Abstract
We address the problem of non-parametric estimation of the recently proposed measures of statistical dispersion of positive continuous random variables. The measures are based on the concepts of differential entropy and Fisher information and describe the “spread” or “variability” of the random variable from a different point of view than the ubiquitously used concept of standard deviation. The maximum penalized likelihood estimation of the probability density function proposed by Good and Gaskins is applied and a complete methodology of how to estimate the dispersion measures with a single algorithm is presented. We illustrate the approach on three standard statistical models describing neuronal activity.
Highlights
IntroductionThe dispersion (variability) of measured data needs to be described
The dispersion of measured data needs to be described
Spike train consists of times of spike occurrences τ0, τ1, . . . , τn, equivalently described by a set of n interspike intervals (ISIs) ti = τi − τi−1, i = 1 . . . n, and these ISIs are treated as independent realizations of the random variable T ∼ f (t)
Summary
The dispersion (variability) of measured data needs to be described. Standard deviation is used ubiquitously for quantification of variability, such approach has limitations. The dispersion of the probability distribution can be understood in different points of view: as “spread”. With respect to the expected value, “evenness” (“randomness”) or “smoothness”. For example highly variable data might not be random at all if it consists only of “extremely small” and “extremely large”. The probability density function or its estimate provides a complete view, quantitative methods are needed in order to compare different models or experimental results. In a series of recent studies [1,2] we proposed and justified alternative measures of dispersion
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