The ARR2 Prior: Flexible Predictive Prior Definition for Bayesian Auto-Regressions

2024/05/30 by David Kohns, David J. Kohns, Noa Kallioinen +2 · 1 voice · 2 citations
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #econ.EM #stat.CO

paper · pdf · doi:10.1214/25-ba1512

openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We present the ARR2 prior, a joint prior over the auto-regressive components in Bayesian time-series models and their induced R2. 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 covariates, 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.

Citations

• Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC
• Detecting and diagnosing prior and likelihood sensitivity with power-scaling
• Past, Present and Future of Software for Bayesian Inference

Cited by

• R2 priors for Grouped Variance Decomposition in High-dimensional Regression
• Joint Quantile Shrinkage: A State-Space Approach toward Non-Crossing Bayesian Quantile Models

Discussions

• Revised "The ARR2 prior: flexible predictive prior definition for Bayesian auto-regressions" with David Kohns, Noa Kallioinen, Yann McLatchie, adds implied priors on characteristic roots and partial a [bsky, 13 points, 0 comments]

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