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I show how a renormalization group (RG) method can be used to incrementallyintegrate the information in cosmological large-scale structure data sets(including CMB, galaxy redshift surveys, etc.). I show numerical tests forGaussian fields, where the method allows arbitrarily close to exact computationof the likelihood function in order $\sim N$ time, even for problems with nosymmetry, compared to $N^3$ for brute force linear algebra (where $N$ is thenumber of data points -- to be fair, methods already exist to solve theGaussian problem in at worst $N \log N$ time, and this method will notnecessarily be faster in practice). The method requires no sampling or otherMonte Carlo (random) element. Non-linearity/non-Gaussianity can be accountedfor to the extent that terms generated by integrating out small scale modes canbe projected onto a sufficient basis, e.g., at least in the sufficientlyperturbative regime. The formulas to evaluate are straightforward and requireno understanding of quantum field theory, but this paper may also serve as apedagogical introduction to Wilsonian RG for astronomers.

Renormalization group computation of likelihood functions for cosmological data sets