Generic identification of binary-valued hidden Markov processes

Schönhuth A (2011)
Journal of Algebraic Statistics 5(1): 72-99.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The generic identification problem is to decide whether a stochastic process $(X_t)$ is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend 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 is rooted in algebraic statistics hence it is geometric in nature. We find that the algebraic varieties associated with the probability distributions of binary-valued hidden Markov processes are zero sets of determinantal equations which draws a connection to well-studied objects from algebra. As a consequence, our solution allows for algorithmic implementation based on elementary (linear) algebraic routines.
Erscheinungsjahr
2011
Zeitschriftentitel
Journal of Algebraic Statistics
Band
5
Ausgabe
1
Seite(n)
72-99
eISSN
1309-3452
Page URI
https://pub.uni-bielefeld.de/record/2941814

Zitieren

Schönhuth A. Generic identification of binary-valued hidden Markov processes. Journal of Algebraic Statistics. 2011;5(1):72-99.
Schönhuth, A. (2011). Generic identification of binary-valued hidden Markov processes. Journal of Algebraic Statistics, 5(1), 72-99.
Schönhuth, A. (2011). Generic identification of binary-valued hidden Markov processes. Journal of Algebraic Statistics 5, 72-99.
Schönhuth, A., 2011. Generic identification of binary-valued hidden Markov processes. Journal of Algebraic Statistics, 5(1), p 72-99.
A. Schönhuth, “Generic identification of binary-valued hidden Markov processes”, Journal of Algebraic Statistics, vol. 5, 2011, pp. 72-99.
Schönhuth, A.: Generic identification of binary-valued hidden Markov processes. Journal of Algebraic Statistics. 5, 72-99 (2011).
Schönhuth, Alexander. “Generic identification of binary-valued hidden Markov processes”. Journal of Algebraic Statistics 5.1 (2011): 72-99.

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