Path integral marginalization for cosmology: scale-dependent galaxy bias and intrinsic alignments

We present a path integral likelihood formalism that extends parametrized likelihood analyses to include continuous functions. The method finds the maximum-likelihood point in function-space, and marginalizes over all possible functions, under the assumption of a Gaussian-distributed function-space. We apply our method to the problem of removing unknown systematic functions in two topical problems for dark energy research: scale-dependent galaxy bias in redshift surveys and galaxy intrinsic alignments in cosmic shear surveys. We find that scale-dependent galaxy bias will degrade information on cosmological parameters unless the fractional variance in the bias function is known to 10 per cent. Measuring and removing intrinsic alignments from cosmic shear surveys with a flat prior can reduce the dark energy figure of merit by 20 per cent, however provided that the scale and redshift dependence is known to better than 10 per cent with a Gaussian prior, the dark energy figure of merit can be enhanced by a factor of 2 with no extra assumptions.