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The goal of a well-controlled study is to remove unwanted variation when estimating the causal effect of the intervention of interest. Experiments conducted in the basic sciences frequently achieve this goal using experimental controls, such as negative and positive controls, which are measurements designed to detect systematic sources of unwanted variation. Here, we introduce clear, mathematically precise definitions of experimental controls using potential outcomes. Our definitions provide a unifying statistical framework for fundamental concepts of experimental design from the biological and other basic sciences. These controls are defined in terms of whether assumptions are being made about a specific treatment level, outcome, or contrast between outcomes. We discuss experimental controls as tools for researchers to wield in designing experiments and detecting potential design flaws, including using controls to diagnose unintended factors that influence the outcome of interest, assess measurement error, and identify important subpopulations. We believe that experimental controls are powerful tools for reproducible research that are possibly underutilized by statisticians, epidemiologists, and social science researchers.
Unobserved confounding presents a major threat to the validity of causal inference from observational studies. In this paper, we introduce a novel framework that leverages the information in multiple parallel outcomes for identification and estimatio
Thompson sampling is a popular algorithm for solving multi-armed bandit problems, and has been applied in a wide range of applications, from website design to portfolio optimization. In such applications, however, the number of choices (or arms) $N$
Poverty is a multidimensional concept often comprising a monetary outcome and other welfare dimensions such as education, subjective well-being or health, that are measured on an ordinal scale. In applied research, multidimensional poverty is ubiquit
Scientists have been interested in estimating causal peer effects to understand how peoples behaviors are affected by their network peers. However, it is well known that identification and estimation of causal peer effects are challenging in observat
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densi