nemos.observation_models.PoissonObservations.estimate_scale#

PoissonObservations.estimate_scale(y, predicted_rate, dof_resid)[source]#

Assign 1 to the scale parameter of the Poisson model.

For the Poisson exponential family distribution, the scale parameter \(\phi\) is always 1. This property is consistent with the fact that the variance equals the mean in a Poisson distribution. As given in the general exponential family expression:

\[\text{var}(Y) = \frac{V(\mu)}{a(\phi)},\]

for the Poisson family, it simplifies to \(\text{var}(Y) = \mu\) since \(a(\phi) = 1\) and \(V(\mu) = \mu\).

Parameters:

  • y (Array) – Observed spike counts.

  • predicted_rate (Array) – The predicted rate values. This is not used in the Poisson model for estimating scale, but is retained for compatibility with the abstract method signature.

  • dof_resid (Union[float, Array]) – The DOF of the residuals.

Return type:

Union[float, Array]