On the permutation entropy Bayesian estimation

Abstract

We present the Bayesian estimation of Permutation Entropy. In particular, we studied the bias and the mean squared error in the entropy estimation when the length of the time series embedded in the m-dimension space is much less than the limit 5m! necessary for all the patterns to be expressed. Using objective Dirichlets distributions as priors, we found that for low dimensions, when there are few missing patterns, the Bayes-Laplace distribution is the one that presents the best performance, while for high dimensions, when many missing patterns can be present, the Perk's distribution minimizes the mean square error and bias. We also show how the posterior distribution of each parameter could behave in presence of missing values and give some discussion about the potential uses of this new approach for Permutation Entropy estimation.