K. E. Basford

Mixture models : inference and applications to clustering

General Introduction Introduction History of Mixture Models Background to the General Classification Problem Mixture Likelihood Approach to Clustering Identifiability Likelihood Estimation for Mixture Models via EM Algorithm Start Values for EMm Algorithm Properties of Likelihood Estimators for Mixture Models Information Matrix for Mixture Models Tests for the Number of Components in a Mixture Partial Classification of the Data Classification Likelihood Approach to Clustering Mixture Models with Normal Components Likelihood Estimation for a Mixture of Normal Distribution Normal Homoscedastic Components Asymptotic Relative Efficiency of the Mixture Likelihood Approach Expected and Observed Information Matrices Assessment of Normality for Component Distributions: Partially Classified Data Assessment of Typicality: Partially Classified Data Assessment of Normality and Typicality: Unclassified Data Robust Estimation for Mixture Models Applications of Mixture Models to Two-Way Data Sets Introduction Clustering of Hemophilia Data Outliers in Darwins Data Clustering of Rare Events Latent Classes of Teaching Styles Estimation of Mixing Proportions Introduction Likelihood Estimation Discriminant Analysis Estimator Asymptotic Relative Efficiency of Discriminant Analysis Estimator Moment Estimators Minimum Distance Estimators Case Study Homogeneity of Mixing Proportions Assessing the Performance of the Mixture Likelihood Approach to Clustering Introduction Estimators of the Allocation Rates Bias Correction of the Estimated Allocation Rates Estimated Allocation Rates of Hemophilia Data Estimated Allocation Rates for Simulated Data Other Methods of Bias Corrections Bias Correction for Estimated Posterior Probabilities Partitioning of Treatment Means in ANOVA Introduction Clustering of Treatment Means by the Mixture Likelihood Approach Fitting of a Normal Mixture Model to a RCBD with Random Block Effects Some Other Methods of Partitioning Treatment Means Example 1 Example 2 Example 3 Example 4 Mixture Likelihood Approach to the Clustering of Three-Way Data Introduction Fitting a Normal Mixture Model to Three-Way Data Clustering of Soybean Data Multidimensional Scaling Approach to the Analysis of Soybean Data References Appendix

Seed compositional and disease resistance differences among gene pools in cultivated common bean

It is widely accepted that two major gene pools exist in cultivatedcommon bean, one Middle American and one Andean. Recently another gene pool,designated as North Andean and a fourth group (not considered to be adistinct gene pool) have been reported by the senior author and hiscolleagues. Many of the agronomic and seed compositional attributes of the twomajor gene pools are well known, but the seed compositional value and diseaseresistance of the North Andean gene pool has not yet been characterized. Torectify this situation, the seed compositional characters, percentage of proteinconcentrations (phaseolin, lectin and α-amylaseinhibitor), the nutrient elements (calcium, phosphorus, iron andzinc) and the disease and pest attributes (angular leaf spot,anthracnose, common bacterial blight and empoasca damage) were considered.The Middle American gene pool gave higher lectin, calcium, phosphorus, sulfurand zinc than the Andean gene pool but lower phaseolin and iron. The NorthAndean gene pool is more like the Andean gene pool for phaseolin, resistance toangular leaf spot and anthracnose from Andean pathogen isolates, but more likethe Middle American gene pool for lectin, zinc, sulfur and resistance toanthracnose from Middle American pathogen isolates. On the other hand, it hadthe highest iron concentration and was more resistant to common bacterialblight. These results indicate the potential value of this gene pool in a commonbean breeding program.

The mixture method of clustering applied to three-way data

Clustering or classifying individuals into groups such that there is relative homogeneity within the groups and heterogeneity between the groups is a problem which has been considered for many years. Most available clustering techniques are applicable only to a two-way data set, where one of the modes is to be partitioned into groups on the basis of the other mode. Suppose, however, that the data set is three-way. Then what is needed is a multivariate technique which will cluster one of the modes on the basis of both of the other modes simultaneously. It is shown that by appropriate specification of the underlying model, the mixture maximum likelihood approach to clustering can be applied in the context of a three-way table. It is illustrated using a soybean data set which consists of multiattribute measurements on a number of genotypes each grown in several environments. Although the problem is set in the framework of clustering genotypes, the technique is applicable to other types of three-way data sets.

Evaluation of experimental designs and spatial analyses in wheat breeding trials

Abstract Thirty-three wheat breeding trials were conducted from 1994 to 1996 in the Northern Grains Region (QLD and Northern NSW) of Australia to evaluate the influence of experimental designs and spatial analyses on the estimation of genotype effects for yield and their impact on selection decisions. The relative efficiency of the alternative designs and analyses was best measured by the average standard error of difference between line means. Both more effective designs and spatial analyses significantly improved the efficiency relative to the randomised complete block model, with the preferred model (which combined the design information and spatial trends) giving an average relative efficiency of 138% over all 33 trials. When the Czekanowski similarity coefficient was used, none of the studied models were in full agreement with the randomised complete block model in the selection of the top lines. The agreement was influenced by selection proportions. Hence, the use of these methodologies can impact on the selection decisions in plant breeding.

