STAMPS@CMU presents:

Climate models, large spatial datasets, and harnessing deep learning for a statistical computation

by Douglas Nychka (Department of Applied Mathematics and Statistics, Colorado School of Mines)

Online webinar September 10, 2021 at 1:30-2:30 PM ET.
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Numerical simulations of the motion and state of the Earth’s atmosphere and ocean yield large and complex data sets that require statistics for their interpretation. Typically climate and weather variables are in the form of space and time fields and it is useful to describe their dependence using methods from spatial statistics. Throughout these problems is the need for estimating covariance functions over space and time and accounting for the fact that the covariance may not be stationary. This talk focuses on a new computational technique for fitting covariance functions using maximum likelihood. Estimating local covariance functions is a useful way to represent spatial dependence but is computationally intensive because it requires optimizing a local likelihood over many windows of the spatial field. Thus the problem we tackle here is having numerous (tens of thousands) small spatial estimation problems and is in contrast to other research that attempts a single, global estimate for a massive spatial data set. In this work we show how a neural network (aka deep learning) model can be trained to give accurate maximum likelihood estimates based on the spatial field or its empirical variogram. Why train a neural network to reproduce a statistical estimate? The advantage is that the neural network model evaluates very efficiently and gives speedups on the order of a factor of a hundred or more. In this way computations that could take hours are reduced to minutes or tens of seconds and facilitates a more flexible and iterative approach to building spatial statistical models. An example of local covariance modeling is given using the large ensemble experiment created by the National Center for Atmospheric Research.

See: Gerber, Florian, and Douglas Nychka. “Fast covariance parameter estimation of spatial Gaussian process models using neural networks.” Stat 10.1 (2021): e382.


Douglas Nychka is a statistician and data scientist whose areas of research include the theory, computation and application of curve and surface fitting with a focus on geophysical and environmental applications. Currently he is a Professor in the Department of Applied Mathematics and Statistics at the Colorado School of Mines and Senior Scientist Emeritus at the National Center for Atmospheric Research (NCAR), Boulder, Colorado. Before moving to Mines he directed the Institute for Mathematics Applied to Geosciences at NCAR. His current focus in research has been efficient computation of spatial statistics methods for large data sets and the migration of these methods into easy to use R packages. He is a Fellow of the American Statistical Association and the Institute for Mathematical Statistics.