Pseudolikelihood
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In statistical theory, a pseudolikelihood is an approximation to the joint probability distribution of a collection of random variables. The practical use of this is that it can provide an approximation to the likelihood function of a set of observed data which may either provide a computationally simpler problem for estimation, or may provide a way of obtaining explicit estimates of model parameters.
The pseudolikelihood approach was introduced by
Definition
Given a set of random variables the pseudolikelihood of is
in discrete case and
in continuous one. Here is a vector of variables, is a vector of values, is conditional density and is the vector of parameters we are to estimate. The expression above means that each variable in the vector has a corresponding value in the vector and means that the coordinate has been omitted. The expression is the probability that the vector of variables has values equal to the vector . This probability of course depends on the unknown parameter . Because situations can often be described using state variables ranging over a set of possible values, the expression can therefore represent the probability of a certain state among all possible states allowed by the state variables.
The pseudo-log-likelihood is a similar measure derived from the above expression, namely (in discrete case)
One use of the pseudolikelihood measure is as an approximation for inference about a Markov or Bayesian network, as the pseudolikelihood of an assignment to may often be computed more efficiently than the likelihood, particularly when the latter may require marginalization over a large number of variables.
Properties
Use of the pseudolikelihood in place of the true likelihood function in a
References
- JSTOR 2987782
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