  Estimation of permutation entropy (PE) using Bayesian statistical methods is
presented for systems where the ordinal pattern sampling follows an
independent, multinomial distribution. It is demonstrated that the PE posterior
distribution is closely approximated by a standard Beta distribution, whose
hyperparameters can be estimated directly from moments computed analytically
from observed ordinal pattern counts. Equivalence with expressions derived
previously using frequentist methods is also demonstrated. Because Bayesian
estimation of PE naturally incorporates uncertainty and prior information, the
orthodox requirement that $N \gg D!$ is effectively circumvented, allowing PE
to be estimated even for very short time series. Self-similarity tests on PE
posterior distributions computed for a semiconductor laser with optical
feedback (SLWOF) system show its PE to vary periodically over time.
