The filter - smoother finds the most probable values of given observations. (667-per-cm.net)
One interesting point I noted (and your paper confirms) is that if you reduce the forcing uncertainty from the IPCC level, but don't change the IPCC's best estimate of forcing, the most probable value of ECS increases very slightly, but the high sensitivity tail (eg total probability for sensitivity above 3.5 C per doubling) almost disappears. (judithcurry.com)
For St. Joe, book value is adjusted to reflect probable values for undeveloped land. (mjwhitman.pressbooks.com)