RESUMO
This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull-Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.
RESUMO
Polycyclic aromatic hydrocarbons (PAHs) are considered potentially toxic, even carcinogenic, because of their affection to public health and the environment. It is necessary to know their ambient levels and the origin of these pollutants in order to mitigate them. A concerning scenario is the one in which commercial/administrative, industrial, and residential activities coexist. In this context, Gran La Plata (Argentina) presents such characteristics, in addition to the presence of one of the most important petrochemical complexes in the country and intense vehicular traffic. The source apportionment of PAH emission in the region, associated to 10-µm and 2.5-µm particulate matter fractions, was studied. First, different missing value imputation methods were evaluated for PAH databases. GSimp presented a better performance, with mean concentrations of ∑PAHs of 65.8 ± 40.2 ng m-3 in PM10 and 39.5 ± 18.0 ng m-3 in PM2.5. For both fractions, it was found that the highest contribution was associated with low molecular weight PAHs (3 rings), with higher concentrations of anthracene. Emission sources were identified by using principal component analysis (PCA) together with multiple linear regression (MLR) and diagnostic ratios of PAHs. The results showed that the main emission source is associated with vehicular traffic in both fractions. Classification by discriminant analysis showed that emissions can be identified by region and that fluoranthene, benzo(a)anthracene, and anthracene in PM10 and anthracene and phenanthrene in PM2.5 are a characteristic of emissions from the petrochemical complex.