Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How do Markov approximations compare with other methods for large
  spatial data sets?   The Mat\'ern covariance function is a popular choice for modeling dependence
in spatial environmental data. Standard Mat\'ern covariance models are,
however, often computationally infeasible for large data sets. In this work,
recent results for Markov approximations of Gaussian Mat\'{e}rn fields based on
Hilbert space approximations are extended using wavelet basis functions. These
Markov approximations are compared with two of the most popular methods for
efficient covariance approximations; covariance tapering and the process
convolution method. The results show that, for a given computational cost, the
Markov methods have a substantial gain in accuracy compared with the other
methods.

2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an