On the Cramér-Rao bound applicability and the role of Fisher information in computational neuroscience

Neuronal systems exhibit impressive capabilities in decision making and action coordination by employing the encoded information about both external and internal environments. Despite the tremendous effort of neuroscientists, the exact nature of the neuronal code remains elusive. Various experimental and theoretical techniques have been used to resolve the question in recent decades, with methods of signal estimation and detection theory playing an important part. In this paper we review the particular approach which relies on the concepts of Fisher information and Cramér-Rao bound. These concepts essentially investigate the neuronal coding problem by addressing the theoretical limits on the decoding precision, be it in single neurons or in their populations. Despite the success of this approach in many instances, the underlying mathematical theory is not free of certain restrictive assumptions which might complicate the inference in some cases of interest. We recapitulate the assumptions and examine the practical extent of their validity.