nemos.observation_models.GammaObservations.deviance#
- GammaObservations.deviance(neural_activity, predicted_rate, scale=1.0)[source]#
Compute the residual deviance for a Gamma model.
- Parameters:
neural_activity (
Array) – The spike coun activity. Shape (n_time_bins, ) or (n_time_bins, n_neurons) for population models.predicted_rate (
Array) – The predicted firing rates. Shape (n_time_bins, ) or (n_time_bins, n_neurons) for population models.scale (
Union[float,Array]) – Scale parameter of the model.
- Return type:
Array- Returns:
The residual deviance of the model.
Notes
The deviance is a measure of the goodness of fit of a statistical model. For a Gamma model, the residual deviance is computed as:
\[\begin{split}\begin{aligned} D(y_{tn}, \hat{y}_{tn}) &= 2 \left[ -\log \frac{ y_{tn}}{\hat{y}_{tn}} + \frac{y_{tn} - \hat{y}_{tn}}{\hat{y}_{tn}}\right]\\\ &= 2 \left( \text{LL}\left(y_{tn} | y_{tn}\right) - \text{LL}\left(y_{tn} | \hat{y}_{tn}\right) \right) \end{aligned}\end{split}\]where \(y\) is the observed data, \(\hat{y}\) is the predicted data, and \(\text{LL}\) is the model log-likelihood. Lower values of deviance indicate a better fit.