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Periodic multivariate normal hidden markov models for the analysis of water quality time series
Author(s) -
Spezia Luigi,
Futter Martyn N.,
Brewer Mark J.
Publication year - 2011
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1051
Subject(s) - multivariate statistics , markov chain monte carlo , series (stratigraphy) , hidden markov model , reversible jump markov chain monte carlo , markov chain , time series , bayesian probability , computer science , variable order markov model , bayesian inference , statistics , mathematics , markov model , econometrics , artificial intelligence , paleontology , biology
Abstract The modelling of multivariate riverine water quality time series poses some challenging problems including: weak dependency between observations; nonlinearity; non‐Normality; seasonality and missing data. We demonstrate that periodic multivariate Normal hidden Markov models (MNHMMs) are appropriate tools to analyse riverine water quality time series. We introduce a fully Bayesian inference procedure for this class of models, where the number of hidden states of the Markov process is unknown and reversible jump Markov chain Monte Carlo (RJMCMC) methods are developed. We present a case study using long‐term dissolved inorganic nitrogen time series measured in three Scottish rivers. Our results show the strength of the hidden Markov multistate approach for analysing long‐term multivariate riverine water quality time series. Copyright © 2010 John Wiley & Sons, Ltd.