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In this paper we discuss a method, which we call Minimum ConditionalDescription Length (MCDL), for estimating the parameters of a subset of siteswithin a Markov random field. We assume that the edges are known for the entiregraph $G=(V,E)$. Then, for a subset $U\subset V$, we estimate the parametersfor nodes and edges in $U$ as well as for edges incident to a node in $U$, byfinding the exponential parameter for that subset that yields the bestcompression conditioned on the values on the boundary $\partial U$. Ourestimate is derived from a temporally stationary sequence of observations onthe set $U$. We discuss how this method can also be applied to estimate aspatially invariant parameter from a single configuration, and in so doing,derive the Maximum Pseudo-Likelihood (MPL) estimate.

Minimum Conditional Description Length Estimation for Markov Random Fields