What does the hierarchical model look like when having missing in observed?

[junpenglao]

@yangwufl

As a concrete example, say \mu ~ N(0,1), observed Y | \mu ~ N(\mu, 1). Inference would be done based on p(\mu | Y) while Y has no missing.

It is the same when missing value is presented. Internally, PyMC3 isolate the Y_m and Y_nm, and do p(\mu | Y_nm). The Y_m is internally added to the model as a free random variable, and Y_m ~ Y | \mu, Y_nm. In the above example, Y_m | \mu_posterior ~ N(\mu_posterior, 1) where , \mu_posterior ~ p(\mu | Y_nm).