A Generalized Ideal Observer Model for Decoding Sensory Neural Responses

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