Kappa 2 Prior
The kappa1 parameter of the TN93 model (Tamura, Nei, 1993) represents how large transition rate C <-> T is when all transversion rates are set to 1. Since this is a rate parameter, a distribution with a range from 0 upwards is appropriate.
Rosenberg et al, 2003 found that a
lognormal(M=1,S=1.25) distribution fits transition rates well based on empirical observations, so this is the default prior in BEAST.
Rosenberg MS, Subramanian S, Kumar S. Patterns of transitional mutation biases within and among mammalian genomes. Molecular biology and evolution. 2003 Jun 1;20(6):988-93. doi:10.1093/molbev/msg113.
Tamura K, Nei M. Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees. Molecular biology and evolution. 1993 May 1;10(3):512-26. doi:10.1093/oxfordjournals.molbev.a040023.