A Metropolis-within-Gibbs sampler for piecewise convex hyperspectral unmixing and endmember extraction is presented. The standard linear mixing model used for hyperspectral unmixing assumes that hyperspectral data reside in a single convex region. However, hyperspectral data are often nonconvex. Furthermore, in standard endmember extraction and unmixing methods, endmembers are generally represented as a single point in the high-dimensional space. However, the spectral signature for a material varies as a function of the inherent variability of the material and environmental conditions. Therefore, it is more appropriate to represent each endmember as a full distribution and use this information during spectral unmixing. The proposed method searches for several sets of endmember distributions. By using several sets of endmember distributions, a piecewise convex mixing model is applied, and given this model, the proposed method performs spectral unmixing and endmember estimation given this nonlinear representation of the data. Each set represents a random simplex. The vertices of the random simplex are modeled by the endmember distributions. The hyperspectral data are partitioned into sets associated with each of the extracted sets of endmember distributions using a Dirichlet process prior. The Dirichlet process prior also estimates the number of sets. Thus, the Metropolis-within-Gibbs sampler partitions the data into convex regions, estimates the required number of convex regions, and estimates endmember distributions and abundance values for all convex regions. Results are presented on real hyperspectral and simulated data that indicate the ability of the method to effectively estimate endmember distributions and the number of sets of endmember distributions.

MOTIVATION: The program MBBC 2.0 clusters time-course microarray data using a Bayesian product partition model. RESULTS: The Bayesian product partition model in Booth et al. (2007) simultaneously searches for the optimal number of clusters, and assigns cluster memberships based on temporal changes of gene expressions. MBBC 2.0 to makes this method easily available for statisticians and scientists, and is built with three free computer language software packages: Ox, R and C++, taking advantage of the strengths of each language. Within MBBC, the search algorithm is implemented with Ox and resulting graphs are drawn with R. A user-friendly graphical interface is built with C++ to run the Ox and R programs internally. Thus, MBBC users are not required to know how to use Ox, R or C++, but they must be pre-installed. AVAILABILITY: A self-extractable zip file, MBBC20zip.exe, is available at the MBBC webpage www.stat.ufl.edu/~casella/mbbc/, which contains MBBC.exe, source files, and all other related files. The current version works only in the Windows operating system. A free installation program and overview for Ox is available at www.doornik.com. A detailed installation guide for Ox is provided by MBBC, and is accessible without installing Ox. R is available at www.r-project.org/.

SUMMARY: Understanding the genetic control of growth is fundamental to agricultural, evolutionary and biomedical genetic research. In this article, we present a statistical model for mapping quantitative trait loci (QTL) that are responsible for genetic differences in growth trajectories during ontogenetic development. This model is derived within the maximum likelihood context, implemented with the expectation-maximization algorithm. We incorporate mathematical aspects of growth processes to model the mean vector and structured antedependence models to approximate time-dependent covariance matrices for longitudinal traits. Our model has been employed to map QTL that affect body mass growth trajectories in both male and female mice of an F2 population derived from the Large and Small mouse strains. The results from this model are compared with those from the autoregressive-based functional mapping approach. Based on results from computer simulation studies, we suggest that these two models are alternative to one another and should be used simultaneously for the same dataset.

SUMMARY: FunMap is a Web-based user interface designed to map quantitative trait loci (QTL) affecting function-valued traits or infinite-dimensional traits in well-structured pedigrees or natural populations. User input includes three files: longitudinal trait data, marker genotypes and/or a linkage map. This software allows for a systematic genome-wide scan and significance test of QTL throughout the map. The dynamic change of QTL effects during the time course of growth is automatically drawn, from which specific biological hypotheses regarding the genetic control mechanisms of growth and development can be tested. AVAILABILITY: http://web.biostat.ufl.edu/~cma/genetics/software.html