Intuitive joint priors for Bayesian linear multilevel models: The R2D2M2 prior

Aguilar, Javier Enrique; Bürkner, Paul‐Christian

doi:10.1214/23-ejs2136

Cited by 12 publications

(1 citation statement)

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“…In this work, we propose a principled prior framework for Gaussian process spatial models by leveraging a Bayesian coefficient of determination, R 2 n , (Gelman et al, 2019) and the R2D2 prior framework (Zhang et al, 2022). This extends Zhang et al (2022), Yanchenko et al (2021) and Aguilar and Bürkner (2023) to spatial models. We show that a beta prior distribution on R 2 n is (approximately) equivalent to a conditional generalized beta prime distribution on the linear predictor variance, which includes the marginal spatial variance.…”

Section: Introductionmentioning

confidence: 99%

Spatial regression modeling via the R2D2 framework

Yanchenko,

Bondell,

Reich

2023

Environmetrics

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Spatially dependent data arises in many applications, and Gaussian processes are a popular modeling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these complex models remains a difficult task. In this work, we propose a principled approach for setting prior distributions on model variance components by placing a prior distribution on a measure of model fit. In particular, we derive the distribution of the prior coefficient of determination. Placing a beta prior distribution on this measure induces a generalized beta prime prior distribution on the global variance of the linear predictor in the model. This method can also be thought of as shrinking the fit towards the intercept‐only (null) model. We derive an efficient Gibbs sampler for the majority of the parameters and use Metropolis–Hasting updates for the others. Finally, the method is applied to a marine protection area dataset. We estimate the effect of marine policies on biodiversity and conclude that no‐take restrictions lead to a slight increase in biodiversity and that the majority of the variance in the linear predictor comes from the spatial effect.

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Section: Introductionmentioning

confidence: 99%

Spatial regression modeling via the R2D2 framework

Yanchenko,

Bondell,

Reich

2023

Environmetrics

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

McLatchie,

Vehtari

2024

Stat Comput

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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.

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