Bayesian nonparametric modelling has recently attracted a lot of attention, mainly due to the advancement\ud of various simulation techniques, and especially Monte Carlo Markov Chain (MCMC)\ud methods. In this thesis I propose some Bayesian nonparametric models for grouped data, which\ud make use of dependent random probability measures. These probability measures are constructed\ud by normalising infinitely divisible probability measures and exhibit nice theoretical properties. Implementation\ud of these models is also easy, using mainly MCMC methods. An additional step in\ud these algorithms is also proposed, in order to improve mixing. The proposed models are applied\ud on both simulated and real-life data and the posterior inference for the parameters of interest are\ud investigated, as well as the effect of the corresponding simulation algorithms. A new, n-dimensional\ud distribution on the unit simplex, that contains many known distributions as special cases, is also\ud proposed. The univariate version of this distribution is used as the underlying distribution for modelling\ud binomial probabilities. Using simulated and real data, it is shown that this proposed model is\ud particularly successful in modelling overdispersed count data
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