Markov dependency based on Shannon´s entropy and its application to neural spike trains

A measure of simplified dependency is introduced representing Markovian characteristics based on Shannon´s entropy and conditional entropy under the Gaussian assumption. It is considered to be the most concise measure for expressing the higher order statistical properties of a time series and, in this regard, to be superior to a correlation or spectral measure. Simplified dependency is shown to be closely related to the prediction error in the autoregressive analysis of a time series and to be applicable also to non-Gaussian processes. Both the truncation method of distribution and the ensemble dependency analysis are informative for clarifying the statistical characteristics of interval sequence of a skewed distribution in a heterogeneous time series. These techniques serve to clarify the neural modulation mechanism.