@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={AbstractStudies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.}, 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_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={AbstractGeostatistical 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_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} }