total_pop: Evaluate Posterior Distribution of Total Population Size
In conting: Bayesian Analysis of Contingency Tables

Description Usage Arguments Details Value Author(s) See Also Examples

This function uses the MCMC output of a "bict" object to derive an MCMC sample from the posterior distribution of the total population size.

1	total_pop(object, n.burnin = 0, thin = 1, prob.level = 0.95)

`object`	An object of class `"bict"`.
`n.burnin`	An optional argument giving the number of iterations to use as burn-in. The default value is 0.
`thin`	An optional argument giving the amount of thinning to use, i.e. the computations are based on every `thin`-th value in the MCMC sample. The default value is 1, i.e. no thinning.
`prob.level`	An optional argument giving the target probability content of the highest posterior density intervals for the total population size. The default value is 0.95.

The use of thinning is recommended when the number of MCMC iterations and/or the number of log-linear parameters in the maximal model are/is large, which may cause problems with comuter memory storage.

This function will return an object of class "totpop" which is a list with the following components.

`TOT`	A vector of length (`n.sample`-`n.burnin`) giving the MCMC sample from the posterior distribution of the total population size.
`int`	The 100*`prob.level`% highest posterior density interval (HPDI) for the total population size.
`meanTOT`	The posterior mean of the total population size.
`prob.level`	The argument `prob.level`.

Antony M. Overstall A.M.Overstall@soton.ac.uk.

bict, print.totpop.

set.seed(1)
## Set seed for reproducibility

data(spina)
## Load spina data

test1<-bict(formula=y~(S1+S2+S3+eth)^2,data=spina,n.sample=100,prior="UIP")

## For the spina dataset. We do 100 iterations under the unit information 
## prior. The maximal model is the model with two-way interactions and we 
## start from this model at the posterior model

tp<-total_pop(test1,n.burnin=10)
## Use a burn-in phase of 10 iterations
tp
## Print out results. Will get:

#Posterior mean of total population size = 727.0667 
#95 % highest posterior density interval for total population size = ( 706 757 )

## Could do a plot
## Not run: plot(tp)

## Do a summary of MCMC sample from total population size
summary(tp$TOT)
## Will get

#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#  697.0   716.2   727.0   727.1   735.8   763.0