The model used in mrf2d
is very flexible, but many
simpler and popular models of the Markov Random Field literature can be
written as particular cases. It considers the probability function:
where ζθ
is the normalizing constant and ℛ is a
set of relative positions (mrfi
objects). The probability
function of many other models like the Ising model and the Potts model
can be written by adding constraints to the array θa, b, r.
Important tasks like extracting sufficient statistics and estimating
the parameters θa, b, r
must be able to reflect the parameter restrictions required by those
less general models. Functions which result is affected by those
restrictions take a family
argument which determines what
kind of restriction is considered. 5 families are available in
mrf2d
and this short article describes each them.
'onepar'
A single parameter for all different-valued pairs in all interacting positions.
'oneeach'
One parameter for all different-valued pairs for each interacting position.
'absdif'
One parameter for each absolute difference of interacting pairs d = |b − a| in each relative position.
'dif'
One parameter for each difference of interacting pairs d = b − a in each relative position.