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Abstract:
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Solving spatiotemporal missing data problems will always be of interest; due to data-gathering methods like satellite images, we are constantly collecting data with missingness due to cloud cover, precipitation, or other environmental forces. In spatiotemporal problems, there are many well-studied methods for imputing this missing data, the most popular of which is the Gaussian process. This work is motivated by a real-world problem: downscaling two large surface temperature datasets, one with high spatial resolution and one with high temporal resolution, in order to obtain more accurate temperature data for use in modeling. This problem is complicated by the fact that the (lat, long) pairs are not common to both datasets. With large amounts of data, fitting a standard GP can be very computationally expensive, which has led to many alternatives, one of which is NNGPs, the nearest-neighbor variant. The computational advantage of nearest-neighbor algorithms is that they create sparse covariance matrices, drastically speeding up computation time. We introduce and test ordering schemes for applying directed acyclic graph methodology to gaussian processes.
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