where g~x|K(K{1)=2 is the prior expected number of edges in graph G. We entertain two prior choices for P. Diagonal vector (p 1 , . . . , p K ) is the stationary distribution for the CTMC when all edges are included in the graph G. For this complete graph, as the length of the random walk t??, one expects that X (t)~S k with probability p k . One natural choice says that there exists no spatial preference over the long-run and fixes p k~1 =K for all k. However, sites may expound spatial preference over the long-run; for example, such preference can relate to known or unknown quantities such as population-size or geographic size of the site. In these situations, we estimate P simultaneously with the rest of the model by imposing the flat prior (p 1 , . . . , p K )*Dirichlet(1, . . . , 1). Also non-informatively for small values, we take m*Exponential (1) .