Unsupervised Bayesian classification for models with scalar and functional covariates.

We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of the L components of a mixture model which incorporates scalar and functional covariates. This process can be thought as a hierarchical model with the first level modelling a scalar response according to a mixture of parametric distributions and the second level modelling the mixture probabilities by means of a generalized linear model with functional and scalar covariates. The traditional approach of treating functional covariates as vectors not only suffers from the curse of dimensionality, since functional covariates can be measured at very small intervals leading to a highly parametrized model, but also does not take into account the nature of the data. We use basis expansions to reduce the dimensionality and a Bayesian approach for estimating the parameters while providing predictions of the latent classification vector. The method is motivated by two data examples that are not easily handled by existing methods. The first example concerns identifying placebo responders on a clinical trial (normal mixture model) and the other predicting illness for milking cows (zero-inflated mixture of the Poisson model).

The usefulness of amplified fragment length polymorphism markers for taxon discrimination across graduated fine evolutionary levels in Caribbean Anolis lizards.

Fine-level taxon discrimination is important in biodiversity assessment and ecogeographical research. Genomic markers are often required for studies on closely related taxa, however, most existing mitochondrial and nuclear markers require prior knowledge of the genome and are impractical for use in small conservation projects. This study describes the application of amplified fragment length polymorphism (AFLP) to discriminate at four progressively finer evolutionary levels of Caribbean Anolis lizards from the central Lesser Antilles. AFLP is shown to be a rapid and effective method for discriminating between species. Separation increases with primer pair number and choice of primer combination appears to be noncritical. Initial population-level results show markedly less discriminatory power. A screening technique for the identification of population informative markers combining principal component and principal coordinate analyses is presented and assessed. Subsequent results show selected conspecific AFLP data to be remarkably congruent with those of mitochondrial DNA, microsatellite and morphological markers. The use of AFLP as a low-cost nuclear marker in species-level taxon discrimination is supported, whereas population level application demands further consideration.