Amanda Lenzi

Amortised Bayesian inference for structured statistical models

Amortised and simulation-based approaches provide flexible tools for Bayesian inference in models with intractable or computationally demanding likelihoods. Most modern methods aim to approximate the full joint posterior distribution using highly expressive neural architectures. However, in many statistical settings, inference focuses on low-dimensional structural parameters, and accurate marginal posteriors may suffice. In this talk, I present a structured variational framework that directly approximates marginal posterior distributions via amortised neural networks under Gaussian assumptions. This approach avoids learning a full joint posterior and can lead to stable and computationally efficient inference in structured statistical models. I illustrate the methodology in a spatial modelling context and discuss its statistical properties and practical performance. I conclude by outlining broader questions about when marginal amortisation is appropriate, how posterior dependence affects approximation quality, and what challenges arise when extending these ideas to models with stronger latent structure.