The human microbiome is the totality of all microbes in and on the human body, and its importance in health and disease has been increasingly recognized. High-throughput sequencing technologies have recently enabled scientists to obtain an unbiased quantification of all microbes constituting the...

Motivated by analysis of gene expression data measured over different tissues or over time, we consider matrix-valued random variable and matrix-normal distribution, where the precision matrices have a graphical interpretation for genes and tissues, respectively. We present a l1 penalized...

Motivated by the analysis of genetical genomic data, we consider the problem of estimating high-dimensional sparse precision matrix adjusting for possibly a large number of covariates, where the covariates can affect the mean value of the random vector. We develop a two-stage estimation...

Multi-way tensor data are prevalent in many scientific areas such as genomics and biomedical imaging. We consider a K-way tensor-normal distribution, where the precision matrix for each way has a graphical interpretation. We develop an l1 penalized maximum likelihood estimation and an efficient...

Complex human diseases are often due to multiple disease genes with variable age of onset, as well as both genetic and environmental risk factors. In order to simultaneously consider two possible disease loci and to incorporate age of onset and covariate information into genetic linkage...