What is it about?
Assume we have some observations and we would like to interpolate these data onto new locations. A typical example is: weather stations in Germany measure weather only locally around these stations, how to predict weather on the whole territory of Germany? One of the methods is Kriging (also called statistical interpolation). From linear algebra point of view, this is only solution of a linear system and matrix-vector product. Another task is how to improve already existing weather prediction model is some new measurement data become available? Or another task, where are the optimal positions for the weather stations to maximize the information gain. All these are very time-consuming tasks. We speed up computations by combining low-rank tensor methods and Fats Fourier Transformation. We can achieve speed up factors 10, 100 or even 1000. This is not for free; we do certain assumptions about the covariance matrix and require axes parallel mesh.
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Why is it important?
Nowadays we deal with huge amount of data, the data are high-dimensional. In spatio-temporal statistics the time intervals and the spatial areas are huge. The satellite data are huge. All these require very fast and efficient numerical techniques.
Perspectives
We apply the multi-linear algebra techniques, which are well known in the research area "numerical methods for PDEs" to solve typical statistical tasks. These techniques are already well tested in PDEs and it is not surprising that they are working also in spatio-temporal statistic.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: Kriging and Spatial Design Accelerated by Orders of Magnitude: Combining Low-Rank Covariance Approximations with FFT-Techniques, Mathematical Geosciences, April 2013, Springer Science + Business Media,
DOI: 10.1007/s11004-013-9453-6.
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