If you want an optimal value, you could always run a variable k model and take the value with the maximum posterior density. But choosing an optimal value when the true value is unknown seems to me to be deliberately ignoring an aspect of uncertainty that we know is there. It’s equivalent to calibrating a radiocarbon date and just using the mode of the posterior distribution. For that reason I’d always go for a variable-k model over a fixed-k model unless there are strong reasons to think that we can estimate k a priori.
Dr. Andrew Millard
Associate Professor of Archaeology,
Durham University, UK
Personal page: https://www.dur.ac.uk/directory/profile/?id=160
Scottish Soldiers Project: https://www.dur.ac.uk/scottishsoldiers
Dunbar 1650 MOOC: https://www.futurelearn.com/courses/battle-of-dunbar-1650