Abstract
Often, in dynamical systems such as farmer’s crop choices, the dynamics are driven by external non-stationary factors, such as rainfall, temperature and agricultural input and output prices. Such dynamics can be modelled by a non-stationary Markov chain, where the transition probabilities are multinomial logistic functions of such external factors. We extend previous work to investigate the problem of estimating the parameters of the multinomial logistic model from data. We use conjugate analysis with a fairly broad class of priors, to accommodate scarcity of data and lack of strong prior expert opinion. We discuss the computation of bounds for the posterior transition probabilities. We use the model to analyse some scenarios for future crop growth.
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References
Agresti, A.: Categorical data analysis, 2nd edn. John Wiley and Sons (2002)
Berger, J.O.: The robust Bayesian viewpoint. In: Kadane, J.B. (ed.) Robustness of Bayesian Analyses, pp. 63–144. Elsevier Science, Amsterdam (1984)
Bernado, J.M., Smith, A.F.M.: Bayesian theory. John Wiley and Sons (1994)
Boardman, J., Evans, R., Favis-Mortlock, D.T., Harris, T.M.: Climate change and soil erosion on agricultural land in England and Wales. Land Degradation and Development 2(2), 95–106 (1990)
Boole, G.: An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Walton and Maberly, London (1854)
Chen, M.-H., Ibrahim, J.G.: Conjugate priors for generalized linear models. Statistica Sinica 13, 461–476 (2003)
de Cooman, G., Hermans, F., Quaeghebeur, E.: Imprecise Markov chains and their limit behavior. Probability in the Engineering and Informational Sciences 23(4), 597–635 (2009)
Diaconas, P., Ylvisaker, D.: Conjugate priors for exponential families. The Annals of Statistics 7(2), 269–281 (1979)
Keynes, J.M.: A treatise on probability. Macmillan, London (1921)
Data collected by the Met Office, http://www.metoffice.gov.uk/climate/uk/stationdata/ (accessed: February 11, 2013)
Nelder, J.A., Wedderburn, R.W.M.: Generalized linear models. Journal of the Royal Statistical Society. Series A 135(3), 370–384 (1972)
Nix, J.: Farm management pocketbook. Agro Business Consultants Ltd. (1993-2004)
Data collected by the Rural Payments Agency under the integrated administration and control system for the administration of subsidies under the common agricultural policy
Troffaes, M.C.M., Paton, L.: Logistic regression on Markov chains for crop rotation modelling. In: Cozman, F., Denœux, T., Destercke, S., Seidenfeld, T. (eds.) ISIPTA 2013: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications (Compiègne, France), pp. 329–336. SIPTA (July 2013)
Walley, P.: Statistical reasoning with imprecise probabilities. Chapman and Hall, London (1991)
Walley, P.: Inferences from multinomial data: Learning about a bag of marbles. Journal of the Royal Statistical Society, Series B 58(1), 3–34 (1996)
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Paton, L., Troffaes, M.C.M., Boatman, N., Hussein, M., Hart, A. (2014). Multinomial Logistic Regression on Markov Chains for Crop Rotation Modelling. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_49
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DOI: https://doi.org/10.1007/978-3-319-08852-5_49
Publisher Name: Springer, Cham
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