Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

Models to assess the impact of a college on the local economy are examined. A primary objective was to derive equations for which data could be obtained from normal records kept by colleges, local governments, and businesses. The models, which are designed to be used by college presidents and their staffs, are linear cash-flow formulas, including…