Precision dominates individual linear.predictor standard deviation

[JJ Hubbard]

Hello,

I have noticed that my model$summary.linear.predictor$sd values are typically two orders of magnitude smaller than the standard deviation from 1/sqrt(precision of the guassian observations).

I have been approximating the posteriors with a technique Haavard gave me previously with model$summary.linear.predictor$mean and sqrt(model$summary.linear.predictor$sd^2 + (1/sqrt(precision))^2)

Is it normal that the posteriors all have similar standard deviations because the precision dominates? Are my covariates just not informative enough for INLA to learn about the variance of each observation's posterior?

1/sqrt(precision) in my case is about 0.64, while a given observation's linear.predictor sd is .005 to .01