BiasedMatch

BiasedMatch implements the two-urn biased sampling model of Puza and Bonfrer (2018). Two overlapping sets of items are sampled without replacement, with items common to both sets given a selection weight that favours their inclusion. The package computes the distribution of the number of matching items, performs maximum likelihood and Bayesian inference for the bias parameter, and provides Metropolis-Hastings samplers for hierarchical extensions.

Installation

Install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("andrebonfrer/BiasedMatch")

Usage

The full distribution, mean and variance of the number of matches:

library(BiasedMatch)

# Probability of exactly 3 matches (Example 1 of the paper, w = 2)
PROBM(m = 3, N1 = 37, N2 = 45, N = 16, m1 = 12, m2 = 8, w = 2)

# Full distribution with mean and variance
DISTM(N1 = 37, N2 = 45, N = 16, m1 = 12, m2 = 8, w = 2)

Inference on the selection bias w from an observed number of matches (reproducing the marketing application, Problem 3):

inferW(m = 13, N1 = 292, N2 = 350, N = 192, m1 = 90, m2 = 59)
#> $mle              1.5265
#> $posterior_mode   1.3029
#> $p_value          0.1737

likW() returns the standardised likelihood and posterior curves for plotting, and the MHALG() family of functions performs hierarchical Metropolis-Hastings inference when several experiments are pooled.

See vignette("biasedmatch") for a full walkthrough that reproduces the tables and figures of the paper.

Reference

Puza, B. and Bonfrer, A. (2018). A series of two-urn biased sampling problems. Communications in Statistics - Theory and Methods, 47(1), 80-91. https://doi.org/10.1080/03610926.2017.1300282

Licence

MIT (see the LICENSE file).