What is meant by 'P(R|Yobs)'?

Abstract

Missing at Random (MAR) is a central concept in incomplete data methods, and often it is stated as $P(R\mspace{3mu}|\,Y_{obs}, Y_{mis}) = P(R\mspace{3mu}|\,Y_{obs})$. This notation has been used in the literature for more than three decades and has become the de facto standard. In some cases, the notation has been misinterpreted to be a statement about conditional independence. While previous work has sought to clarify the required definitions, a clear explanation of how to interpret the standard notation is lacking, and a definition of the function $P(R\mspace{3mu}|\,Y_{obs})$ for non-MAR mechanisms is difficult to locate in the literature. The aim of this paper is to fill these gaps.