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Cluster results for the RAxML and MrBayes clusters on the mibc data. Table S1. The threshold values and corresponding clustering results for RAxML on the mibc data. Table S2. The threshold values and corresponding clustering results for MrBayes on the mibc data. (PDF 108 kb)

Performs simulation studies involving a variety of tree topologies. Figure S1. The clustering results obtained by the Gap Procedure (ARI = 0.4489) when applied to a 4-group simulation with a star-like ancestor tree. Figure S2. The clustering results obtained by the Gap Procedure (ARI = 0.5994) when applied to a 4-group simulation with a random bifurcating ancestor tree. Figure S3. The clustering results obtained by the Gap Procedure (ARI = 0.4066) when applied to a 4-group simulation with a random bifurcating ancestor tree. Figure S4. The clustering results obtained by the Gap Procedure (ARI = 0.6152) when applied to a 4-group simulation with a random bifurcating ancestor tree. Table S1. The clustering results obtained by the Gap Procedure on Simulation 1 with varying ancestor/descendant tree heights. Table S2. The clustering results for the Gap Procedure on Simulation 1 while relaxing the star-phylogeny assumption. (PDF 182 kb)

Side-by-side boxplots. Figure S1. Boxplots for the within and between cluster pairwise distances for Simulation 1. Figure S2. Plots the sorted pairwise distances and nearest neighbours for Simulation 1. Figure S3. Boxplots for the within and between cluster pairwise distances for the mibc data. Figure S4. Plots the sorted pairwise distances and nearest neighbours for the mibc data. (PDF 195 kb)

Details regarding the Gap Procedureâ s scheme for combating the effects of outliers. Figure S1. Plots the sorted pairwise distances for a 3-group simulation. Figure S2. Plots the sorted pairwise distances for a 3-group simulation with an outlier. (PDF 109 kb)

Describes how to construct phylogenetic trees used for generating sequence data. Figure S1. Plots the step-by-step construction a 6-group phylogenetic tree. (PDF 147 kb)

Describes the details for computing adjusted JC69 (aJC69) and adjusted K80 (aK80) distances. Figure S1. Side-by-side boxplots comparing K80 and aK80 distances. (PDF 228 kb)

Model-based classification uses finite mixture models to infer a group structure in data. Three species of classification include unsupervised classification (cluster- ing), semi-supervised classification (or simply classification), and supervised classification (discriminant analysis). We expound on these classical methods and present several flexible extensions. The first area we explore is finite mixtures of skewed distributions; namely, model-based clustering via skew-normal and skew- t mixture models. The algorithms used to fit these models are established and some approximations that were used in the computationally intractable E-steps are also presented. The second area of investigation involves two new ‘families’ of parsimonious mixture models. These families are constructed by imposing constraints on the decomposed component scale matrices of skew-normal and skew-t mixtures, thereby reducing the number of free parameters to be estimated. These models are tailored for skewed data but have the added capability of reverting to the symmetric Gaussian (or multivariate t) counterparts when appropriate. Finally, we introduce a generalized classification procedure, wherein any level of supervision — ranging from unsupervised to supervised — can be attained. We develop this novel approach, termed fractionally-supervised classification, using a weighted likelihood. This new method is tested on some benchmark data sets and the optimal choice of relevance weight is explored.

Individual-level models (ILMs), as defined by Deardon et al. (2010), are a class of models originally designed to model the spread of infectious disease. However, they can also be considered as a tool for modelling the spatio-temporal dynamics of fire. We consider the much simplified problem of modelling the combustion dynamics on a piece of wax paper under relatively controlled conditions. The models are fitted in a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. The focus here is on choosing a model that best fits the combustion pattern.

Cluster results for the RAxML and MrBayes clusters on simulated data with T d = 0.4,0.5. Table S1. Cluster results for the RAxML clusters on simulated data with T d = 0.4, 0.5. Table S2. Cluster results for the MrBayes clusters on simulated data with T d = 0.4, 0.5. (PDF 114 kb)

Cluster results for the RAxML and MrBayes clusters on simulated data with T d = 0.4,0.5. Table S1. Cluster results for the RAxML clusters on simulated data with T d = 0.4, 0.5. Table S2. Cluster results for the MrBayes clusters on simulated data with T d = 0.4, 0.5. (PDF 114 kb)