Capture recapture models are frequently used to estimate the size of an elusive population. In this research we will focus on specific criminal populations as drug traffickers and prostitution exploiters. We will investigate the possibility to take account of heterogeneity of these illegal populations by using mixture models. Moreover, since these populations present also particular behavioral effects that may affect the capture patterns we will consider capture recapture models where such behaviors are accounted for by inflating specific capture histories. The methodology proposed will be evaluated by official data sets provided by the Ministry of Justice. In addition we will use also real data available from the literature on capture-recapture models , where the issues of heteregeneity and behavioral effect have been recognized.
This project aims to obtain several important advancements of knowledge with respect to the state of the art. The first set of advancements will be from a methodological point of view. In fact, in order to estimate the proposed mixture and one inflated models from a Bayesian point of view we will need to find new simulation algorithms able to produce the posterior inference for these class of models. In particular we think that a Gibbs sampler algorithm will be the natural approach for both the models. Note that the exact details of such algorithm for the one-inflated class of models will permit to evaluate numerically the marginal likelihood of each model by using the approximation technique introduced in Chib (1995). Moreover in order to compare non inflated models with respect to those presenting one-inflation we will also have the possibility to implement more advanced techniques like the reversible jump algorithm introduced by Green (1997). In particular our aim is to consider non-inflated and one-inflated Poisson and Negative Binomial models in order to produce a model averaging approach. The details of the reversible jump algorithm for comparing inflated against non inflated models have not still presented in the literature hence may represent an interesting finding for Bayesian researchers.
The other group of important advancements of knowledge with respect to the state of the art will be the possibility to have estimates of the size of several criminal populations based on official data. To our knowledge, our proposed methodology has never been applied in this context. Moreover, it is also very difficult to have reliable estimates of the illegal phenomena that we aim to analyze. Hence our estimates will represent useful statistical approximations for evaluate the intensity of several criminal activities in Italy that can be used to all researchers working in the field of the crime science.
Chib, S. (1995). Marginal likelihood from the Gibbs output. Journal of the American Statistical Association, 90(432), 1313¿1321.
Green, P. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711¿732.