B2Z-package: Bayesian Two-Zone Models (B2ZM)
Description
The B2Z R-package fits the Bayesian two-zone model proposed by Zhang et al. (2009). Denote $CN(t)$ and $CF(t)$ by the concentrations at time $t$ in the near and far fields, respectively. The deterministic equations in the two-zone modeling are given by:
$$(d/dt)CN(t) = Beta/VN(CF(t)- CN(t) + G/Beta) (1)$$
$$(d/dt)CF(t) = Beta/VF(CN(t) - (1 + Q/Beta)CF(t)) (2)$$
where Beta is the interzonal air flow rate; Q is the supply and exhaust flow rate; and G is the contaminant emission rate. We assume that CN(0) = CF(0) = 0.
Denote $YN(t)$ and $YF(t)$ by the observed log concentrations at time $(t)$ in the near and far fields, respectively. Zhang et al. (2009) assume that the joint probability distribution of $YN(t)$ and $YF(t)$ is a bivariate normal distribution where the mean is the solution of the differential equations (1) and (2), and the covariance matrix is composed by unknown parameters: $TauN$ (variance of the measurement error at the near field), $TauNF$ (covariance between the measurements at the near and far fields) and $TauF$ (variance of the measurement error at the far field). If the near and far field measurements error processes are independent, then $TauNF = 0$. Both dependent (default) and independent models are provided in this R-package.
Several options as prior distribution for $Beta$, $Q$ and $G$ are provided. In the independent model, the priors distributions for $TauN$ and $TauF$ are inverse gamma distributions; and in the dependent model the prior joint distribution of $TauN$, $TauNF$ and $TauF$ is the Inverse Wishart Distribution.
Three sample methods are available: Gibbs with Metropolis step, Incremental Mixture Importance Sampling (IMIS) and Sampling Importance Resampling (SIR). In addition,
estimation using the Bayesian central limit theorem (Laplace approximation) is also available (BCLT). The user can fit the Bayesian two-zone model by using the function B2ZM and in this function
specifying which sampler method to use OR using one of the functions:
B2ZM_MCMC, B2ZM_IMIS, B2ZM_SIR and B2ZM_BCLT. In any case, the output is valid as an input for the functions summary and plot.Details
ll{
Package: B2Z
Type: Package
Version: 1.4
Date: 2011-07-16
License: GPL-2
LazyLoad: yes
}References
Monteiro, J. V. D., Banerjee, S. and Ramachandran, G. (2011). B2Z: An R Package for Bayesian Two-Zone Models. Journal of Statistical Software 43 (2) 1--23. http://www.jstatsoft.org/v43/i02/
Raftery, A. E. and Bao, L. (2009). Estimating and Projecting Trends in HIV/AIDS Generalized Epidemics Using Incremental Mixture Importance Sampling. http://www.stat.washington.edu/research/reports/2009/tr560.pdf
Zhang, Y., Banerjee, S., Yang,R., Lungu,C. and Ramachandran, G. (2009). Bayesian Modeling of Exposure and Airflow Using Two-Zone Models. The Annals of Occupational Hygiene,
53, 409-424. http://www.biostat.umn.edu/~sudiptob/ResearchPapers/ZBYLR.pdf