HEWITT, HOETING, DONE, AND TOWLER 2015, Section 9.6.2). An Inverse-Wishart prior Λ ∼ IW ( I, 2) is used for Λ = Cov ( θ ( s )) and a dispersed normal prior is used for the fixed effects β ∼ N ( 0 , 10 I ). We use σ 2 ∼ IG (2 , 1) and ρ ∼ U (1 , 600) for the prior distribution of the Mat´ ern covariance with fixed smoothness ν = . 5 for the model’s spatial correlation. Pointwise regression models are commonly used to downscale climate data (e.g., Towler et al., 2016). The ENSO-T model predicts precipitation P ( s , t$_{0}$ ) at a location s and new time point t$_{0}$ by applying a regression of training data P ( s , t ) onto local surface air temperature T ( s , t ) and the score a$_{1}$ ( t ) for the first sea surface temperature EOF ψ$_{1}$ : D$_{Y}$ → $_{R}$. The ENSO-T downscaler provides a comparison model that accounts for both local and remote effects, but not spatial dependence. Canonical correlation analysis uses the empirical correlation structure of sea surface temper- ature SST and precipitation P vectors to linearly map these variables to a space in which the transformed vectors are maximally correlated (von Storch & Zwiers, 1999, Chapter 14). This mapping may be used in a multivariate regression context with sea surface tempera- tures at new time points to predict precipitation. The mapping is often developed with some amount of smoothing by removing higher order EOFs from the data. We retain 16 EOFs in our use of CCA because this lets us capture approximately 90% of the variability in the predictors SST and predictand P . The CCA downscaler provides a comparison model that only accounts for remote effects and indirectly accounts for spatial dependence. Climatologists use the unconditional distribution of precipitation P ( s , t ) at a location s . When no other information is available, the average value of precipitation E$_{t}$ [ P ( s , t )] is 3.3.4 Climatological reference (CLIM) 20 3.3.3 Canonical correlation analysis (CCA) 3.3.2 Hybrid local and non-local regression (ENSO-T)