  Due to the intractable partition function, the exact likelihood function for
a Markov random field (MRF), in many situations, can only be approximated.
Major approximation approaches include pseudolikelihood and Laplace
approximation. In this paper, we propose a novel way of approximating the
likelihood function through first approximating the marginal likelihood
functions of individual parameters and then reconstructing the joint likelihood
function from these marginal likelihood functions. For approximating the
marginal likelihood functions, we derive a particular likelihood function from
a modified scenario of coin tossing which is useful for capturing how one
parameter interacts with the remaining parameters in the likelihood function.
For reconstructing the joint likelihood function, we use an appropriate copula
to link up these marginal likelihood functions. Numerical investigation
suggests the superior performance of our approach. Especially as the size of
the MRF increases, both the numerical performance and the computational cost of
our approach remain consistently satisfactory, whereas Laplace approximation
deteriorates and pseudolikelihood becomes computationally unbearable.
