On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior

Piironen, Juho; Vehtari, Aki

doi:10.48550/arxiv.1610.05559

Cited by 15 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We propose a dynamic horseshoe process as the prior for the innovations ω t in model we scale by the observation error variance and the sample size (Piironen and Vehtari, 2016).…”

Section: Bayesian Trend Filtering With Dynamic Shrinkage Processesmentioning

confidence: 99%

Dynamic Shrinkage Processes

Kowal

Matteson

Ruppert

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

Summary We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on 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 between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute‐by‐minute Twitter central processor unit 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.

show abstract

“…We propose a dynamic horseshoe process as the prior for the innovations ω t in model we scale by the observation error variance and the sample size (Piironen and Vehtari, 2016).…”

Section: Bayesian Trend Filtering With Dynamic Shrinkage Processesmentioning

confidence: 99%

Dynamic Shrinkage Processes

Kowal

Matteson

Ruppert

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

show abstract

“…For the slope parameters β µ , we anticipated a set of sparse effects; i.e., of the large number of predictors and interactions between predictors, we assumed that many of the associated effects would be below the noise threshold, but some fraction will have significant effects on the survival time. Thus, we used a regularized horseshoe prior ( 23 ) to induce sparsity in the joint distribution of effect size parameters, β µ . This sparsity-inducing prior allows us to model the full range of pairwise interaction terms and their effects on survival, without making specific assumptions about which terms to keep and which to discard.…”

Section: Randomized Controlled Trials Are Inefficientmentioning

confidence: 99%

“…Thus, we used a regularized horseshoe prior (23) to induce sparsity in the joint distribution of effect size parameters, β µ . This sparsity-inducing prior allows us to model the full range of pairwise interaction terms and their effects on survival, without making specific assumptions about which terms to keep and which to discard.…”

mentioning

confidence: 99%

Virtual Trials: Causally-validated treatment effects efficiently learned from an observational cancer registry

Wasserman¹,

Musella

Shapiro³

et al. 2021

Preprint

View full text Add to dashboard Cite

Randomized controlled trials (RCTs) offer a clear causal interpretation of treatment effects, but are inefficient in terms of information gain per patient. Moreover, because they are intended to test cohort-level effects, RCTs rarely provide information to support precision medicine, which strives to choose the best treatment for an individual patient. If causal information could be efficiently extracted from widely available real-world data, the rapidity of treatment validation could be increased, and its costs reduced. Moreover, inferences could be made across larger, more diverse patient populations. We created a "virtual trial" by fitting a multilevel Bayesian survival model to treatment and outcome records self-reported by 451 brain cancer patients. The model recovers group-level treatment effects comparable to RCTs representing over 3200 patients. The model additionally discovers the feature-treatment interactions needed to make individual-level predictions for precision medicine. By learning causally-valid information from heterogeneous real-world data, without artificially-limiting the patient population, virtual trials can generate more information from fewer patients, demonstrating their value as a complement to large randomized controlled trials, especially in highly heterogeneous or rare diseases.

show abstract

“…The shrinkage parameters λ j,k and λ j are common for all times t, and provide factor-and predictor-specific shrinkage: for each predictor j, λ j,k allows some factors k to be nonzero, while λ j operators as a group shrinkage parameter that may effectively remove predictor j from the model. Lastly, the global shrinkage parameter λ 0 controls the global level of sparsity, and is scaled by 1/ √ T − 1 following Piironen and Vehtari (2016). In the case of the non-dynamic FOSR and FOSR-AR models, we simply remove one level of the hierarchy:…”

Section: Shrinkage Priors For the Modelmentioning

confidence: 99%

Dynamic Function-on-Scalars Regression

Kowal¹

2018

Preprint

View full text Add to dashboard Cite

We develop a modeling framework for dynamic function-on-scalars regression, in which a time series of functional data is regressed on a time series of scalar predictors. The regression coefficient function for each predictor is allowed to be dynamic, which is essential for applications where the association between predictors and a (functional) response is time-varying. For greater modeling flexibility, we design a nonparametric reduced-rank functional data model with an unknown functional basis expansion, which is data-adaptive and, unlike most existing methods, modeled as unknown for appropriate uncertainty quantification. Within a Bayesian framework, we introduce shrinkage priors that simultaneously (i) regularize time-varying regression coefficient functions to be locally static, (ii) effectively remove unimportant predictor variables from the model, and (iii) reduce sensitivity to the dimension of the functional basis.A simulation analysis confirms the importance of these shrinkage priors, with notable improvements over existing alternatives. We develop a novel projection-based Gibbs sampling algorithm, which offers unrivaled computational scalability for fully Bayesian functional regression. We apply the proposed methodology (i) to analyze the time-varying impact of macroeconomic variables on the U.S. yield curve and (ii) to characterize the effects of socioeconomic and demographic predictors on age-specific fertility rates in South and Southeast Asia.

show abstract

On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior

Cited by 15 publications

References 0 publications

Dynamic Shrinkage Processes

Dynamic Shrinkage Processes

Virtual Trials: Causally-validated treatment effects efficiently learned from an observational cancer registry

Dynamic Function-on-Scalars Regression

Contact Info

Product

Resources

About