arXiv subjects

Yann McLatchie

Publications and source records attributed to Yann McLatchie.

7 recordsLinked to original sources

arXiv2026

Predictively Oriented Posteriors

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a consequence of predictive ability. We show that these posteriors converge to the predictively optimal model average and predictively dominate both classical and generalised Bayes posterior predictive distributions. Further, PrO posteriors adapt to the level of model misspecification: while they concentrate around the true model in the same way as classical and generalised Bayesian strategies if the model can recover the data-generating distribution, they do not concentrate around a single model in the presence of non-trivial forms of model misspecification. Instead, they stabilise towards a non-degenerate predictively optimal posterior distribution that represents a form of irreducible uncertainty due to model misspecification. We put forward a sampling algorithm for PrO posteriors based on mean field Langevin dynamics, and verify the practical significance of our theoretical developments on a number of numerical examples.

stat.ME↗

arXiv2025

Predictive performance of power posteriors

We analyse the impact of using tempered likelihoods in the production of posterior predictions. While the choice of temperature has an impact on predictive performance in small samples, we formally show that in moderate-to-large samples, tempering does not impact posterior predictions.

math.ST↗

arXiv2025

The ARR2 prior: flexible predictive prior definition for Bayesian auto-regressions

We present the ARR2 prior, a joint prior over the auto-regressive components in Bayesian time-series models and their induced $R^2$. Compared to other priors designed for times-series models, the ARR2 prior allows for flexible and intuitive shrinkage. We derive the prior for pure auto-regressive models, and extend it to auto-regressive models with exogenous inputs, and state-space models. Through both simulations and real-world modelling exercises, we demonstrate the efficacy of the ARR2 prior in improving sparse and reliable inference, while showing greater inference quality and predictive performance than other shrinkage priors. An open-source implementation of the prior is provided.

stat.CO↗

arXiv2024

Efficient estimation and correction of selection-induced bias with order statistics

Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible bias when the cross-validation estimates of predictive performance are marred by excessive noise. In finite data regimes, cross-validated estimates can encourage the statistician to select one model over another when it is not actually better for future data. While this bias remains negligible in the case of few models, when the pool of candidates grows, and model selection decisions are compounded (as in step-wise selection), the expected magnitude of selection-induced bias is likely to grow too. This paper introduces an efficient approach to estimate and correct selection-induced bias based on order statistics. Numerical experiments demonstrate the reliability of our approach in estimating both selection-induced bias and over-fitting along compounded model selection decisions, with specific application to forward search. This work represents a light-weight alternative to more computationally expensive approaches to correcting selection-induced bias, such as nested cross-validation and the bootstrap. Our approach rests on several theoretic assumptions, and we provide a diagnostic to help understand when these may not be valid and when to fall back on safer, albeit more computationally expensive approaches. The accompanying code facilitates its practical implementation and fosters further exploration in this area.

stat.ME↗

arXiv2024

Advances in projection predictive inference

The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to building and selecting predictive models. Projection predictive inference in particular has shown promise to this end, finding application across a broad range of fields. It is less prone to over-fitting than naïve selection based purely on cross-validation or information criteria performance metrics, and has been known to out-perform other methods in terms of predictive performance. We survey the core concept and contemporary contributions to projection predictive inference, and present a safe, efficient, and modular workflow for prediction-oriented model selection therein. We also provide an interpretation of the projected posteriors achieved by projection predictive inference in terms of their limitations in causal settings.

stat.ME↗

arXiv2023

Bayesian order identification of ARMA models with projection predictive inference

Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, and as such the identification of model orders remains a fundamental task. We propose a novel method of ARMA order identification through projection predictive inference, which benefits from improved stability through the use of a reference model. The procedure consists of two steps: in the first, the practitioner incorporates their understanding of underlying data-generating process into a reference model, which we latterly project onto possibly parsimonious submodels. These submodels are optimally inferred to best replicate the predictive performance of the reference model. We further propose a search heuristic amenable to the ARMA framework. We show that the submodels selected by our procedure exhibit predictive performance at least as good as those chosen by AIC over simulated and real-data experiments, and in some cases out-perform the latter. Finally we show that our procedure is robust to noise, and scales well to larger data.

stat.ME↗

arXiv2023

Locking and Quacking: Stacking Bayesian model predictions by log-pooling and superposition

Combining predictions from different models is a central problem in Bayesian inference and machine learning more broadly. Currently, these predictive distributions are almost exclusively combined using linear mixtures such as Bayesian model averaging, Bayesian stacking, and mixture of experts. Such linear mixtures impose idiosyncrasies that might be undesirable for some applications, such as multi-modality. While there exist alternative strategies (e.g. geometric bridge or superposition), optimising their parameters usually involves computing an intractable normalising constant repeatedly. We present two novel Bayesian model combination tools. These are generalisations of model stacking, but combine posterior densities by log-linear pooling (locking) and quantum superposition (quacking). To optimise model weights while avoiding the burden of normalising constants, we investigate the Hyvarinen score of the combined posterior predictions. We demonstrate locking with an illustrative example and discuss its practical application with importance sampling.

stat.ML↗