  In this paper we discuss a method, which we call Minimum Conditional
Description Length (MCDL), for estimating the parameters of a subset of sites
within a Markov random field. We assume that the edges are known for the entire
graph $G=(V,E)$. Then, for a subset $U\subset V$, we estimate the parameters
for nodes and edges in $U$ as well as for edges incident to a node in $U$, by
finding the exponential parameter for that subset that yields the best
compression conditioned on the values on the boundary $\partial U$. Our
estimate is derived from a temporally stationary sequence of observations on
the set $U$. We discuss how this method can also be applied to estimate a
spatially invariant parameter from a single configuration, and in so doing,
derive the Maximum Pseudo-Likelihood (MPL) estimate.
