- Thesis:
- Bachelor in Mathematics
- Author:
- Henning Stein
- Title:
- Likelihood-Quotienten Tests in Hidden Markov Modellen
- Supervisors:
- Jan JOHANNES
- Christian Rüschoff (KSB Company)
- Abstract:
- Hidden Markov Models (HMMs) have been used successfully in various scientific fields to model weakly dependent random variables. Being composed of two stochastic processes we can see them as both a extension of Markov chains and of mixture models. As shown by Leroux B. G. (1992), the maximum-likelihood estimator (MLE) in HMMs is consistent under some constraints. Following the works of Bickel et al. (1998) and Giudice et al. (2000) we built upon that to show asymptotic normality of the MLE, develop likelihood-ratio tests in such models showing their convergence to a χ2-distribution and the subsequent asymptotic power of the test. We use this result to formalize the notion of predictability for the on/off-behavior of machines. We show, using data from real world applications, that we can use HMMs to predict 40% of machines significantly better than by random guessing. Our results demonstrate that HMMs are a capable tool in modelling the on/off-behavior of machines and distinguishing between predictable and non-predictable ones. We also give a short insight into how the works of this thesis may be extended using more adapted modelling or step-by-step testing to find the most suitable models for any given machine.
- References:
- P. Giudici, T. Ryden, and P. Vandekerkhove. Likelihood-ratio tests for Hidden Markov models, Biometrics, 56(3):742–747, 2000.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |