“…HMMs are probabilistic models that describe observable events that depend on unobservable internal factors [2], based on the Markov property that the probability of transitioning to a future state depends only on the current state and not on previous states. Their applications have been diverse, encompassing facial recognition, speech recognition, genetic prediction, bioinformatics analysis, automatic classification of electrocardiograms (ECGs), neuronal activity in the visual cortex, epileptic seizures, tracking the movement of living organisms using ultrasound, aligning protein structure sequences, detecting homogeneous segments in DNA sequences, learning non-singular phylogenies, genetic mutation analysis of HIV sequences, and human genome analysis [3]- [5].…”