• Bayesian inference;
  • conditional independence;
  • confounding;
  • marked point processes;
  • predictive distributions

Abstract.  This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so-called do-probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.