3.3 Estimation
After defining the causal estimands and specifying the necessary conditions for the estimand to be identified, the next step is doing the actual estimation from the observed data. In this section, we will introduce Bayesian modeling for causal effect estimation. Bayesian causal mediation analysis combines Bayesian modeling with the identification assumptions discussed in 3.2 to compute a posterior distribution over the causal estimands of interest.Suppose we observe data In addition to the probability model for the conditional distribution of the outcome and the mediator (the likelihood), Bayesian inference requires a probability distribution over the unknown parameter vector, Bayesian estimation of causal effects rely on Bayesian analog of the g-formula (standardisation) and bootstrap estimation of the confounder distribution. The Bayesian analog to the g-formula [Integration over the parameters and the confounder distribution as well as the computation of causal effects involve the following 5 steps.Given Using the classical bootstrap, sample Get the potential outcome values
Simulate the potential values of the mediator. Using the resampling of Given the potential value for the mediator, simulate the potential value for the outcome. For example, Compute draw of the causal effect estimates.
NDE: NIE: Get summary of causal effect estimates by taking the mean and quantiles of the causal effect estimates draws.