A Generalized ideal observer model for decoding sensory neural responses

We show that many ideal observer models used to decode neural activity can be generalized to a conceptually and analytically simple form. This enables us to study the statistical properties of this class of ideal observer models in a unified manner. We consider in detail the problem of estimating the performance of this class of models. We formulate the problem de novo by deriving two equivalent expressions for the performance and introducing the corresponding estimators. We obtain a lower bound on the number of observations (N) required for the estimate of the model performance to lie within a specified confidence interval at a specified confidence level. We show that these estimators are unbiased and consistent, with variance approaching zero at the rate of 1/N. We find that the maximum likelihood estimator for the model performance is not guaranteed to be the minimum variance estimator even for some simple parametric forms (e.g., exponential) of the underlying probability distributions. We discuss the application of these results for designing and interpreting neurophysiological experiments that employ specific instances of this ideal observer model.