SpatioTemporal (version 1.1.2)

MCMC.mesa.model: Example of a mcmcSTmodel Structure

Description

The output from a Metropolis-Hastings algorithm, implemented in MCMC.STmodel), run for the model in mesa.model

format

A list with elements, see the return description in MCMC.STmodel.

source

Contains parametere estimates for the Spatio-Temporal model applied to monitoring data from the MESA Air project, see Cohen et.al. (2009) and mesa.data.raw for details.

References

M. A. Cohen, S. D. Adar, R. W. Allen, E. Avol, C. L. Curl, T. Gould, D. Hardie, A. Ho, P. Kinney, T. V. Larson, P. D. Sampson, L. Sheppard, K. D. Stukovsky, S. S. Swan, L. S. Liu, J. D. Kaufman. (2009) Approach to Estimating Participant Pollutant Exposures in the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air). Environmental Science & Technology: 43(13), 4687-4693.

See Also

createSTmodel for creation of the originating STmodel object.

Other example data: est.cv.mesa, est.mesa.model, mesa.data, mesa.data.raw, mesa.model, pred.mesa.model

Examples

##load data
data(mesa.model)
##and results of estimation
data(est.mesa.model)

##strating point
x <- coef(est.mesa.model)
##Hessian, for use as proposal matrix
H <- est.mesa.model$res.best$hessian.all
##run MCMC
  MCMC.mesa.model <- MCMC(mesa.model, x$par, N = 5000, Hessian.prop = H)
##lets load precomputed results instead
data(MCMC.mesa.model)

####TODO: NEEDS S3-update
##Examine the results
print(MCMC.mesa.model)

##and contens of result vector
names(MCMC.mesa.model)
 
##Summary
summary(MCMC.mesa.model)

##MCMC tracks for four of the parameters
par(mfrow=c(5,1),mar=c(2,2,2.5,.5))
plot(MCMC.mesa.model$l, ylab="", xlab="", type="l",
     main="log-likelihood")
for(i in c(4,9,13,15)){
  plot(MCMC.mesa.model$par[,i], ylab="", xlab="", type="l",
       main=colnames(MCMC.mesa.model$par)[i])
}

##And estimated densities for the log-covariance parameters.
##The red line is the approximate normal distribution given by
##the maximum-likelihood estimates, e.g. ML-estimate and standard 
##deviation from the observed information matrix.
par(mfrow=c(3,3),mar=c(4,4,2.5,.5))
for(i in 9:17){
  xd <- sort(unique(MCMC.mesa.model$par[,i]))
  yd <- dnorm(xd, mean=x$par[i],sd=x$sd[i])
  dens <- density(MCMC.mesa.model$par[,i])
  plot(dens, ylim=c(0,max(c(dens$y,yd))), main =
       colnames(MCMC.mesa.model$par)[i])
  lines(xd,yd,col=2)
}