Computational methods for a class of network models.

Area of Science:

• Computational Statistics
• Network Science
• Statistical Modeling

Background:

• Parameter inference in network models is computationally challenging.
• The duplication attachment model's likelihood function is often intractable.
• Existing methods like importance sampling (IS) suffer from high variance.

Purpose of the Study:

• To develop exact computational methods for parameter inference in partially observed network models.
• To address the computational intractability of likelihood evaluation for the duplication attachment model.
• To propose more stable and efficient approximation methods for likelihood estimation.

Main Methods:

• Utilized sequential Monte Carlo (SMC) methods for approximating network model likelihoods.
• Proved that SMC methods exhibit polynomial, not exponential, growth in relative variance.
• Developed particle Markov chain Monte Carlo (pMCMC) algorithms for Bayesian inference.

Main Results:

• SMC methods offer significant improvements in variance compared to IS for likelihood approximation.
• pMCMC algorithms effectively perform Bayesian parameter estimation using SMC.
• Numerical illustrations demonstrate the practical applicability of the developed approaches.

Conclusions:

• The proposed SMC and pMCMC methods provide efficient and stable computational tools for network model analysis.
• These methods overcome limitations of traditional importance sampling techniques.
• The study advances the field of statistical inference for complex network structures.