Data with strong spatial dependence is common in fields as diverse as agriculture, mining, astronomy, environmental science, sports analytics and microchip manufacturing. Since they are flexible and parsimonious, Gaussian Process models are frequently used for describing spatial phenomenon. Carrying out statistical inference for spatial Gaussian processes presents unique statistical and computational challenges: the spatial dependence significantly complicates asymptotic analysis, and estimating covariance parameters is statistically challenging. Moreover, fitting these models involves either an inversion or Cholesky decomposition of the covariance matrix. The number of operations required scales cubically with the dataset size.

Recent trends in spatial statistics research have been to develop efficient methods to estimate spatial models, and to develop efficient estimation methods for more complex topologies. Computational tools, such as INLA and LatticeKrig, provide computational tools that can efficiently estimate these models. New estimation procedures approach this by developing algorithms that have better scaling. Examples include using reduced-rank models or hierarchical matrices to approximate the likelihood, and the Inversion Free algorithm. For more complex topologies such as spheres or rivers, researchers are developing spherical covariance functions and network models, respectively.  

This year's Statistics Graduate Student Research Day will focus on theoretical and methodological questions associated with spatial statistics, as well as novel applications of these methods. The invited speakers will form a diverse panel, including both Canadian and non-Canadian researchers, working on theoretical and applied problems. The contributed speakers will be three graduate students and/or post-doctoral fellows from the department of statistical sciences, computer science, mathematics, and related disciplines.

This event is supported in part from funding and resources made available by the Fields Institute and CANSSI.