Renormalization group computation of likelihood functions for
  cosmological data sets
  I show how a renormalization group (RG) method can be used to incrementally
integrate the information in cosmological large-scale structure data sets
(including CMB, galaxy redshift surveys, etc.). I show numerical tests for
Gaussian fields, where the method allows arbitrarily close to exact computation
of the likelihood function in order $\sim N$ time, even for problems with no
symmetry, compared to $N^3$ for brute force linear algebra (where $N$ is the
number of data points -- to be fair, methods already exist to solve the
Gaussian problem in at worst $N \log N$ time, and this method will not
necessarily be faster in practice). The method requires no sampling or other
Monte Carlo (random) element. Non-linearity/non-Gaussianity can be accounted
for to the extent that terms generated by integrating out small scale modes can
be projected onto a sufficient basis, e.g., at least in the sufficiently
perturbative regime. The formulas to evaluate are straightforward and require
no understanding of quantum field theory, but this paper may also serve as a
pedagogical introduction to Wilsonian RG for astronomers.
