Ioulia Papageorgiou

Multivariate mixtures of normals with unknown number of components

We present full Bayesian analysis of finite mixtures of multivariate normals with unknown number of components. We adopt reversible jump Markov chain Monte Carlo and we construct, in a manner similar to that of Richardson and Green (1997), split and merge moves that produce good mixing of the Markov chains. The split moves are constructed on the space of eigenvectors and eigenvalues of the current covariance matrix so that the proposed covariance matrices are positive definite. Our proposed methodology has applications in classification and discrimination as well as heterogeneity modelling. We test our algorithm with real and simulated data.

Latent class models for mixed variables with applications in Archaeometry

Latent class models are used in social sciences for classifying individuals or objects into distinct groups/classes based on responses to a set of observed indicators. The latent class model for mixed binary and metric variables (Br. J. Math. Statist. Psych. 49 (1996) 313) is extended to accommodate any type of data (including ordinal and nominal) and its use in Archaeometry for classifying archaeological findings/objects into groups is discussed. The models proposed are estimated using a full maximum like-lihood with the EM algorithm. Two data sets from archaeological findings are used to illustrate the methodology.

Model-based cluster analysis of artefact compositional data

Cluster analysis is the most widely used multivariate technique in archaeometry, with the majority of applications being exploratory in nature. Model-based methods of clustering have their advocates, but have seen little application to archaeometric data. The paper investigates two such methods. They have potential advantages over exploratory techniques, if successful. Mixture maximum-likelihood worked well using low-dimensional lead isotope data, but had problems coping with higher-dimensional ceramic compositional data. For our most challenging example, classification maximum-likelihood performed comparably with more standard methods, but we find no evidence to suggest that it should supplant these.

Model-complete strategies for sampling from convex autocorrelated finite populations

Sampling from finite populations when there is autocorrelation between the population units, is the subject of study in this paper. The case when the autocorrelation function for the population is convex is examined. We provide, in the first instance, the best unbiased predictor of the population mean under the assumptions of the assumed model. For this predictor, the optimum class of sampling strategies under the model-complete criterion is determined. For practical applications, a subclass of the above class of strategies is considered and it is shown in Section 4 that the centrally located is the optimal one. Finally, some numerical examples and comparison study has been carried out in order to see, in practice, the merit of the optimal strategies suggested in the present paper.

Sampling of pairs in pairwise likelihood estimation for latent variable models with categorical observed variables

Pairwise likelihood is a limited information estimation method that has also been used for estimating the parameters of latent variable and structural equation models. Pairwise likelihood is a special case of composite likelihood methods that uses lower-order conditional or marginal log-likelihoods instead of the full log-likelihood. The composite likelihood to be maximized is a weighted sum of marginal or conditional log-likelihoods. Weighting has been proposed for increasing efficiency, but the choice of weights is not straightforward in most applications. Furthermore, the importance of leaving out higher-order scores to avoid duplicating lower-order marginal information has been pointed out. In this paper, we approach the problem of weighting from a sampling perspective. More specifically, we propose a sampling method for selecting pairs based on their contribution to the total variance from all pairs. The sampling approach does not aim to increase efficiency but to decrease the estimation time, especially in models with a large number of observed categorical variables. We demonstrate the performance of the proposed methodology using simulated examples and a real application.