Abstract
The analysis of partially-observable discrete stochastic systems reconstructs the unobserved behavior of real-world systems. An example for such a system is a production facility where indistinguishable items are produced by two machines in stochastically distributed time intervals and are then tested by a single quality tester. Here, the source of each defective item can be reconstructed later based solely on the time-stamped test protocol.
While existing algorithms can reconstruct various characteristics of the unobserved behavior, a fully specified discrete stochastic model needs to exist. So far, model parameters themselves cannot be reconstructed.
In this paper, we present two new approaches that enable the reconstruction of some unknown parameter values in the model specification, namely constant probabilities. Both approaches are shown to work correctly and with acceptable computational effort. They are a first step towards general model parameter inference for partially-observable discrete stochastic systems.
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References
van der Aalst, W.M.P.: Analysis of discrete-time stochastic petri nets. Statistica Neerlandica 54(2), 237–255 (2000)
Aoki, M.: State space modeling of time series. Springer-Verlag New York, Inc., New York (1986)
Bobbio, A., Puliafito, A., Telek, M., Trivedi, K.S.: Recent developments in non-markovian stochastic petri nets. Journal of Systems Circuits and Computers 8(1), 119–158 (1998)
Borshchev, A., Filippov, A.: From system dynamics and discrete event to practical agent based modeling: Reasons, techniques, tools. In: Proceedings of 22nd International Conference of the System Dynamics Society, Oxford, England (July 2004)
Boys, R.J., Wilkinson, D.J., Kirkwood, T.B.: Bayesian inference for a discretely observed stochastic kinetic model. Statistics and Computing 18, 125–135 (2008)
Buchholz, R., Krull, C., Horton, G.: Efficient event-driven proxel simulation of a subclass of hidden non-markovian models. In: 7th EUROSIM Congress on Modelling and Simulation (2010)
Buchholz, R., Krull, C., Horton, G., Strigl, T.: Using hidden non-markovian models to reconstruct system behavior in partially-observable systems. In: 3rd International ICST Conference on Simulation Tools and Techniques (2010)
FSF. The gnu multiprecision library (gmp), http://gmplib.org
Gibson, G.J., Renshaw, E.: Estimating parameters in stochastic compartmental models using markov chain methods. Mathematical Medicine and Biology 15(1), 19–40 (1998)
Horton, G.: A new paradigm for the numerical simulation of stochastic petri nets with general firing times. In: European Simulation Symposium. SCS European Publishing House, Dresden (2002)
Krull, C., Buchholz, R., Horton, G.: Matching hidden non-markovian models: Diagnosing illnesses based on recorded symptoms. In: The 24th annual European Simulation and Modelling Conference (October 2010)
Krull, C., Horton, G.: Hidden non-markovian models: Formalization and solution approaches. In: Proceedings of 6th Vienna International Conference on Mathematical Modelling, Vienna, Austria (February 2009)
Lazarova-Molnar, S.: The Proxel-Based Method: Formalisation, Analysis and Applications. Ph.D. thesis, Otto-von-Guericke University Magdeburg (2005)
Malyarenko, A., Vasiliev, V.: On guaranteed parameter estimation of discrete-time stochastic systems. In: Second International Conference on Innovative Computing, Information and Control ICICIC 2007, p. 140 (September 2007)
Rabiner, L.R.: A tutorial on hidden markov models and selected applications in speech recognition. Proceedings of the IEEE 77(2), 257–286 (1989)
Wang, Y., Christley, S., Mjolsness, E., Xie, X.: Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent. BMC Systems Biology 4(1), 99 (2010)
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Buchholz, R., Krull, C., Horton, G. (2011). Reconstructing Model Parameters in Partially-Observable Discrete Stochastic Systems. In: Al-Begain, K., Balsamo, S., Fiems, D., Marin, A. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2011. Lecture Notes in Computer Science, vol 6751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21713-5_12
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DOI: https://doi.org/10.1007/978-3-642-21713-5_12
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