On Making Valid Inferences by Integrating Data from Surveys and Other Sources

Survey samplers have long been using probability samples from one or more sources in conjunction with census and administrative data to make valid and efficient inferences on finite population parameters. This topic has received a lot of attention more recently in the context of data from non-probability samples such as transaction data, web surveys and social media data. In this paper, I will provide a brief overview of probability sampling methods first and then discuss some recent methods, based on models for the non-probability samples, which could lead to useful inferences from a non-probability sample by itself or when combined with a probability sample. I will also explain how big data may be used as predictors in small area estimation, a topic of current interest because of the growing demand for reliable local area statistics.