Alright I guess simplify the problem. Switch to like a 2 day month, or put a poll on every day and try that.
Then there’s only one timestep to inform phi by, but presumably then the prior should take over and the sampling should still be okay?
And if phi tries to go to zero then that is fishy?
Not sure just trying to come up with ideas to test.
phi wanting to be zero here seems very strange. Can you do plot the fits themselves somehow to see what is happening?
I will have to do more testing but it now looks fine. I separated the total variance parameter for the random walk for the prior position and the random walk for the observation period but I am not sure whether that’s the cause of the improvement.
Probably going to vary the number of units, time points, and polls to see how that affects the fit.
Running simulations now here comparing the true phi against the probability that it’s bigger than the draws. This doesn’t really look like desired behavior.
Ooooo maybe estimate an initial condition parameter?
And I wanna see a plot of the marginals of mu_b vs. time with the MLE estimates for mu_b vs. time.
Not sure, this just looks kinda like phi is being regularized right? Which is what you want the prior to do
