The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation: illustration with biochemical oxygen demand data
Resúmenes
Environmental scientists often face situations where: (i) stimulus-response relationships are non-linear; (ii) data is rare or imprecise; (iii) facts are uncertain and stimulus-responses relationships are questionable.
In this paper, we focus on the first two points. A powerful and easy-to-use statistical method, the Metropolis-Hastings algorithm, allows the quantification of the uncertainty attached to any model response. This stochastic simulation technique is able to reproduce the statistical joint distribution of the whole parameter set of any model. The Metropolis-Hastings algorithm is described and illustrated on a typical environmental model: the biochemical oxygen demand (BOD). The aim is to provide a helpful guideline for further, and ultimately more complex, models. As a first illustration, the MH-method is also applied to a simple regression example to demonstrate to the practitioner the ability of the algorithm to produce valid results.
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Mots-clés :
incertitude, simulation Monte-Carlo, chaînes de Markov, inférence bayésienne, modèle non-linéaire, Demande Biologique en Oxygène (DBO), algorithme de Metropolis-HastingsKeywords :
parameter uncertainty, Markov chains, Monte Carlo simulation, bayesian inference, non linear modeling/modelling, BOD, Metropolis-Hastings algorithmPara citar este artículo
Referencia electrónica
Franck Torre, Jean-Jacque Boreux y Eric Parent, « The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation: illustration with biochemical oxygen demand data », Cybergeo: European Journal of Geography [En línea], Informes temáticos, documento 187, Publicado el 28 febrero 2001, consultado el 29 marzo 2024. URL : http://journals.openedition.org/cybergeo/4750 ; DOI : https://doi.org/10.4000/cybergeo.4750
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