Consistent inference of a general model using the pseudolikelihood method

Area of Science:

• Statistical physics
• Information theory
• Computational statistics

Background:

• Maximum pseudolikelihood (MPL) inference is a powerful technique for statistical models where the true likelihood function is computationally intractable.
• Existing methods often rely on approximations or alternative statistical frameworks to handle these complex models.
• A deeper theoretical understanding of the relationship between pseudolikelihood and likelihood is needed.

Purpose of the Study:

• To establish a formal connection between pseudolikelihood and likelihood functions using information theory.
• To rigorously demonstrate the consistency of the maximum pseudolikelihood (MPL) inference method.
• To validate the applicability of MPL for general statistical models with intractable likelihoods.

Main Methods:

• Utilizing principles from information theory to derive a mathematical relationship between pseudolikelihood and likelihood.
• Applying theoretical analysis to prove the consistency of the MPL estimation procedure.
• Generalizing the findings to encompass a broad class of statistical models.

Main Results:

• A novel information-theoretic derivation explicitly links pseudolikelihood and likelihood functions.
• The consistency of the maximum pseudolikelihood (MPL) method is formally proven for a general class of models.
• The findings confirm the theoretical underpinnings and practical utility of MPL in statistical physics.

Conclusions:

• The information-theoretic framework provides a rigorous justification for using maximum pseudolikelihood (MPL) inference.
• The demonstrated consistency of MPL enhances its reliability for analyzing complex statistical physics models.
• This work offers a foundational understanding for the broader application of MPL in statistical modeling.