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FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain

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  • Villacorta, Pablo J.
  • Verdegay, José L.
Abstract
Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature which characterizes certain kinds of Markov chains is their stationary distribution, which stands for the global fraction of time the system spends in each state. The computation of the stationary distribution requires precise knowledge of the transition probabilities. When the only information available is a sequence of observations drawn from the system, such probabilities have to be estimated. Here we review an existing method to estimate fuzzy transition probabilities from observations and, with them, obtain the fuzzy stationary distribution of the resulting fuzzy Markov chain. The method also works when the user directly provides fuzzy transition probabilities. We provide an implementation in the R environment that is the first available to the community and serves as a proof of concept. We demonstrate the usefulness of our proposal with computational experiments on a toy problem, namely a time-homogeneous Markov chain that guides the randomized movement of an autonomous robot that patrols a small area.

Suggested Citation

  • Villacorta, Pablo J. & Verdegay, José L., 2016. "FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i08).
    • Handle: RePEc:jss:jstsof:v:071:i08
    DOI: http://hdl.handle.net/10.18637/jss.v071.i08
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    References listed on IDEAS

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    1. Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2011. "DEoptim: An R Package for Global Optimization by Differential Evolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i06).
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    5. Wai-Ki Ching & Michael K. Ng, 2006. "Markov Chains: Models, Algorithms and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-29337-0, April.
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    7. Nicky J. Welton & A. E. Ades, 2005. "Estimation of Markov Chain Transition Probabilities and Rates from Fully and Partially Observed Data: Uncertainty Propagation, Evidence Synthesis, and Model Calibration," Medical Decision Making, , vol. 25(6), pages 633-645, November.
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    Cited by:

    1. Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.

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