used to generate the data. In these cases, the $L=49$ model performs nearly as well as the correct $L=25$ model. For these simulation settings, we conclude that using too few knots can lead to poor results, especially for the scale parameter, but that including too many knots does not degrade performance.

For the data generated with $L_0=10\mbox{,}000$ knots in Figure \[fsim\](b), we use knots grids with $L = 25,36,\ldots,144$ points. For comparison with the kernel bandwidth, rather than plotting the results by $L$, we plot results by the spacing between adjacent knots in the same column or row, which ranges from 0.70 for $L=144$ to 2.00 for $L=25$. The coverage probabilities are near or above the nominal level for all grid spacings at or below the bandwidth, $\tau=1.0$, and the RMSE appears to be fairly constant for all grid spacings at least as small as the bandwidth. Therefore, this appears to be a reasonable rule of thumb for selecting the number of knots.

We also computed RMSE for the spatial dependence parameters $\alpha$ and $\tau$ (not shown in Figure \[fsim\]) for this final case. For $\alpha$, the average (over data sets) RMSE was 0.049 (coverage percentage 96%), 0.060 (88%), and 