  A Gaussian process is proposed as a model for the posterior distribution of
the local predictive ability of a model or expert, conditional on a vector of
covariates, from historical predictions in the form of log predictive scores.
Assuming Gaussian expert predictions and a Gaussian data generating process, a
linear transformation of the predictive score follows a noncentral chi-squared
distribution with one degree of freedom. Motivated by this we develop a
non-central chi-squared Gaussian process regression to flexibly model local
predictive ability, with the posterior distribution of the latent GP function
and kernel hyperparameters sampled by Hamiltonian Monte Carlo. We show that a
cube-root transformation of the log scores is approximately Gaussian with
homoscedastic variance, which makes it possible to estimate the model much
faster by marginalizing the latent GP function analytically. Linear pools based
on learned local predictive ability are applied to predict daily bike usage in
Washington DC.
