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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).

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.