Roland Rau writes:
After many years of applying frequentist statistical methods in mortality research, I just began to learn about the application of Bayesian methods in demography. Since I also wanted to change a part of my research focus on spatial models, I discovered your 1999 paper with Phil Price, All maps of parameter estimates are misleading. As this article is already 17 years old, I wanted to ask whether you think that the last part of the final sentence of the article—“we know of no satisfactory solution to the problem of generating maps for general use”—is still valid. Or would you recommend some other technique to avoid the pitfalls of plotting observed rates or posterior means/medians?
For the reasons discussed in our article, I think that there is inherently no way to avoid a map of parameter estimates being misleading in some way (unless variation is tiny or the data have some symmetry so that all sample sizes are identical). It’s just not possible to project the globe of multivariate uncertainty onto the plane of point estimates.
That said, there could well be new ideas in how best to map uncertainty and variation. So I expect there has been progress in mapping parameter estimates in the past twenty years, even if there are fundamental mathematical constraints that will always be with us.