Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

Дата публикации: 04-08-2026 00:00:00

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,...

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