# Dynamic Shrinkage Processes

arXiv: https://arxiv.org/abs/1707.00763 · HTML: https://mlsanity.com/paper/1707.00763/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2017.

## Built on by (most cited first, 7 of 7)

- [Bayesian Spillover Graphs for Dynamic Networks](https://mlsanity.com/paper/2203.01912/) (2022)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Bayesian adaptive and interpretable functional regression for exposure profiles](https://mlsanity.com/paper/2203.00784/) (2022)
- [Interpretable Latent Variables in Deep State Space Models](https://mlsanity.com/paper/2203.02057/) (2022)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Logistic-beta processes for dependent random probabilities with beta marginals](https://mlsanity.com/paper/2402.07048/) (2024)
- [Graph-dependent shrinkage priors for Bayesian trend filtering](https://mlsanity.com/paper/2608.23802/) (2026)

## Abstract (arXiv)

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence among the local scale parameters. The resulting processes inherit the desirable shrinkage behavior of popular global-local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modeling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a P'olya-Gamma scale mixture representation of the proposed process. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than competing methods, and apply the model for irregular curve-fitting of minute-by-minute Twitter CPU usage data. In addition, we develop an adaptive time-varying parameter regression model to assess the efficacy of the Fama-French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that with the exception of the market risk, no other risk factors are significant except for brief periods.