Bayesian inference for a large class of discretetime capturerecapture models under closed population with special emphasis on behavioural effect modelling including also the meaningful behavioral covariate approach proposed in Alunni Fegatelli (2013) [PhD thesis]. Many of the standard classical models such as M_0, M_b, M_{c_1}, M_t or M_{bt} can be regarded as particular instances of the aforementioned approach. Other flexible alternatives can be fitted through a careful choice of a meaningful behavioural covariate and a possible partition of its admissible range
1 2 3 4 5 6 7 8 9  BBRecap (data,last.column.count=FALSE, neval = 1000, by.incr = 1,
mbc.function = c("standard","markov","counts","integer","counts.integer"),
mod = c("linear.logistic", "M0", "Mb", "Mc", "Mcb", "Mt", "Msubjective.cut",
"Msubjective"), nsim = 5000, burnin = round(nsim/10),
nsim.ML = 1000, burnin.ML = round(nsim.ML/10), num.t = 50,
markov.ord=NULL, prior.N = c("Rissanen","Uniform","one.over.N","one.over.N2"),
meaningful.mat.subjective = NULL, meaningful.mat.new.value.subjective = NULL,
z.cut=NULL, output = c("base", "complete", "complete.ML"))

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 
neval 
a positive integer. 
by.incr 
a positive integer. 
mbc.function 
a character string with possible entries (see Alunni Fegatelli (2013) for further details)

mod 
a character. 
nsim 
a positive integer. 
burnin 
a positive integer. 
nsim.ML 
a positive integer. 
burnin.ML 
a positive integer. 
num.t 
a positive integer. 
markov.ord 
a positive integer. 
prior.N 
a character. 
meaningful.mat.subjective 

meaningful.mat.new.value.subjective 

z.cut 
numeric vector. 
output 
a character. 
Independent uniform distributions are considered as default prior for the nuisance parameters. If model="linear.logistic"
or model="Msubjective"
and output="complete.ML"
the marginal likelihood estimation is performed through the power posteriors method suggested in Friel and Pettit (2008). In that case the BBRecap
procedure is computing intensive for high values of neval
and nsim
.
Model 
model considered 
Prior 
prior distribution for N 
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 
z.matrix 
meaningful behavioural covariate matrix for the observed data 
vec.cut 
cut point used to set up meaningful partitions the set of the partial capture histories according to the value of the value of the meaningful behavioural covariate 
N.vec 
simulated values from the posterior marginal distribution of N 
mean.a0 
posterior mean of the parameter a0 
mean.a0 
highest posterior density interval estimate of the parameter a0 
a0.vec 
simulated values from the posterior marginal distribution of a0 
mean.a1 
posterior mean of the parameter a1 
mean.a1 
highest posterior density interval estimate of the parameter a1 
a1.vec 
simulated values from the posterior marginal distribution of a1 
Danilo Alunni Fegatelli and Luca Tardella
Friel, N. and Pettitt, A. N. (2008) Marginal likelihood estimation via power posteriors. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(3):589–607
Farcomeni A. (2011) Recapture models under equality constraints for the conditional capture probabilities. Biometrika 98(1):237–242
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
1 2 3 4 5 6 7  ## Not run:
data(greatcopper)
mod.Mb=BBRecap(greatcopper,mod="Mb")
str(mod.Mb)
## End(Not run)

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