Scalable Bayesian Inference using Hierarchical Approaches and Surrogates

Explore scalable Bayesian inference methods through hierarchical approaches and surrogate models in this academic seminar. Learn advanced computational techniques for handling complex statistical inference problems when traditional methods become computationally prohibitive. Discover how hierarchical modeling structures can decompose complex problems into manageable components, enabling efficient computation across multiple scales. Examine the role of surrogate models as computational shortcuts that approximate expensive likelihood evaluations while maintaining statistical rigor. Understand the mathematical foundations underlying these approaches, including multilevel Monte Carlo methods, Gaussian process surrogates, and hierarchical Bayesian frameworks. Gain insights into practical applications where these methods prove essential, such as uncertainty quantification in large-scale simulations, inverse problems in engineering, and parameter estimation in complex physical systems. Analyze the trade-offs between computational efficiency and statistical accuracy when implementing these scalable approaches. Study convergence properties and error analysis for hierarchical inference algorithms. Explore recent developments in combining machine learning techniques with traditional Bayesian methods to create more efficient surrogate models. This presentation is part of the "Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning" research programme at the Isaac Newton Institute for Mathematical Sciences.