Capture-Recapture Estimation using Bayesian Model Averaging

Performs Bayesian model averaging for capture-recapture. This includes code to stratify records, check the strata for suitable overlap to be used for capture-recapture, and some functions to plot the estimated population size.

DGA

Performs capture-recapture estimation by averaging over decomposable graphical models. This implements the approach introduced in Madigan and York (1997).

Installation

Stable CRAN release:

install.packages("dga")

Example usage

Five lists example from Madigan and York (1997):

library(dga)

# Number of lists and prior hyperparameter
p <- 5
data(graphs5) # Decomposable graphical models on 5 lists.
delta <- 0.5
Nmissing <- 1:300 # Reasonable range for the number of unobserved individuals.

# Counts corresponding to list inclusion patterns.
Y <- c(0,27,37,19,4,4,1,1,97,22,37,25,2,1,3,5,83,36,34,18,3,5,0,2,30,5,23,8,0,3,0,2)
Y <- array(Y, dim=c(2,2,2,2,2))
N <- sum(Y) + Nmissing

# Model-wise posterior probaiblities on the total population size.
# weights[i,j] is the posterior probability for j missing individuals under model graphs5[[j]].
weights <- bma.cr(Y,  Nmissing, delta, graphs5)

# Plot of the posterior distribution.
plotPosteriorN(weights, N)

References

• David Madigan and Jeremy C. York. "Bayesian methods for estimation of the size of a closed population." Biometrika. Vol. 84, No. 1 (Mar., 1997), pp. 19-31.
• Mauricio Sadinle (2018) Bayesian propagation of record linkage uncertainty into population size estimation of human rights violations. Annals of Applied Statistics Vol. 12 No. 2 pp. 1013-1038

Written by James Johndrow, Kristian Lum, and Patrick Ball.

copyright (c) 2015 Human Rights Data Analysis Group (HRDAG) https://hrdag.org