Synthesis of hidden Markov models based on finite sample paths and applications to computational biology

In this paper, we study the problem of modelling a given stationary stochastic process using a hidden Markov model (HMM). In particular, we show how to construct a HMM for an arbitrary stochastic process so as to match perfectly its statistics up to a prespecified order, and to match optimally its statistics of higher order. This approach is applied to two problems in computational biology, namely: distinguishing between the coding and non-coding regions of a Prokaryote genome, and classifying a protein into a small family of proteins.