A Hidden Markov Model With Binned Duration Algorithm

The hidden Markov model with duration (HMMD) is critically important when the distributions on state intervals deviate significantly from the geometric distribution, such as for multimodal distributions and heavy-tailed distributions. Heavy-tailed distributions, in particular, are widespread in describing phenomena across the sciences, where the log-normal, student´s-T, and Pareto distributions are heavy-tailed distributions that are almost as common as the normal and geometric distributions in descriptions of physical phenomena or man-made phenomena. The standard hidden Markov model (HMM) constrains state occupancy durations to be geometrically distributed, while HMMD avoids this limitation, but at significant computational expense. We propose a new algorithm, hidden Markov model with binned duration, whose result shows no loss of accuracy compared to the HMMD decoding performance and a computational expense that only differs from the much simpler and faster HMM decoding by a constant factor.