maximum likelihood
Definition
Maximum likelihood refers to a statistical estimation method that identifies parameter values by maximizing the probability of observing the data. In the context of the Ising model, maximum likelihood estimation (MLE) based on the exact likelihood is the most accurate method for estimating parameters; however, it is computationally feasible only for small networks because the normalizing constant requires evaluation of an exponentially growing number of terms. As an alternative, maximum pseudolikelihood estimation using joint pseudolikelihood (JPL) or disjoint pseudolikelihood (DPL) approximations provides computationally efficient parameter estimation for larger graphs, though with varying degrees of accuracy depending on network structure and sample size.
Sources: Keetelaar et al. (2024)
Related Terms
Applications
Maximum Likelihood and the Ising Model
Maximum likelihood estimation is directly applied to the Ising model. The exact likelihood-based MLE provides accurate parameter estimates but becomes computationally infeasible as the number of variables increases due to the exponential growth of the normalizing constant.
Sources: Keetelaar et al. (2024)
Maximum Likelihood and Pseudolikelihood Estimation
Maximum likelihood estimation can be approximated through maximum pseudolikelihood (MPL) estimation methods, which replace the intractable exact likelihood with computationally manageable alternatives. The joint pseudolikelihood (JPL) and disjoint pseudolikelihood (DPL) approaches yield estimators that approximate maximum likelihood estimates with varying accuracy depending on network characteristics and sample size.
Sources: Keetelaar et al. (2024)