Genotype-by-management interactions for grain yield and grain protein concentration of wheat

The magnitude of genotype-by-management (G x M) interactions for grain yield and grain protein concentration was examined in a multi-environment trial (MET) involving a diverse set of 272 advanced breeding lines from the Queensland wheat breeding program. The MET was structured as a series of management-regimes imposed at 3 sites for 2 years. The management-regimes were generated at each site-year as separate trials in which planting time, N fertiliser application rate, cropping history, and irrigation were manipulated. irrigation was used to simulate different rainfall regimes. From the combined analysis of variance, the G x M interaction variance components were found to be the largest source of G x E interaction variation for both grain yield (0.117 +/- 0.005 t(2) ha(-2); 49% of total G x E 0.238 +/- 0.028 t(2) ha(-2)) and grain protein concentration (0.445 +/- 0.020%(2); 82% of total G x E 0.546 +/- 0.057%(2)), and in both cases this source of variation was larger than the genotypic variance component (grain yield 0.068 +/- 0.014 t(2) ha(-2) and grain protein 0.203 +/- 0.026%(2)). The genotypic correlation between the traits varied considerably with management-regime, ranging from -0.98 to -0.31, with an estimate of 0.0 for one trial. Pattern analysis identified advanced breeding lines with improved grain yield and grain protein concentration relative to the cultivars Hartog, Sunco and Meteor. It is likely that a large component of the previously documented G x E interactions for grain yield of wheat in the northern grains region are in part a result of G x M interactions. The implications of the strong influence of G x M interactions for the conduct of wheat breeding METs in the northern region are discussed

Using molecular markers to assess the effect of introgression on quantitative attributes of common bean in the Andean gene pool

Progress in bean breeding programs requires the exploitation of genetic variation that is present among races or through introgression across gene pools of Phaseolus vulgaris L. Of the two major common bean gene pools, the Andean gene pool seems to have a narrow genetic base, with about 10% of the accessions in the CIAT core collection presenting evidence of introgression. The objective of this study was to quantify the degree of spontaneous introgression in a sample of common bean landraces from the Andean gene pool. The effects of introgression on morphological, economic and nutritional attributes were also investigated. Homogeneity analysis was performed on molecular marker data from 426 Andean-type accessions from the primary centres of origin of the CIAT common bean core collection and two check varieties. Quantitative attribute diversity for 15 traits was studied based on the groups found from the cluster analysis of marker prevalence indices computed for each accession. The two-group summary consisted of one group of 58 accessions (14%) with low prevalence indices and another group of 370 accessions (86%) with high prevalence indices. The smaller group occupied the outlying area of points displayed from homogeneity analysis, yet their geographic origin was widely distributed over the Andean region. This group was regarded as introgressed, since its accessions displayed traits that are associated with the Middle American gene pool: high resistance to Andean disease isolates but low resistance to Middle American disease isolates, low seed weight and high scores for all nutrient elements. Genotypes generated by spontaneous introgression can be helpful for breeders to overcome the difficulties in transferring traits between gene pools.

Likelihood Estimation with Normal Mixture Models

We consider some of the problems associated with likelihood estimation in the context of a mixture of multivariate normal distributions. Unfortunately with mixture models, the likelihood equation usually has multiple roots and so there is the question of which root to choose. In the case of equal covariance matrices the choice of root is straightforward in the sense that the maximum likelihood estimator exists and is consistent. However, an example is presented to demonstrate that the adoption of a homoscedastic normal model in the presence of some heteroscedasticity can considerably influence the likelihood estimates, in particular of the mixing proportions, and hence the consequent clustering of the sample at hand.

Genetic variability in cultivated common bean beyond the two major gene pools

It is generally accepted that two major gene pools exist in cultivatedcommon bean (Phaseolus vulgaris L.), a MiddleAmerican and an Andean one. Some evidence, based on unique phaseolin morphotypesand AFLP analysis, suggests that at least one more gene pool exists incultivated common bean. To investigate this hypothesis, 1072 accessions from acommon bean core collection from the primary centres of origin, held at CIAT,were investigated. Various agronomic and morphological attributes (14categorical and 11 quantitative) were measured. Multivariate analyses,consisting of homogeneity analysis and clustering for categorical data,clustering and ordination techniques for quantitative data and nonlinearprincipal component analysis for mixed data, were undertaken. The results ofmost analyses supported the existence of the two major gene pools. However, theanalysis of categorical data of protein types showed an additional minor genepool. The minor gene pool is designated North Andean and includes phaseolintypes CH, S and T; lectin types 312, Pr, B and K; and mostly A5, A6 and A4 typesα-amylase inhibitor. Analysis of the combined categorical data ofprotein types and some plant categorical data also suggested that some othergermplasm with C type phaseolin are distinguished from the major gene pools.

Reliability and validity of lower third molar space-assessment techniques

Present techniques for predicting eruption or impaction of lower third molars are based on measurements of the space between the second molar and the ramus. This study was designed to investigate the reliability and validity of radiographic techniques often used for assessing this space. Rotational tomograms (O.P.G.s) yielded the best estimates of the Space Width Ratio (found by dividing the space available by the mesiodistal width of the lower third molar) as measured directly on dried skulls. Estimates for lateral cephalograms were unreliable. The use of Xi point to lower second molar for assessing the space for lower third molars is not supported.

ImmunoGrid, an integrative environment for large-scale simulation of the immune system for vaccine discovery, design and optimization

Vaccine research is a combinatorial science requiring computational analysis of vaccine components, formulations and optimization. We have developed a framework that combines computational tools for the study of immune function and vaccine development. This framework, named ImmunoGrid combines conceptual models of the immune system, models of antigen processing and presentation, system-level models of the immune system, Grid computing, and database technology to facilitate discovery, formulation and optimization of vaccines. ImmunoGrid modules share common conceptual models and ontologies. The ImmunoGrid portal offers access to educational simulators where previously defined cases can be displayed, and to research simulators that allow the development of new, or tuning of existing, computational models. The portal is accessible at .