Sampling from a variable dimension mixture model posterior

Goal of the thesis is the analysis of a real dataset concerning a biological problem that obtained an increasing interest in recent years. Commercial stocks of fish are not sufficient anymore to satisfy the global demand. Hence, fishermen are beginning to catch species living in the deep. As little is known about these species, there is an actual risk of extinction of these species. As it is typically difficult and expensive to gather the ages of fish, in order to implement stock management policies, it is necessary to build up reliable growth models to infer ages from length data. The lengths, if we don't observe the ages, come from a mixture distribution, in which the components are the different cohorts. As MCMC methods are not always satisfactory for the analysis of mixture models, to estimate the parameters of the model and the number of cohorts that form the sample, it is employed a Population Monte Carlo algorithm for mixtures generalized to the case of unknown number of components.