Statistical methods for absorbing Markov-chain models for learning: Estimation and identification

General algorithms for computing the likelihood of any sequence generated by an absorbing Markov-chain are described. These algorithms enable an investigator to compute maximum likelihood estimates of parameters using unconstrained optimization techniques. The problem of parameter identifiability is reformulated into questions concerning the behavior of the likelihood function in the neighborhood of an extremum. An alternative characterization of the concept of identifiability is proposed. A procedure is developed for deciding whether or not this definition is satisfied.This research was undertaken within the Institute for the Study of Intellectual Behavior, University of Colorado, and is Publication No. 42 of the Institute. The work was supported by NSF Grant GB-34077X. The logic underlying Algorithm I was suggested by Clint Schumacher.