Numerically Stable Hidden Markov Model Implementation

Application of Hidden Markov Models to long observation sequences entails the computation of extremely small probabilities. These probabilities introduce numerical instability in the computations used to determine the probability of an observed sequence given a model, the most likely sequence of states, and the maximum likelihood model updates given an observation sequence. This paper explains how to handle small probabilities by working with the logarithms of probabilities, rather than resorting to alternative rescaling procedures.