Fig 1. Synthetic inference based on some data X_obs and the SID likelihood $P_X^M(\widehat{\theta }$).

The count data X₁, … X_M represents household level diarrhea cases among adults and juveniles under and contaminated (V = 1) and clean (V = 0) environments and is used to fit the generative model (observed likelihood) ${\ell }_M\left(\widehat{\eta }\right)$ based on (1). The generated pseudo-data $X_1^M,\dots X_n^M$ are then used to fit the SID model $P_X^M\left(\widehat{\theta }\right)$ based on (2) and (3).