HEWITT, HOETING, DONE, AND TOWLER results (Banerjee et al., 2015, Example 5.2) yield the posterior distribution α $^{∗}$( s ) | Y ( s ) , β , R $^{∗}$, c $^{∗}$, σ 2 s ∼ N $^{(}$σ − 2 s Ψ Z $^{∗}$( Y ( s ) − X ( s ) β ) , Ψ ) (15) Ψ = $^{(}$R ∗ − 1 + σ − 2 s Z $^{∗}$Z ∗ T ) − 1 . for The connection to Bayesian linear regression lends intuition for inference on the remote effects α $^{∗}$( s ). In particular, the connection provides intuition for using the RESP model when some local covariates x ( s , t ) are also teleconnected with remote covariates z$_{t}$ . Remote coefficients can be interpreted as residual teleconnection effects in the sense that they model the impact of remote covariates on the response after removing local effects X ( s ) β . Prop- erties of regressions also imply patterns in maps of posterior means for α $^{∗}$( s ) may resemble patterns in maps that show pointwise correlations Cor$_{t}$ ( z $^{∗}$( r $^{∗}$, t ) , Y ( s , t )) between remote covariates at r ∗ and responses at s . Similar regression-based interpretations can be derived for the reparameterized teleconnection coefficients (12). The RESP model (3) is applied here using remote and local covariates to estimate Colorado winter precipitation. Winter precipitation is important to estimate because it strongly in influences Colorado’s annual water supply. We investigate the utility of our RESP model for this application because there is considerable uncertainty regarding precipitation that is directly predicted by GCMs. Further, the RESP model can be applied without specifying teleconnection indices a priori, as many common approaches require. Let Y ( s , t ) denote 3 Climate application: Colorado winter precipitation 14