Negative binomial in addition about pybats HOT 6 OPEN

Hi,

A detail hidden within the Poisson DGLM is that the forecast distribution is negative binomial. A full discussion is given in this book, Chapter 14.

Briefly, the amount of dispersion in the forecast distribution increases with the uncertainty in the DGLM coefficients. As noted in the documentation, the forecast distribution is:

$$y_t \sim Pois(\mu_t)$$

However, there is a prior distribution on $\mu_t$:
$$\mu_t \sim Ga(\alpha_t, \beta_t)$$

If you integrate out $\mu_t$, then marginally the forecast distribution becomes negative binomial.

On a practical note, if you are working with data that has greater than Poisson dispersion, you can also use the hyperparameter $\rho$. $0 \lt \rho \lte 1$, and the smaller $\rho$ becomes, the larger the forecast variance. You can set this in the analysis function, or when you define a Poisson DGLM yourself, with rho=0.5, or some other value.

Thanks,
Isaac

from pybats.

from pybats.

The model name corresponds to the observation equation conditioned on knowing all the parameters. For a Poisson DGLM, when you condition on $mu_t$, then the forecast distribution is Poisson.

Full details on DGLM theory is given in this book, Chapter 14. Additionally, here is the Wikipedia article on the Gamma-Poisson mixture.

from pybats.

from pybats.

Thanks for linking to the Mixture Density network, it looks like a very interesting model and good research. However, the goal of the Mixture Density network seems quite different than the goals of PyBATS. PyBATS is primarily focused on time series, especially computationally efficient models that can be run quickly. I appreciate the suggestion, but I'm not sure that I see them directly connecting.

from pybats.

from pybats.