Transfer functions in dynamic generalized linear models

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

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“…[36] including covariates with constant coefficients for time accompanied by covariates modeled by transfer functions. Malhão et al .…”

Section: Introductionmentioning

confidence: 99%

Bayesian dynamic modeling of time series of dengue disease case counts

2017

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“…The last 10 observations are excluded from the fit with the purpose of comparing the forecasts, and thus n = 386. Time series of sulfur dioxide SO 2 ( x 1 t ) and carbon monoxide CO ( x 2 t ), t = 1, … , n , also shown in Figure , were considered as covariates since exposure to these air pollutants can increase the risk of respiratory illnesses (Ferris et al ., ; Alves et al ., ). These series were chosen because, usually, high concentrations of CO, produced by vehicles, are found in urban areas and the fuels based on the sulfur (for instance, oils) in combustion produce SO 2 .…”

Section: Application To Real Time Seriesmentioning

confidence: 97%

A Non‐gaussian Family of State‐space Models With Exact Marginal Likelihood

Friel

Santos

Franco

2013

Journal Time Series Analysis

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The Gaussian assumption generally employed in many state-space models is usually not satisfied for real time series. Thus, in this work, a broad family of non-Gaussian models is defined by integrating and expanding previous work in the literature. The expansion is obtained at two levels: at the observational level, it allows for many distributions not previously considered, and at the latent state level, it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion considerably increases the applicability of the models and solves many previously existing problems such as long-term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed because of the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared with other non-Gaussian state-space models available. The methodology is applied to Gaussian and non-Gaussian dynamic linear models with timevarying means and variances and provides a computationally simple solution to inference in these models. The methodology is illustrated in a number of examples. . The books by Durbin and Koopman (2001) and Fahrmeir and Tutz (2001) also present and discuss these models in addition to providing alternatives for analyzing non-Gaussian time series. The problem with this class of models is that the analytical form is easily lost, even using simple model components. Thus, the predictive distribution, which is essential for the inference process, can only be obtained approximately.Many researchers have worked in the last decades in auxiliary procedures in order to make inference for non-Gaussian SSM under the Bayesian approach. Gamerman (1998) proposed a GLM-based Markov chain Monte Carlo (MCMC) algorithm for inference, Frühwirth-Schnatter and Wagner (2006) used auxiliary mixture sampling and Pitt and Walker (2005) utilized auxiliary variables for constructing stationary time series. Andrieu and Doucet (2002) and Carvalho et al. (2010) are just a sample of a large community devoted to inference via sequential Monte Carlo or particle filtering in the SSM context. However, it is important to emphasize that these methods are approximate and the computing time can be large.The objective of this paper is to present a family of models that allows for exact, analytical computation of the marginal likelihood and thus the predictive distribution. This family is obtained by generalizations of results from Smith and Miller (1986). They considered an exponential observational model and an exact evolution equation that enables the analytical integration of the state and the attainment of the one-step-ahead predictive distributions. Harvey and Fernandes (1989) and Shephard (1994) showed that the same tractability...

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“…As discussed in Frühwirth‐Schnatter (1995) and Alves et al (2010), when analyzing time series data one should choose that model which performs best in terms of future predictions. The expression in can be used to evaluate posterior model probabilities of any collection of models (Frühwirth‐Schnatter, 1995).…”

Section: Proposed Modelsmentioning

confidence: 99%

“…Gelfand & Ghosh (1998) mention that ordering of models is typically insensitive to the choice of k, therefore we fix k = 100. Notice that at each iteration of the MCMC we can obtain replicates of the observations given the sampled values of the parameters and then compute D As discussed in Frühwirth-Schnatter (1995) and Alves et al (2010), when analyzing time series data one should choose that model which performs best in terms of future predictions. The expression in equation (8) can be used to evaluate posterior model probabilities of any collection of models (Frühwirth-Schnatter, 1995).…”

Section: Model Comparisonmentioning

confidence: 99%

Modelling Time Series of Counts in Epidemiology

Schmidt¹,

Pereira²

2011

International Statistical Review

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We review generalized dynamic models for time series of count data. Usually temporal counts are modelled as following a Poisson distribution, and a transformation of the mean depends on parameters which evolve smoothly with time. We generalize the usual dynamic Poisson model by considering continuous mixtures of the Poisson distribution. We consider Poisson-gamma and Poisson-log-normal mixture models. These models have a parameter for each time t which captures possible extra-variation present in the data. If the time interval between observations is short, many observed zeros might result. We also propose zero inflated versions of the models mentioned above. In epidemiology, when a count is equal to zero, one does not know if the disease is present or not. Our model has a parameter which provides the probability of presence of the disease given no cases were observed. We rely on the Bayesian paradigm to obtain estimates of the parameters of interest, and discuss numerical methods to obtain samples from the resultant posterior distribution. We fit the proposed models to artificial data sets and also to a weekly time series of registered number of cases of dengue fever in a district of the city of Rio de Janeiro, Brazil, during 2001 and 2002.

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Transfer functions in dynamic generalized linear models

Cited by 21 publications

References 32 publications

Bayesian dynamic modeling of time series of dengue disease case counts

Bayesian dynamic modeling of time series of dengue disease case counts

A Non‐gaussian Family of State‐space Models With Exact Marginal Likelihood

Modelling Time Series of Counts in Epidemiology

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