3 Missing Data and Partially Known Parameters
Bayesian inference supports a general approach to missing data in which any missing data item is represented as a parameter that is estimated in the posterior (Gelman et al. 2013). If the missing data are not explicitly modeled, as in the predictors for most regression models, then the result is an improper prior on the parameter representing the missing predictor.
Mixing arrays of observed and missing data can be difficult to include in Stan, partly because it can be tricky to model discrete unknowns in Stan and partly because unlike some other statistical languages (for example, R and Bugs), Stan requires observed and unknown quantities to be defined in separate places in the model. Thus it can be necessary to include code in a Stan program to splice together observed and missing parts of a data structure. Examples are provided later in the chapter.
Gelman, Andrew, J. B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. Third Edition. London: Chapman & Hall / CRC Press.