A trick for handling a non-random sampling problem
particularly common in survey data.
MRP, a.k.a. Mister P,
is one method for correcting for non-response bias and other suc bias sampling.
I have not used this tool practically and so am not at all qualified to comment.
What I can do is link to my reading list of examples and explainers:
Dan Simpson does Mr P.
worked example is interesting reading in this context, explaining
Thomas Lumley’s post.
There are implementations also by Adam Haber using Tensorflow Probability and
Lauren Kennedy and Jonah Gabry in
Bareinboim, Elias, and Judea Pearl. 2016. “Causal Inference and the Data-Fusion Problem.” Proceedings of the National Academy of Sciences
113 (27): 7345–52. https://doi.org/10.1073/pnas.1510507113
Gao, Yuxiang, Lauren Kennedy, Daniel Simpson, and Andrew Gelman. 2019. “Improving Multilevel Regression and Poststratification with Structured Priors.”
August 19, 2019. http://arxiv.org/abs/1908.06716
Gelman, Andrew. 2007. “Struggles with Survey Weighting and Regression Modeling.” Statistical Science
22 (2): 153–64. https://doi.org/10.1214/088342306000000691
Gelman, Andrew, and John B. Carlin. 2000. “Poststratification and Weighting Adjustments.”
. http://www.stat.columbia.edu/ gelman/research/published/handbook5.pdf
Kennedy, Edward H., Jacqueline A. Mauro, Michael J. Daniels, Natalie Burns, and Dylan S. Small. 2019. “Handling Missing Data in Instrumental Variable Methods for Causal Inference.” Annual Review of Statistics and Its Application
6 (1): 125–48. https://doi.org/10.1146/annurev-statistics-031017-100353
Krivitsky, Pavel N., and Martina Morris. 2017. “Inference For Social Network Models From Egocentrically Sampled Data, With Application To Understanding Persistent Racial Disparities In Hiv Prevalence In The Us.” The Annals of Applied Statistics
11 (1): 427–55. https://doi.org/10.1214/16-AOAS1010
Little, R. J. A. 1993. “Post-Stratification: A Modeler’s Perspective.” Journal of the American Statistical Association
88 (423): 1001–12. https://doi.org/10.1080/01621459.1993.10476368
Little, Roderick JA. 1991. “Inference with Survey Weights.” Journal of Official Statistics 7 (4): 405.