G. M. Bernstein, W. d'Assignies, M A Troxel, A. Alarcon, A. Amon, G. Giannini, B. Yin, M. Aguena, S. S. Allam, F. Andrade-Oliveira, D. Brooks, A. Carnero Rosell, J. Carretero, L. N. da Costa, M. E. S. Pereira, J. De Vicente, S. Everett, J Frieman, J García-Bellido, D. Gruen, S. R. Hinton, D. L. Hollowood, K. Honscheid, D. J. James, S. Lee, J. L. Marshall, J. Mena-Fernández, R. Miquel, A. A. Plazas Malagón, E. Sanchez, D. Sanchez Cid, I. Sevilla-Noarbe, T. Shin, M. Smith, E. Suchyta, M E C Swanson, N. Weaverdyck, J Weller, P. Wiseman
Abstract A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior p ( q , n ∣ D ) ∝ L ( D ∣ q , n ) p ( q ) p ( n ) , where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p ( n ) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p ( n ) at arbitrary values of n , i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u , which projects away directions in n space that cannot appreciably alter L . The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p ( n ) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n ( z ) of the galaxies.