Algebraic identification of binary-valued hidden Markov processes
Alexander Schoenhuth

The complete identification problem is to decide whether a stochastic process 
$(X_t)$ is a hidden Markov process and if yes to infer a corresponding 
parametrization. So far only partial answers to either the decision or the 
inference part had been available all of which depend on further assumptions on 
the processes which are usually centered around stationarity. Here we present a 
full, general solution for binary-valued hidden Markov processes. Our approach 
is rooted in algebraic statistics and therefore geometric in nature. We 
demonstrate that the algebraic varieties which describe the probability 
distributions associated with binary-valued hidden Markov processes are zero 
sets of determinantal equations which draws a connection to well-studied 
objects from (linear) algebra. Therefore our solution immediately gives rise to 
algorithmic tests in form of elementary algebraic routines.