Distributed and recursive Bayesian inference for Big Data and complex spatio-temporal models

2026-07-25

AI Summary

This work addresses the computational burden, streaming nature, and privacy constraints inherent in Bayesian inference for large-scale, complex spatiotemporal data by proposing a distributed recursive Bayesian inference framework based on Integrated Nested Laplace Approximation (INLA). The approach synergistically integrates distributed computing, federated learning, and recursive updating mechanisms to substantially reduce computational complexity while preserving inferential accuracy. Implemented within the R-INLA framework, the method enables scalable, adaptive, and privacy-preserving Bayesian analysis. Empirical evaluations across multiple case studies demonstrate that the proposed framework achieves performance comparable to centralized full-data inference, even under streaming data conditions and stringent privacy requirements.

Abstract

The rapid growth of massive and complex datasets in fields such as econometrics, environmental sciences, risk management, and public policy has reshaped statistical modeling while introducing significant computational and methodological challenges. These challenges arise not only from data scale and model complexity, but also from the sequential or streaming nature of modern applications and from data-privacy constraints that prevent sharing raw data and thus limit joint analysis. To address these challenges, we introduce a novel and comprehensive Bayesian framework for distributed and recursive inference, grounded in the Integrated Nested Laplace Approximations (INLA) methodology and implemented using the R-INLA software. Our contributions include the partitioning both data and structured model components, reducing computational complexity while preserving accuracy relative to centralized full-data inference. We demonstrate the effectiveness of the proposed framework through case studies that highlight its applicability in large-scale, streaming, and privacy-sensitive settings. By integrating distributed, federated, and recursive paradigms, this work offers scalable, adaptive, and generalizable tools for modern Bayesian inference.

Problem

• Big Data
• spatio-temporal models
• data privacy
• streaming data
• Bayesian inference

Innovation

• distributed Bayesian inference
• recursive inference
• INLA
• federated learning
• spatio-temporal models