arXiv subjects

Adam Bretherton

Publications and source records attributed to Adam Bretherton.

3 recordsLinked to original sources

arXiv2026

Flexible Transformations for Bayesian Score Calibration

Modern statistical models are growing increasingly complex in an effort to realistically capture system dynamics. Using standard simulation-based inference, these models may be computationally prohibitive, necessitating the use of model calibration methods. Bayesian score calibration is a computationally efficient framework for model calibration with strong theoretical guarantees. This framework learns an appropriate correction for an approximate model using a small number of simulations from the data-generating process. Currently, only a location-scale transformation has been explored, which may lack the flexibility to correct the complex error introduced by some approximate models. In this paper, we develop two flexible transformations for use in the Bayesian score calibration framework. The first is a polynomial extension, which can appropriately adjust approximate models with location-varying error. The second is a sequential application of Bayesian score calibration, which can accommodate approximate models with posteriors that have low support for the true parameter values. We also discuss an additional diagnostic for use with this framework. We demonstrate the increased flexibility these two approaches provide over Bayesian score calibration in two illustrative simulation studies.

stat.ME↗

arXiv2025

A Principled Approach to Bayesian Transfer Learning

Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the observed target dataset which may have been collected under slightly different settings. The use of related information can be useful when the target dataset is scarce, for example. There exist various Bayesian transfer learning methods that decide how to incorporate the related data in different ways. Unfortunately, there is no principled approach for comparing Bayesian transfer methods in real data settings. Additionally, some Bayesian transfer learning methods, such as the so-called power prior approaches, rely on conjugacy or costly specialised techniques. In this paper, we find an effective approach to compare Bayesian transfer learning methods is to apply leave-one-out cross validation on the target dataset. Further, we introduce a new framework, $\textit{transfer sequential Monte Carlo}$, that efficiently implements power prior methods in an automated fashion. We demonstrate the performance of our proposed methods in two comprehensive simulation studies.

stat.ME↗

arXiv2022

Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products.

stat.AP↗