Age-specific probability of childbirth. Smoothing via bayesian nonparametric mixture of rounded kernels

The municipality of Milan is one of the most important areas in Italy being the center of many economic activities and the destination of strong national and international immigration. In this context, policy makers are interested in understanding socio-demographical and economical differences among the different urban areas. In this paper we concentrate in estimating differences in fertility among the nine areas of Milan. The knowledge of age-specific fertility indicators, indeed, is extremely useful in order to decide where to build a new nursery-school, where to increase obstetrics departments in hospitals, or which kind of services can be offered to families.To estimate the age-specific probabilities of child-births in the municipality of Milan, we use open-data on the births residents in Milan in 2011. It has recently been observed that the patterns of fertility of developed countries show a deviation from the classic right-skewed shape due to the fact that women tend to have children later. Also, when a large component of immigrants is present, the age-specific fertility rate exhibits an almost bimodal shape, the curve shows a little hump between 20 and 25 years of the woman, presumably due to the presence of subpopulations. To deal with this phenomena and to compare fertility between the nine urban areas of the municipality of Milan, we apply a Bayesian nonparametric mixture model which can account for skewness and multimodality and we estimate the age-specific probability of childbirth