Editing Random field (section)

=== Example properties ===

An MRF exhibits the [[Markov property]]

: <math>P(X_i=x_i|X_j=x_j, i\neq j) =P(X_i=x_i|X_j=x_j,j\in\partial_i), \,</math>

for each choice of values <math>(x_j)_j</math>. Here each <math>\partial_i</math> is the set of neighbors of  <math>i</math>. In other words, the probability that a random variable assumes a value depends on its immediate neighboring random variables.  The probability of a random variable in an MRF{{what|reason=Or in any probability measure, since the denominator is always 1.|date=October 2023}} is given by

:<math> P(X_i=x_i|\partial_i) = \frac{P(X_i=x_i, \partial_i)}{\sum_k P(X_i=k, \partial_i)},  </math>

where the sum (can be an integral) is over the possible values of k.{{what|reason=What is the content of this equation? The sum in the denominator is automatically 1 since P is a probability measure.|date=October 2023}} It is sometimes difficult to compute this quantity exactly.