This function processes gamma prediction results to calculate the mean age predictions, scale, and shape parameters efficiently.
process_gamma_predictions(gamma_prediction)
A list containing the following elements: - `mean_age_pred`: A vector of mean age predictions. - `scale_hat`: A vector of mean scale parameters. - `shape_hat`: A vector of mean shape parameters.
A list containing `scale_pred` and `shape_pred` matrices from the gamma prediction model.