Generic Identication of Binary-Valued Hidden Markov Processes
The generic identication problem is to decide whether a stochastic process (Xt) is ahidden Markov process and if yes to infer its parameters for all but a subset of parametrizationsthat form a lower-dimensional subvariety in parameter space. Partial answers so far availabledepend on extra assumptions on the processes, which are usually centered around stationarity.Here we present a general solution for binary-valued hidden Markov processes. Our approach isrooted in algebraic statistics hence it is geometric in nature. We nd that the algebraic varietiesassociated with the probability distributions of binary-valued hidden Markov processes are zerosets of determinantal equations which draws a connection to well-studied objects from algebra. Asa consequence, our solution allows for algorithmic implementation based on elementary (linear)algebraic routines.