  Here we present an investigation into using nested sampling algorithms in
cosmological likelihood analysis. We present a new nested sampling algorithm,
ESNested, that uses Evolution Strategies for sample proposals. This quickly
finds the maximum for complex likelihoods and provides an accurate measure of
the Bayesian evidence, with no prior assumptions about the shape of the
likelihood surface. We present the first cosmological constraints using
Evolution Strategies, from WMAP 7, HST and SNIa data using likelihood and data
provided with CosmoMC. We find a significantly higher maximum likelihood than
that found with other methods. We compare the performance of ESNested with the
publicly available MultiNest and CosmoNest algorithms, in i) finding the
maximum likelihood ii) calculating confidence contours in projected parameter
spaces and iii) calculating the Bayesian evidence. We find that none of the
algorithms provide a single solution for all of these products in general. Our
recommendation is that multiple sampling methods should be used in cosmological
likelihood analysis and that algorithms should be tailored to perform optimally
for each of these requirements. These results have a resonance with the
well-known No Free Lunch theorem.
