David Kohns, Noa Kallioinen, Yann McLatchie, Aki Vehtari
arXiv 30 May 2024 · Statistics — Computation · publishedBayesian Analysis (2025)
arXiv:2405.19920 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Aguilar, J. E. and Bürkner, P.-C (2023) Intuitive joint priors for Bayesian linear multilevel models: The R2D2M2 prior | 0.961 | 9 | 4 | 89% |
| 2 | Zhang, Y. D., Naughton, B. P., Bondell, H. D., and Reich, B. J (2022) Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior | 0.956 | 8 | 4 | 88% |
| 3 | Stan Development Team (2025) Stan User's Guide and Reference Manual | 0.843 | 4 | 3 | 75% |
| 4 | Yanchenko, E., Bondell, H. D., and Reich, B. J (2024) The R2D2 Prior for Generalized Linear Mixed Models | 0.843 | 3 | 3 | 100% |
| 5 | Chan, J. C (2021) Minnesota-type adaptive hierarchical priors for large Bayesian VARs | 0.737 | 4 | 4 | 50% |
| 6 | Harvey, A. C (1990) Forecasting, Structural Time Series Models and the Kalman Filter | 0.737 | 4 | 2 | 75% |
| 7 | Heaps, S. E (2022) Enforcing stationarity through the prior in vector autoregressions | 0.737 | 3 | 3 | 67% |
| 8 | Hamilton, J. D (2020) Time series analysis | 0.737 | 3 | 2 | 100% |
| 9 | Piironen, J. and Vehtari, A (2017) On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior self | 0.737 | 3 | 2 | 100% |
| 10 | Doan, T., Litterman, R., and Sims, C (1984) Forecasting and conditional projection using realistic prior distributions | 0.644 | 2 | 2 | 100% |
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