About
I am an assistant professor specialized in Computational and Spatial Statistics in the Department of Mathematics at The University of Houston. I worked as a postdoc with Dr. Matthias Katzfuss at Texas A&M University. I obtained my Ph.D. degree in Statistics at King Abdullah University of Science and Technology (KAUST), advised by Dr. Marc Genton. Prior to that, I obtained a B.S. in Mathematics from University of Science and Technology of China.
My research focuses on scalable Gaussian Process (GP) regression, including truncated GP, latent GP, multivariate GP, and high-dimensional GP. During my postdoc, I worked on scalable Gaussian process regression and variable selection, transport maps, and variational Bayes, most of which are based on the Vecchia approximation of Gaussian processes. During my PhD, I studied scalable evaluations of multivariate normal probabilities, mainly exploiting low-rank matrices and efficient quasi-Monte Carlo sampling rules. My research is mostly related to applications in spatial statistics, climate science, and argricultural science.
- Computational statistics
- Conditional independence approximation
- Gaussian-process-related machine learning
- Multivariate normal probability
- Truncated multivariate normal
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Bachelor in Applied Mathematics, 2014
University of Science and Technology of China
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Master in Finance, 2016
Shanghai Jiaotong University
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PhD in Statistics, 2020
King Abdullah University of Science and Technology
Awards and Honors
- Al-Kindi Statistics Student Research Award, 2020
- Best Student Paper, 2019
Publications
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Cao, Jian and Katzfuss, Matthias (2025). Linear-Cost Vecchia Approximation of Multivariate Normal Probabilities. in revision for Journal of the American Statistical Association.
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Cao, Jian and Katzfuss, Matthias (2025). Scalable Sampling of Truncated Multivariate Normals Using Sequential Nearest-Neighbor Approximation. in revision for Journal of Computational and Graphical Statistics.
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Cao, Jian and Zhang, Jingjie and Sun, Zhuoer and Katzfuss, Matthias (2024). Locally anisotropic nonstationary covariance functions on the sphere. Journal of Agricultural, Biological and Environmental Statistics, 29(2), 212--231.
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Abdulah, Sameh and Li, Yuxiao and Cao, Jian and Ltaief, Hatem and Keyes, David E and Genton, Marc G and Sun, Ying (2023). Large-scale environmental data science with ExaGeoStatR. Environmetrics, 34(1), e2770.
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Cao, Jian and Kang, Myeongjong and Jimenez, Felix and Sang, Huiyan and Schaefer, Florian Tobias and Katzfuss, Matthias (2023). Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization. International Conference on Machine Learning.
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Cao, Jian and Durante, Daniele and Genton, Marc G (2022). Scalable computation of predictive probabilities in probit models with Gaussian process priors. Journal of Computational and Graphical Statistics, 31(3), 709--720.
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Cao, Jian and Genton, Marc G and Keyes, David E and Turkiyyah, George M (2022). tlrmvnmvt: Computing high-dimensional multivariate normal and student-t probabilities with low-rank methods in r. Journal of Statistical Software, 101, 1--25.
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Cao, Jian and Guinness, Joseph and Genton, Marc G and Katzfuss, Matthias (2022). Scalable Gaussian-process regression and variable selection using Vecchia approximations. Journal of machine learning research, 23(348), 1--30.
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Cao, Jian and Genton, Marc G and Keyes, David E and Turkiyyah, George M (2021). Exploiting low-rank covariance structures for computing high-dimensional normal and Student-t probabilities. Statistics and Computing, 31, 1--16.
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Cao, Jian and Genton, Marc G and Keyes, David E and Turkiyyah, George M (2021). Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids. Computational Statistics \& Data Analysis, 157, 107165.
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Huang, Jingfang and Cao, Jian and Fang, Fuhui and Genton, Marc G and Keyes, David E and Turkiyyah, George (2021). An O (N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals. Advances in Computational Mathematics, 47(5), 65.
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Cao, Jian and Genton, Marc G and Keyes, David E and Turkiyyah, George M (2019). Hierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities. Statistics and Computing, 29(3), 585--598.
Teaching
- Statistics for the Sciences, 2023 Fall, University of Houston
- Statistics for the Sciences, 2024 Spring, University of Houston
- Inferential Statistics, 2024 Fall, University of Houston
- Statistics for the Sciences, 2025 Spring, University of Houston
Software
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tlrmvnmvt: Estimating multivariate normal (MVN) probabilities using tile-low-rank (TLR) matrix representation.
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VeccTMVN: Estimating multivariate MVN probabilities and sampling from truncated MVN (TMVN) distributions using Vecchia approximation and exponential tilted importance sampling.
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nntmvn: Using the sequential nearest neighbor (SNN) method to draw samples from the truncated multivariate normal (TMVN) distributions.