Flexible Statistical Methods for the Analysis of Correlated Multivariate Data

University Of Texas At El Paso, El Paso TX

Investigators

Abstract

The proposed research focuses on a number of topics related to the analysis of correlated multivariate data. Bayesian methods in combination with mixture models and nonparametric techniques result in novel flexible methods. In one project, the investigator proposes a method for the analysis of multivariate functional data. Cubic splines will be used to estimate the unknown mean functions, as well as the subject-specific functions. To accommodate correlation and unequally spaced measurement times, the multivariate Ornstein-Uhlenbeck process will be explored. Another topic of interest is parsimonious estimation of the covariance structure of longitudinal data when the assumption of a constant covariance matrix over time is unreasonable. To allow for an evolving parsimonious covariance matrix, the Cholesky decomposition of the inverse covariance matrix will be used along with mixture modeling. In a third project, the investigator's previous work on spectral matrix estimation for stationary multivariate time series will be extended to the case of locally stationary multivariate time series. The estimated spectral matrix along with the spectral envelope technique can be used to analyze categorical time series, such as DNA sequences. This analysis, however, is limited to short DNA sequences for which the assumption of stationarity is reasonable. In this project, local behavior of longer DNA sequences will be accommodated by extending the investigator's previous work via mixture modeling. In another project, modeling a covariance matrix using the spectral decomposition will be explored. This approach can be used as a building block in other applications such as model-based clustering. The proposed research develops novel flexible statistical methods for the analysis of data consisting of several correlated variables. One area of application is psychiatric research, where despite decades of clinical trial experience in major depression, there is only limited understanding of which patients with major depressive disorder respond better to psychotherapy or to pharmacotherapy. Of particular interest is the identification of baseline subject characteristics which differentially predict treatment response in the two groups. The response variables in this case may be different measures of depression taken longitudinally on psychiatric patients. Another area of application is the analysis of DNA sequences. A DNA sequence can be described as genes containing coding regions separated by noncoding regions. Coding regions within genes code for the proteins which determine the organism's structure and functioning. Detecting genes in a DNA sequence is important for analyzing the genome of an organism. A third area of application is clustering of microarray data to identify functional groups of genes. The goal of cluster analysis for microarray data is to group genes into clusters with similar profiles. Knowledge about expression levels of genes from different cells may help in diagnosing diseases or in finding drugs to cure them.