The Living Thing / Notebooks :

Informative sampling

Survivor bias, Informative sample selection Far-from-classical-ANOVA design. non-randomly censored data and solutions…

RaMo15:

When the probabilities of selecting the individuals for the sample depend on the outcome values, we say that the selection mechanism is informative. Under informative selection, individuals with certain outcome values appear more often in the sample and therefore the sample is not representative of the population. As a consequence, usual model-based inference based on the actual sample without appropriate weighting might be strongly biased.

No solution can fix all variants of this problem, but there are many specific fixes. Here’s one attempt at fixing data censoring: “Small Area Estimation”, in RaMo15.

See also directed graphical models, hierarchical models hich include a censoring process, some types of contexual bandit. (How do they do that?)

Reading

CoLi97
Copas, J. B., & Li, H. G.(1997) Inference for Non-random Samples. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59(1), 55–95. DOI.
Pfef93a
Pfeffermann, D. (1993a) Modeling Survey Data. International Statistical Review, 61(2), 317–337.
Pfef93b
Pfeffermann, D. (1993b) The Role of Sampling Weights When Modeling Survey Data. International Statistical Review / Revue Internationale de Statistique, 61(2), 317–337. DOI.
PfKR98
Pfeffermann, D., Krieger, A. M., & Rinott, Y. (1998) PARAMETRIC DISTRIBUTIONS OF COMPLEX SURVEY DATA UNDER INFORMATIVE PROBABILITY SAMPLING. Statistica Sinica, 8(4), 1087–1114.
Rao06
Rao, J. (2006) Interplay between sample survey theory and practice: An appraisal. Survey Methodology, 31(2), 117–138.
RaMo15
Rao, J. N. K., & Molina, I. (2015) Small Area Estimation. . John Wiley & Sons