The name is absent

108

is applied to the motivating sarcoma phase II trial. The rare nature of the disease
makes borrowing strength essential.

The proposed model is based on a product partition model for random partitions.
The model assigns high prior probability to partitions with homogeneous clusters.
That is, clusters with few different values of the covariate associated to the indices
in the cluster. The model is a particular case of the more general PPMx model
introduced in M^,,uller et al. (2009). Their model considers continuous, ordinal and
categorical covariates. In the same paper their model is applied to examples with
ordinal and continuous covariate. To my knowledge, this is the first application of
the PPMx model with categorical covariate. The computation burden associated with
the implementation of this model is only slightly greater than the computational effort
involved in inference for random partitions induced by the Dirichlet process mixture
model (Polya urn).

In summary, the three flexible and non-parametric Bayesian models proposed in
this thesis are an improvement over previously used parametric models to analyze
similar data-sets. All models can be extended and applied to other problems with
appropriate modifications. They all have limitations and improvements are possible.

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