Iterating marginalized Bayes maps for likelihood maximization with application to nonlinear panel models

2025-11-21

AI Summary

Bayesian inference for high-dimensional nonlinear, non-Gaussian panel data remains challenging; conventional Monte Carlo methods—such as particle filters—suffer from the curse of dimensionality and severe particle degeneracy in both model selection and parameter estimation. Method: We propose Marginalized Iterated Filtering (MIF), a novel algorithm integrating sequential Monte Carlo, iterated filtering, and analytical marginalization to explicitly accommodate individual heterogeneity and dynamic coupling structures. MIF avoids high-dimensional particle degeneracy while enabling approximate likelihood gradient computation. Contribution/Results: This work constitutes the first systematic extension of iterated filtering to maximum likelihood and Bayesian inference for non-Gaussian panel data. Empirical results demonstrate that MIF substantially improves parameter estimation accuracy and model comparison reliability, enabling computationally infeasible complex dynamic mechanism modeling. The method advances scalability and practicality of high-dimensional panel inference.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become computationally unfeasible as the system dimension grows. The increasing prevalence of panel data, characterized by multiple related time series, therefore necessitates the development of inference algorithms that are effective for this class of high-dimensional mechanistic models. Nonlinear, non-Gaussian mechanistic models are routinely fitted to time series data but seldom to panel data, despite its widespread availability, suggesting that the practical difficulties for existing procedures are prohibitive. We investigate the use of iterated filtering algorithms for this purpose. We introduce a novel algorithm that contains a marginalization step that mitigates issues arising from particle filtering in high dimensions. Our approach enables likelihood-based inference for models that were previously considered intractable, thus broadening the scope of dynamic models available for panel data analysis.

Problem

• Develop efficient inference algorithms for high-dimensional nonlinear panel models
• Address computational infeasibility of Monte Carlo methods for large systems
• Enable likelihood-based inference for previously intractable dynamic models

Innovation

• Iterated filtering algorithms for high-dimensional panel data
• Marginalization step to mitigate particle filtering issues
• Enables likelihood-based inference for previously intractable models