The authors developed a new method for estimating the causal effects of mediation—the natural effects, both direct and indirect. The goal was to craft an approach that can estimate the effects of an intervention--one that we think may prompt new physical activity, for example--without making strong assumptions about the probability distributions (e.g., normality) of the variables.

This new approach separates the modeling of the observed data (where we use a Bayesian non-parametric approach) via causal assumptions that are used to identify mediation effects.

In our example, this model would offer advantages. Say a research study offers an incentive (an intervention) that the investigators think will directly prompt people to undertake a physical activity. But the incentive might also affect some other variable, such as their belief in their ability to change and their commitment to act. This belief and commitment (known as "self liberation") might itself affect the outcome. Thus the intervention might affect the outcome directly but also affect it indirectly, through a mediator such as self liberation. Causal mediation statistical methods allow us to estimate both direct and indirect effects. The Bayesian nonparametric approach developed here can estimate these effects without making strong assumptions about the surrounding circumstances that influence the distribution of the variables. Thus the new method can potentially yield a more complete, more accurate measure of how effective the intervention truly is.