title: A Formal Treatment of Sequential Ignorability.
abstract: Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property ofextended stability, which allows identification (by means of "[Formula: see text]-computation") of the consequence of a specified treatment strategy if the "unobserved" variables are, in fact, observed-but not generally otherwise. However, under certain additional special conditions we can infersimple stability(orsequential ignorability), which supports [Formula: see text]-computation based on the observed variables alone. One such additional condition issequential randomization, where the unobserved variables essentially behave as random noise in their effects on the actions. Another issequential irrelevance, where the unobserved variables do not influence future observed variables. In the latter case, to deduce sequential ignorability in full generality requires additional positivity conditions. We show here that these positivity conditions are not required when all variables are discrete.
authors.affiliation: Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge , CB3 0WB UK.
authors.forename: A Philip
authors.initials: AP
authors.lastname: Dawid
authors.affiliation: Department of Mathematics, University of Bristol, University Walk, Clifton, Bristol , BS8 1TW UK.
authors.forename: Panayiota
authors.initials: P
authors.lastname: Constantinou
keywords:  Observational study; Causal inference; Influence diagram; Sequential decision theory ; Stability; [Formula: see text]-computation