VonMisesMixtureBinned vs. VonMisesMixture

[rc]

VonMisesMixtureBinned vs. VonMisesMixture

[rc]

The above results are for ~10 repetitions of the smallest raw histogram item, see get_counts_from_lengths(). When this number is increased to 100, the results are essentially the same, also aic and bic for VonMisesMixture is higher, closer to that of VonMisesMixtureBinned. Due to much larger data, fitting with VonMisesMixture then takes ages to finish. Then for 300, the curves are virtually indistinguishable etc.

My conclusion: It is preferable to use VonMisesMixtureBinned, which is much faster, for the analysis, together with the basin-hopping solver (a few (~20) iterations seems to be sufficient) to avoid dependence on the initial guess.

[josef-pkt]

VonMisesMixtureBinned with the original bin sizes from the raw data, is the "correct" approach given that the raw data are already binned. Since this is essentially fitting a histogram, I think, the parameter estimate is independent of the conversion to independent counts, but the inference still requires the sample size.
Did we normalize the sample size for VonsMisesMixtureBinned ?

statsmodels master now has a chisquare function, that tests that the deviation of the data from the estimated model has a minimal size. I was hoping this gives us better test results for the chisquare test, then the 0, 1 we get because of the larger sample size. (I'm going to look for it.)

I also ran the "fit_von_mises.py" script on top of my GenericLikelihood cleanup branch and it didn't change anything for this case.

Are we getting different results, parameters, with basinhopping than with just one set of starting values and bfgs?

[rc]

The VonsMisesMixtureBinned instance is created in analyses.fit_mixture.fit() - it uses the raw data, only the angles are transformed from [-90, 90[ to [-pi, pi[.

Mostly basinhopping and bfgs arrive to the same/very similar results. Only for some data/initial parameter values they differ - for example when bfgs fails with nans due to that integer overflow problem. With basinhopping, L-BFGS-B is used as the local minimizer, see examples/psets/solvers.py. In practice, it seems that a very few iterations of basinhopping is needed, to avoid "pathological" starting values.