@article{lan_reich_guinness_bandyopadhyay_ma_moeller_2022, title={Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging}, volume={78}, ISSN={["1541-0420"]}, DOI={10.1111/biom.13445}, abstractNote={Geostatistical modeling for continuous point-referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive-definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix-variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost-surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix-variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed-form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods.}, number={2}, journal={BIOMETRICS}, author={Lan, Zhou and Reich, Brian J. and Guinness, Joseph and Bandyopadhyay, Dipankar and Ma, Liangsuo and Moeller, F. Gerard}, year={2022}, month={Jun}, pages={548–559} }
 @article{lan_reich_bandyopadhyay_2021, title={A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging}, volume={49}, ISSN={["1708-945X"]}, DOI={10.1002/cjs.11601}, abstractNote={Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique used to characterize microstructural changes in the brain. DTI studies quantify the diffusion of water molecules in a voxel using an estimated 3x3 symmetric positive definite diffusion tensor matrix. Statistical analysis of DTI data is challenging because the data are positive definite matrices. Matrix-variate information is often summarized by a univariate quantity, such as the fractional anisotropy (FA), leading to a loss of information. Furthermore, DTI analyses often ignore the spatial association of neighboring voxels, which can lead to imprecise estimates. Although the spatial modeling literature is abundant, modeling spatially dependent positive definite matrices is challenging. To mitigate these issues, we propose a matrix-variate Bayesian semiparametric mixture model, where the positive definite matrices are distributed as a mixture of inverse Wishart distributions with the spatial dependence captured by a Markov model for the mixture component labels. Conjugacy and the double Metropolis-Hastings algorithm result in fast and elegant Bayesian computing. Our simulation study shows that the proposed method is more powerful than non-spatial methods. We also apply the proposed method to investigate the effect of cocaine use on brain structure. The contribution of our work is to provide a novel statistical inference tool for DTI analysis by extending spatial statistics to matrix-variate data.}, number={1}, journal={CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE}, author={Lan, Zhou and Reich, Brian J. and Bandyopadhyay, Dipankar}, year={2021}, month={Mar}, pages={129–149} }
 @article{lan_zhao_kang_yu_2016, title={Bayesian network feature finder (BANFF): an r package for gene network feature selection}, volume={32}, number={23}, journal={Bioinformatics}, author={Lan, Z. and Zhao, Y. Z. and Kang, J. and Yu, T. W.}, year={2016}, pages={3685–3687} }