Fast and Accurate Binary Response Mixed Model Analysis Via Expectation Propagation

Area of Science:

• Statistics
• Computational Statistics
• Statistical Inference

Background:

• Expectation propagation (EP) is a general method for approximating integrals in statistical inference.
• Existing literature primarily focuses on EP within Bayesian inference frameworks.
• The application of EP to frequentist inference remains less explored.

Purpose of the Study:

• To investigate the utility of expectation propagation for frequentist statistical inference.
• To develop a fast and accurate quadrature-free inference method for binary response mixed models.
• To assess the performance of EP in approximating likelihood surfaces for complex models.

Main Methods:

• Applied expectation propagation to likelihood-based inference for binary response mixed models.
• Utilized a probit link function with multivariate random effects and higher nesting levels.
• Employed asymptotic calculations to analyze the consistency of EP estimation.
• Conducted numerical studies to evaluate the methodology's speed, accuracy, and scalability.

Main Results:

• Demonstrated that expectation propagation can be effectively used for frequentist inference.
• Achieved fast and accurate quadrature-free inference for binary mixed models with probit links.
• Asymptotic calculations confirmed consistent estimation of the exact likelihood surface by EP.
• Numerical results highlighted the methodology's speed, high accuracy, and scalability.

Conclusions:

• Expectation propagation provides a viable and efficient alternative for frequentist inference in binary mixed models.
• The developed method offers a scalable and accurate solution for analyzing complex binary data.
• This work extends the application of expectation propagation beyond Bayesian contexts.