Bayesian inference for behavioural effect models based on a partition of the set of all partial capture histories
Description
Bayesian inference for a general model framework based on the capture probabilities conditioned on each possible partial capture history. As suggested in Alunni Fegatelli and Tardella (2012) the conditional approach originally proposed in Farcomeni (2011) [saturated reparameterization] is reviewed in terms of partitions into equivalence classes of conditional probabilities. In this function the user can directly provide the model as a partition.
Usage
1 2 3 4  BBRecap.custom.part (data,last.column.count=FALSE, partition, neval = 1000,
by.incr = 1, prior.N = c("Rissanen", "Uniform", "one.over.N", "one.over.N2"),
output = c("base", "complete"))

Arguments
data 
can be one of the following:
M is the number of units captured at least once and t is the number of capture occasions. 
last.column.count 
a logical. In the default case 
partition 
list. 
neval 
a positive integer. 
by.incr 
a positive integer. 
prior.N 
a character. 
output 
a character. 
Details
Uniform prior distribution is considered for the nuisance parameters.
Value
Prior 
prior distribution for 
N.hat.mean 
posterior mean for N 
N.hat.median 
posterior median for N 
N.hat.mode 
posterior mode for N 
N.hat.RMSE 
minimizer of a specific loss function connected with the Relative Mean Square Error. 
HPD.N 
95 \% highest posterior density interval estimate for N. 
log.marginal.likelihood 
log marginal likelihood. 
N.range 
values of N considered. 
posterior.N 
values of the posterior distribution for each N considered 
partition 
partition of the set H 
Author(s)
Danilo Alunni Fegatelli and Luca Tardella
References
Alunni Fegatelli, D. and Tardella, L. (2012) Improved inference on capture recapture models with behavioural effects. Statistical Methods & Applications Applications Volume 22, Issue 1, pp 4566 10.1007/s1026001202214
Farcomeni A. (2011) Recapture models under equality constraints for the conditional capture probabilities. Biometrika 98(1):237–242
See Also
partition.ch
,
LBRecap.custom.part
,
BBRecap
Examples
1 2 3 4  data(greatcopper)
partition.Mc1=partition.ch(quant.binary,t=ncol(greatcopper),breaks=c(0,0.5,1))
mod.Mc1=BBRecap.custom.part(greatcopper,partition=partition.Mc1)
str(mod.Mc1)
