Estimating the Firing Rate

Neuronal activity is measured by the number of stereotyped action potentials, called spikes, elicited in response to a stimulus or the behavioral conditions of an animal. Any nonparametric method for grasping the time-varying rate of spike firing contains a single parameter that controls the jaggedness of the estimated rate, such as the binsize of the time histogram or the bandwidth of the kernel smoother. In most neurophysiological studies, the parameter that determines the interpretation of neuronal activity has been selected subjectively by individual researchers. Recently, theories for objectively selecting the parameter have been developed. This chapter introduces the standard rate estimation tools, such as the peri-stimulus time histogram (PSTH), kernel density estimation, or Bayes estimation, and shows ways of selecting their parameters under the principles of minimizing the mean integrated squared error or maximizing the likelihood. We also sum up the methods in handy recipes that may be useful in practical data analysis.