Stochastic Estimation Theory

The stimuli used in Chapters 22 and 23 to characterize the receptive fields of visual neurons were deterministic, but random stimuli can be used as well for this purpose. In this chapter, we derive the general solution to the problem of recovering the mapping between stimulus and firing rate using random stimuli, which is given by the conditional expectation or mean . We then show how to recover the mapping from stimulus to firing rate when the underlying neuron's receptive field is characterized by a linear weighting function. The linear case turns out to be optimal when the stimuli and firing rates are jointly Gaussian. Finally, we show how simple non-linear transformations can be recovered using Gaussian random stimuli.