🎯 dgaFast: Multiple Systems Estimation Using Decomposable Graphical Models

Efficient re-implementation and extension of the dga package of James Johndrow, Kristian Lum and Patrick Ball (2015): "Performs capture-recapture estimation by averaging over decomposable graphical models. This approach builds on Madigan and York (1997)."

Higher performance is needed to account for linkage errors through linkage-averaging and for simulation studies.
Further plotting and posterior summarization functions have been added (bayesEstimator, posteriorMode, posteriorQuantiles, posteriorSummaryTable, adjMatrix, plotGraph, htmlSummary, latexSummary).

Note: the stratification functions and Venn diagram plotting functions from the dga package have not been reproduced in dgaFast. They can be accessed through install.packages("dga"); library(dga).

Example usage

Five lists example from Madigan and York (1997) as implemented in the dga package:

library(dgaFast) # Re-implements 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)

Table of top model estimates (see also dgaFast::latexSummary).

htmlSummary("./figures/posteriorSummary/summaryTable", weights, N, nrows=5, graphs=graphs5)

Prob.	Bayes est.	Mode	0.025	0.975
0.217	627	624	598	663
0.160	615	614	591	645
0.082	613	610	586	648
0.065	610	608	585	640
0.052	616	614	591	647

Performance gain

On a 2013 MacBook Pro 2.6 GHz Intel Core i5, the main routine of dgaFast is about 75 times faster than dga.

if (!require(pacman)) install.packages("pacman")
pacman::p_load(bench, dga)

bench::mark(
     dga::bma.cr(Y, Nmissing, delta, graphs5),
     dgaFast::bma.cr(Y, Nmissing, delta, graphs5), 
     min_iterations=10, check=FALSE)

expression	min	median	itr/sec	mem_alloc	gc/sec
dga	866.8ms	919.6ms	0.994153	55.32MB	9.444453
dgaFast	11.3ms	12.5ms	76.286860	2.17MB	1.956073

Installation

From GitHub:

if (!require(devtools)) install.packages("devtools")
devtools::install_github("OlivierBinette/dgaFast")

References

James Johndrow, Kristian Lum and Patrick Ball (2015). dga: Capture-Recapture Estimation using Bayesian Model Averaging. R package version 1.2. https://CRAN.R-project.org/package=dga
David Madigan and Jeremy C. York (1997) 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