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Activity Number:
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270
- Bayesian Data Science and Analytics
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 4, 2020 : 1:00 PM to 2:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract #312526
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Title:
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Modeling Power Outages via Markov Modulated Compound Poisson Processes: A Bayesian Approach
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Author(s):
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Atilla Ay* and Suleyman Ozekici and Refik Soyer
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Companies:
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George Washington University and Koc University and George Washington University
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Keywords:
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Markov modulated Markov process ;
Hidden Markov model;
Bayesian inference;
Bayesian reliability analysis
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Abstract:
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Markov processes play an important role in reliability analysis, particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. We have a Markov modulated Markov process which can be modeled as a bivariate Markov process and analyzed probabilistically using Markovian analysis. In this setting, we focus on Bayesian analysis when the states of the environmental or modulating process are unobserved based on observed data on the modulated Markov process. We present a computationally tractable approach using Gibbs sampling. We apply a Markov modulated compound Poisson process to describe the reliability of the power system and the number of people affected by the power outages in Northern Virginia.
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Authors who are presenting talks have a * after their name.
