Aspects of causal inference in a non-counterfactual framework
Since the mid 1970s and increasingly over the last decade, causal inference has generated interest and controversy in statistics. Mathematical frame works have been developed to make causal inference in fields ranging from epidemiology to social science. However, most frameworks rely on the existence of counterfactuals, and the assumptions that underpin them are not always made explicit. This thesis analyses such assumptions and proposes an alternative model. This is then used to tackle problems that have been formulated in counterfactual terms. The proposed framework is based on decision theory. Causes are seen in terms of interventions which in turn are seen as decisions. Decisions are thus explicitly included as intervention variables, in both algebraic expressions for causal effects and the in DAGs which represent the probabilistic structure between the variables. The non-counterfactual framework introduces a novel way of determining whether causal quantities are identifiable. Two such quantities are considered and conditions for their identification are presented. These are the direct effect of treatment on response in the presence of a mediating variable, and the effect of treatment on the treated. To determine whether these are identifiable, intervention nodes are introduced on the variables that are thought to be causal in the problem. By manipulating the conditional independences between the observed variables and the intervention nodes it is possible to determine whether the quantities of interest can be expressed in terms of the a) specific settings and/or b) the idle setting of the intervention nodes, corresponding to experimental regimes and the observational regimes of the causal variables. This method can be easily tailored to any specific context, as it relies only on the understanding of conditional independences.