A Non-Homogeneous Hidden Markov Model for the Analysis of Multi-Pollutant Exceedances Data

Lagona, Francesco; Maruotti, Antonello; Picone, Marco

doi:10.5772/14749

Cited by 16 publications

(9 citation statements)

References 30 publications

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“…Inhomogeneous Markov chain models have been employed in other areas such as biomedical research (Perez‐Ocon, Ruiz‐Castro & Gamiz‐Perez ; Hubbard, Inoue & Fann ), landscape (Li ), pollution (Lagona et al . ), and climatic (Rajagopalan, Lall & Tarboton ; Hughes, Guttorp & Charles ) modelling. Overall, the broadly employed stationary Markov chain models work particularly well when the homogeneity assumption is justified, that is when the environmental conditions do not change substantially.…”

Section: Discussionmentioning

confidence: 99%

Modelling of hardwood forest in Quebec under dynamic disturbance regimes: a time‐inhomogeneous Markov chain approach

Liénard

Strigul

2016

Journal of Ecology

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1. We investigate the consequences of global warming scenarios in Quebec forests using an inhomogeneous Markov chain model. This allows us to unify predictions from climate change models and mechanistic models of forest disturbance and growth and allows predicting the potential impacts of climate change on Quebec forests. The model predicts changes in fire rate in Quebec hardwood forests as well as possible growth enhancements due to increasing CO 2 and temperature. 2. Our original method consists of three steps. (i) We estimate biomass transition matrices from forest inventories using the Bayesian method. (ii) We incorporate dynamic disturbance and forest growth scenarios, and (iii) we simulate transient dynamics and stationary states. This modelling approach allows for sensitivity analysis and quantitative assessment effects of variability of climate change scenarios. 3. We have considered published climate change scenarios for Quebec and conducted simulations for the most extreme predictions (the smallest and largest predicted changes). None of the considered scenarios is able to counterbalance the currently observed trend of increasing biomass in the next 40 years. By the beginning of 2090, the extreme scenarios diverge within about AE5% mean biomass. 4. Synthesis. In this work, we have developed an original modelling approach incorporating timeinhomogeneous effects within the Markov chain framework. We applied this approach to examine effects of climate change in Quebec's forests. The results demonstrate that the current trend of increase in forest biomass is robust with respect to a broad range of climate change scenarios. This study was not possible with previously employed homogeneous Markov chain models. The model can also be extended to include different harvesting methods and land-use practices, enabling better long-term management of Quebec's forest. Supporting InformationAdditional Supporting Information may be found in the online version of this article:Appendix S1. Methods overview.Appendix S2. Estimation of biomass.Appendix S3. Monte Carlo Markov Chain methodology.Appendix S4. Biomass transition matrix in Quebec forest subzones.Appendix S5. Stability analysis.Appendix S6. Predictions without higher growth. Appendix S7. Predictions with different temporal progression of forest fires.

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Section: Discussionmentioning

confidence: 99%

Modelling of hardwood forest in Quebec under dynamic disturbance regimes: a time‐inhomogeneous Markov chain approach

Liénard

Strigul

2016

Journal of Ecology

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“…However, under a longitudinal scheme, where observations are recorded at periodic times, hidden states often do have a well‐defined meaning. They can be used to describe disease progression (Cooper & Lipsitch, 2004; Altman & Petkau, 2005; Wall & Lee, 2009), to explain environmental conditions (Betrò et al , 2009; Lagona et al , 2011), to measure changes in biological conditions (Beerenwinkel & Drton, 2007; Gupta et al , 2007), to estimate life expectancy in population studies (van den Hout et al , 2009), or to model financial series (Rydén et al , 1998; Frühwirth‐Schnatter & Kaufmann, 2008; Dias et al , 2010; Bulla, 2011).…”

Section: Modelling Longitudinal Data Via Hidden Markov Modelsmentioning

confidence: 99%

Mixed Hidden Markov Models for Longitudinal Data: An Overview

Maruotti

2011

International Statistical Review

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101

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In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so-called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real-world time-dependent data. We give details of the Expectation-Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.

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“…The joint distribution of multivariate (mixed‐type) data is usually specified as a mixture having products of univariate distributions as components (see e.g. Lagona et al ., ; Lagona and Picone, ; Zhang et al ., ). Bartolucci and Farcomeni () is a notable exception.…”

Section: Introductionmentioning

confidence: 98%

Bayesian hidden Markov modelling using circular‐linear general projected normal distribution

2015

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We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or skewed cluster-specific distributions for the circular variable. Furthermore, we relax the independence assumption between the circular and linear components observed at the same time. Such an assumption is generally used to alleviate the computational burden involved in the parameter estimation step, but it is hard to justify in empirical applications. We carry out a simulation study using different data-generation schemes to investigate model behavior, focusing on well recovering the hidden structure. Finally, the model is used to fit a real data example on a bivariate time series of wind speed and direction.

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A Non-Homogeneous Hidden Markov Model for the Analysis of Multi-Pollutant Exceedances Data

Cited by 16 publications

References 30 publications

Modelling of hardwood forest in Quebec under dynamic disturbance regimes: a time‐inhomogeneous Markov chain approach

Modelling of hardwood forest in Quebec under dynamic disturbance regimes: a time‐inhomogeneous Markov chain approach

Mixed Hidden Markov Models for Longitudinal Data: An Overview

Bayesian hidden Markov modelling using circular‐linear general projected normal distribution

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