used as a climatological point prediction for precipitation, and the empirical distribution is used for probabilistic predictions. The CLIM downscaler provides a baseline comparison model that does not account for spatial dependence, local, or remote effects. 

## 3.4 Results 

Model results are based on 20,000 samples from the posterior distribution after a burn in period of 1,000 samples. Convergence was assessed by examining trace plots, autocorrelation plots, and effective sample sizes in addition to comparing results from multiple runs with randomly initialized parameters. Model adequacy was assessed using residual and qq-normal plots. These diagnostics suggest there are no serious violations of the convergence and distributional assumptions. Variance inflation factors (VIFs) that account for the RESP model design also show no concern for multicollinearity in the fitted model ?? . 

## 3.4.1 Inference 

Parameter estimates for the RESP model yield reasonable scientific interpretations (Table 1). The sign of the regression coefficient β$_{T}$ for the temperature covariate T is consistent with physical processes that influence precipitation (Daly et al., 2008). The local covariance range parameter ρ$_{w}$ implies the dependence between locations s ∈ D$_{Y}$ has an effective range between 500 and 570 km, which is the distance between locations beyond which the Mat´ ern correlation (7) is small ( ≤ . 05). This length scale is in the size range of mesoscale weather processes that produce precipitation (Parker, 2015). The remote covariance range parameter ρ$_{α}$ implies the dependence between locations r ∈ D$_{Z}$ has an effective range between 720 and 2,200 km, which is roughly the size of the mid-sized structures seen in the EOF patterns in Figure 2 A. Since local temperature T is teleconnected with sea surface temperatures SST , remote effects must be interpreted as residual teleconnection effects, as described at the end of Section 2.4. Significant remote effects suggest Colorado’s teleconnection with the Pacific Ocean cannot be represented through a linear relationship with temperature alone; the 

