Bayesian hierarchical modelling for population size estimation: application to Italian data

Bayesian demography developments, global trends for substituting traditional censuses with cheaper methods able to use available information, and new technologies require investigating and providing new models to answer new requirements. In Italy in particular, during the last years Istat worked for launching in October 2018 the ``permanent census of population and housing''. After a first discussion on censuses, changes recommended by organisations such as the UN and the European Union to the National Statistical Institutes, and on new demographic models for population size estimation, the model proposed by Bryant and Graham (2013) is analysed. The model allows for integration of different data sources, for demographic series estimation, and it is very flexible and complex at the same time. Applications of this model to the Italian population are performed, highlighting its advantages and limits. Data for the period considered (2006-2015) and metadata come from Istat. Data are not always consistent, confirming the need of statistical methods able to integrate sources and reconstruct demographic series. As expected, census data and migration flows estimation caused most of the problems. The method still needs further experimentations, therefore applications aim to compare results when varying initial assumptions and to identify their pros and cons rather than provide actual results on the Italian population. Eventually a model extension, along with the first results of its application, is proposed using the Conway-Maxwell Poisson distribution Conway and Maxwell (1962), a flexible two parameters version of the Poisson distribution.