A pseudolikelihood multiplies conditional probabilities rather than the full joint likelihood function. It can be useful for fitting a Markov random field, but using the product itself as a probability density defines a different model unless an additional equivalence is established.
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Pseudolikelihood is a statistical technique used in the context of estimating parameters for models where traditional likelihood methods may be computationally intractable or where the full likelihood is difficult to specify. It is particularly useful in cases involving complex dependencies among multiple variables, such as in spatial statistics, graphical models, and certain machine learning applications. The idea behind pseudolikelihood is to approximate the full likelihood of a joint distribution by breaking it down into a product of conditional likelihoods.