The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data
Environmental scientists often face situations where: (i) stimulus-response relationships are non-linear; (ii) data are 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 stat...
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Unité Mixte de Recherche 8504 Géographie-cités
2001-02-01
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doaj-88809a4486604696a6d610af0539015c2020-11-25T02:23:49ZdeuUnité Mixte de Recherche 8504 Géographie-citésCybergeo1278-33662001-02-0110.4000/cybergeo.4750The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand dataFranck TorreJean-Jacque BoreuxEric ParentEnvironmental scientists often face situations where: (i) stimulus-response relationships are non-linear; (ii) data are 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.http://journals.openedition.org/cybergeo/4750parameter uncertaintyMarkov Chain Monte Carlo samplingbayesian inferencenon linear modellingBODMetropolis-Hastings algorithm |
collection |
DOAJ |
language |
deu |
format |
Article |
sources |
DOAJ |
author |
Franck Torre Jean-Jacque Boreux Eric Parent |
spellingShingle |
Franck Torre Jean-Jacque Boreux Eric Parent The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data Cybergeo parameter uncertainty Markov Chain Monte Carlo sampling bayesian inference non linear modelling BOD Metropolis-Hastings algorithm |
author_facet |
Franck Torre Jean-Jacque Boreux Eric Parent |
author_sort |
Franck Torre |
title |
The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
title_short |
The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
title_full |
The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
title_fullStr |
The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
title_full_unstemmed |
The Metropolis-Hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
title_sort |
metropolis-hastings algorithm, a handy tool for the practice of environmental model estimation : illustration with biochemical oxygen demand data |
publisher |
Unité Mixte de Recherche 8504 Géographie-cités |
series |
Cybergeo |
issn |
1278-3366 |
publishDate |
2001-02-01 |
description |
Environmental scientists often face situations where: (i) stimulus-response relationships are non-linear; (ii) data are 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. |
topic |
parameter uncertainty Markov Chain Monte Carlo sampling bayesian inference non linear modelling BOD Metropolis-Hastings algorithm |
url |
http://journals.openedition.org/cybergeo/4750 |
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