arXiv subjects

Max Anderson Loake

Publications and source records attributed to Max Anderson Loake.

3 recordsLinked to original sources

arXiv2024

Amortising over hyperparameters in Generalised Bayesian Inference

In Bayesian inference prior hyperparameters are chosen subjectively or estimated using empirical Bayes methods. Generalised Bayesian Inference (GBI) also has a learning rate hyperparameter. This is compounded in Semi-Modular Inference (SMI), a GBI framework for multiple datasets (multi-modular problems). As part of any GBI workflow it is necessary to check sensitivity to the choice of hyperparameters, but running MCMC or fitting a variational approximation at each of the hyperparameter values of interest is impractical. Simulation-based Inference has been used by previous authors to amortise over data and hyperparameters, fitting a posterior approximation targeting the forward-KL divergence. However, for GBI and SMI posteriors, it is not possible to amortise over data, as there is no generative model. Working with a variational family parameterised by a conditional normalising flow, we give a direct variational approximation for GBI and SMI posteriors, targeting the reverse-KL divergence, and amortised over prior and loss hyperparameters at fixed data. This can be sampled efficiently at different hyperparameter values without refitting, and supports efficient robustness checks and hyperparameter selection. We show that there exist amortised conditional normalising-flow architectures which are universal approximators. We illustrate our methods with an epidemiological example well known in SMI work and then give the motivating application, a spatial location-prediction task for linguistic-profile data. SMI gives improved prediction with hyperparameters chosen using our amortised framework. The code is available online.

stat.CO↗

arXiv2024

A Bayesian Approach for Earthquake Impact Modelling

Immediately following a disaster event, such as an earthquake, estimates of the damage extent play a key role in informing the coordination of response and recovery efforts. We develop a novel impact estimation tool that leverages a generalised Bayesian approach to generate earthquake impact estimates across three impact types: mortality, population displacement, and building damage. Inference is performed within a likelihood-free framework, and a scoring-rule-based posterior avoids information loss from non-sufficient summary statistics. We propose an adaptation of existing scoring-rule-based loss functions that accommodates the use of an approximate Bayesian computation sequential Monte Carlo (ABC-SMC) framework. The fitted model achieves results comparable to those of two leading impact estimation tools in the prediction of total mortality when tested on a set of held-out past events. The proposed method provides four advantages over existing empirical approaches: modelling produces a gridded spatial map of the estimated impact, predictions benefit from the Bayesian quantification and interpretation of uncertainty, there is direct handling of multi-shock earthquake events, and the use of a joint model between impact types allows predictions to be updated as impact observations become available.

stat.AP↗

arXiv2024

Simultaneous Reconstruction of Spatial Frequency Fields and Sample Locations via Bayesian Semi-Modular Inference

Traditional methods for spatial inference estimate smooth interpolating fields based on features measured at well-located points. When the spatial locations of some observations are missing, joint inference of the fields and locations is possible as the fields inform the locations and vice versa. If the number of missing locations is large, conventional Bayesian Inference fails if the generative model for the data is even slightly mis-specified, due to feedback between estimated fields and the imputed locations. Semi-Modular Inference (SMI) offers a solution by controlling the feedback between different modular components of the joint model using a hyper-parameter called the influence parameter. Our work is motivated by linguistic studies on a large corpus of late-medieval English textual dialects. We simultaneously learn dialect fields using dialect features observed in ``anchor texts'' with known location and estimate the location of origin for ``floating'' textual dialects of unknown origin. The optimal influence parameter minimises a loss measuring the accuracy of held-out anchor data. We compute a (flow-based) variational approximation to the SMI posterior for our model. This allows efficient computation of the optimal influence. MCMC-based approaches, feasible on small subsets of the data, are used to check the variational approximation.

stat.AP↗