total_pop: Evaluate Posterior Distribution of Total Population Size

Description

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

Usage

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

Arguments

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.

Value

This function will return an object of class "totpop" which is a list with the following components.
TOTA vector of length (n.sample-n.burnin) giving the MCMC sample from the posterior distribution of the total population size.
intThe 100*prob.level% highest posterior density interval (HPDI) for the total population size.
meanTOTThe posterior mean of the total population size.
prob.levelThe argument prob.level.

Details

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.

Examples

Run this code

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
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