Weighting, informativeness and causal inference, with an application to rainfall enhancement

Sampling is informative when probabilities of sample inclusion depend on unknown variables that are correlated with a response variable of interest. When sample inclusion probabilities are available, inverse probability weighting can be used to account for informative sampling in such a situation, although usually at the cost of less precise inference. This paper reviews two important research contributions by Chris Skinner that modify these weights to reduce their variability while at the same time retaining consistency of the weighted estimators. In some cases, however, sample inclusion probabilities are not known, and are estimated as propensity scores. This is often the situation in causal analysis, and double robust methods that protect against the resulting misspecification of the sampling process have been the focus of much recent research. In this paper we propose two model-assisted modifications to the popular inverse propensity score weighted estimator of an average treatment effect, and then illustrate their use in a causal analysis of a rainfall enhancement experiment that was carried out in Oman between 2013 and 2018.