Hao Zhang

Professor of Statistics
Department of Statistics
Purdue University
West Lafayette, IN 47907

I am deeply committed to advancing the field through both theoretical innovation and applied research. My work is driven by a steadfast belief that the most transformative statistical contributions emerge from a profound understanding of, and response to, real-world data analysis challenges.

My research is not confined to the theoretical realm but is continually shaped and inspired by pressing research questions across a diverse array of disciplines. I have had the privilege of collaborating with leading experts in various fields, including agriculture, forestry, natural resources, environmental science, and climate science. These interdisciplinary collaborations have not only broadened the scope of my research but have also significantly contributed to the advancement of these critical sectors.

In my current research, I am deeply engaged in the fascinating and rapidly evolving field of spatial and space-time data analysis. This specialized focus is incredibly pertinent across a broad spectrum of disciplines, including climatology, geophysics, geology, natural resources, agriculture, health sciences, economics, and marketing. The technological revolution of recent years has ushered in an era of unprecedented data availability, particularly in the realm of space-time data. We now have the capability to collect and archive this data on an exponentially larger scale than ever before. This explosion of complex, interrelated datasets poses unique and formidable statistical challenges.

My work is at the forefront of addressing these challenges, requiring the development of innovative computational strategies and advanced methodological approaches. Significantly, my research intersects with the dynamic field of machine learning, where these statistical methodologies find critical applications. By leveraging the power of machine learning, I am not only navigating the intricacies of vast datasets but also pioneering new frontiers in statistical analysis.

In my work, I utilize probabilistic, statistical, and computational theories and tools. The breadth of my research topics allows my students to choose from a diverse range of problems, from highly applied to deeply theoretical. Some students concentrate on methodological aspects, deriving interesting asymptotic results, while others focus on computational algorithms or specific applications.

Fundamental Research Areas:

  1. Infill Asymptotics: Asymptotic studies are crucial in understanding how estimators behave with large sample sizes, providing insights applicable to finite sample cases. Spatial statistics’ asymptotic studies are particularly complex due to two distinct frameworks: increasing domain asymptotics and infill (or fixed-domain) asymptotics. Usually when the exploratory data analysis shows the presence of spatial correlation, it is sufficiently strong for the infill asymptotics to explain some behaviors of estimation. For example, the likelihood function can be hard to be maximized. I justified it by showing that some parameters cannot be consistently estimated (H. Zhang 2004). This work has been applied to simplify computations in both Bayesian and frequentist inferences for spatial data. H. Zhang and Zimmerman (2005) provided some guidance on which asymptotic framework to be employed in practical data analysis.

  2. Analysis of Large Spatial Data: Handling large spatial covariance matrices, critical in Kriging and likelihood function analysis, is computationally intensive. Techniques like covariance tapering and low-rank approximation have been pivotal. My collaborative work has established the infill asymptotic properties of maximum likelihood estimators under covariance tapering (Du, Zhang, and Mandrekar 2009). My recent research (Hao Zhang 2023) explores criteria for optimal low-rank approximation.

  3. Kernel Methods in Machine Learning: Kriging is closely related to kernel methods in machine learning. I am involved in developing efficient algorithms for these methods, building on the popularity of kernel learning methods since the 1990s.

  4. Deep Learning for Spatial and Space-time Data: The explosion of deep learning, propelled by algorithmic and computing advances, has revolutionized fields like image and speech recognition. My current research is developing a new framework to apply deep learning for improved spatial prediction, robust to model assumptions and capable of modeling mean function and spatial correlation simultaneously.

Other Research Interests:

My expertise extends to uncertainty quantification, statistical computing, risk and insurance, time series, and various statistical applications.

Du, Juan, Hao Zhang, and V. S. Mandrekar. 2009. “Fixed-Domain Asymptotic Properties of Tapered Maximum Likelihood Estimators.” Annals of Statistics 37 (6A): 3330–61.
Zhang, H. 2004. “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics.” Journal of the American Statistical Association 99 (465): 250–61.
Zhang, Hao. 2023. “Spatial Process Approximations: Assessing Their Necessity.” arXiv Preprint arXiv:2311.03201.
Zhang, H., and D. L. Zimmerman. 2005. “Towards Reconciling Two Asymptotic Frameworks in Spatial Statistics.” Biometrika 92 (4): 921–36.