range parameters are often really bad in spatiotemporal simulations. I wonder if this is due to the fact that the initial estimates are bad and the algorithm never corrects itself. As a first step, it would be worthwhile to feed the procedure more accurate initial estimates and see how it affects the accuracy of the model. If it results in significant improvement, then we should try to find a more intelligent way to choose the initial theta's.

[kyle-messier]

@ericbair-sciome Is this a current problem? I think understanding the effects of [default] initial values for both the thetas and betas is critical. @sciome-bot Switching to version 1.0

[ericbair-sciome]

We did do some research on the initial beta estimates. We found that a better choice of initial beta's did speed things up significantly, but it made almost no difference to the final parameter estimates. My suspicion is that the initial theta estimates are going to make even less difference, but I do want to do some testing to confirm that.

[ericbair-sciome]

I had my intern work on this problem this summer. Basically, she tried a bunch of different starting theta's for a bunch of different simulations. We found that the final theta estimates depend very heavily on the starting theta estimates. That's the bad news. The good news is that the beta's hardly changed at all when the initial theta's changed. Given that the beta's are what we primarily care about it, I don't think I will close this issue quite yet, but I moved it to version 2.0. Even if we don't care as much about the theta's, a good starting estimate does seem to speed up the procedure significantly. However, it's not obvious to me how one would find a "good" initial estimate for the theta's. (If you have any ideas, I would love to hear them.)