statsmodels.genmod.bayes_mixed_glm.PoissonBayesMixedGLM.fit_vb

PoissonBayesMixedGLM.fit_vb(mean=None, sd=None, fit_method='BFGS', minim_opts=None, scale_fe=False, verbose=False, rng=None)

Fit a model using the variational Bayes mean field approximation.

Parameters:

meanarray_like

Starting value for VB mean vector

sdarray_like

Starting value for VB standard deviation vector

fit_methodstr

Algorithm for scipy.minimize

minim_optsdict

Options passed to scipy.minimize

scale_febool

If true, the columns of the fixed effects design matrix are centered and scaled to unit variance before fitting the model. The results are back-transformed so that the results are presented on the original scale.

verbosebool

If True, print the gradient norm to the screen each time it is calculated.

rng{None, int, array_like[int], numpy.random.Generator, numpy.random.RandomState}, optional

If rng is None, a new Generator is created using fresh entropy from the operating system. If rng is an int or array of ints, a new Generator is created, seeded with rng. If rng is already a Generator or RandomState instance, that instance is used. Only used if sd is None.

Notes

The goal is to find a factored Gaussian approximation q1*q2*… to the posterior distribution, approximately minimizing the KL divergence from the factored approximation to the actual posterior. The KL divergence, or ELBO function has the form

E* log p(y, fe, vcp, vc) - E* log q

where E* is expectation with respect to the product of qj.

References

Blei, Kucukelbir, McAuliffe (2017). Variational Inference: A review for Statisticians https://arxiv.org/pdf/1601.00670.pdf