Dynamic Shrinkage Processes

Kowal, Daniel R.; Matteson, David S.; Ruppert, David

doi:10.1111/rssb.12325

Cited by 73 publications

(91 citation statements)

References 68 publications

(174 reference statements)

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“…, p, and is scaled by p −1/2 following Piironen and Vehtari (2016). The horseshoe prior and its variants have been successful in a variety of models and applications, including functional regression (Kowal et al, 2017b;Kowal, 2018).…”

Section: Shrinkage Priorsmentioning

confidence: 99%

Bayesian Function-on-Scalars Regression for High-Dimensional Data

Kowal

Bourgeois

2020

Journal of Computational and Graphical Statistics

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We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional basis. We incorporate shrinkage priors that effectively remove unimportant scalar covariates from the model and reduce sensitivity to the number of (unknown) basis functions. For variable selection in functional regression, we propose a decision theoretic posterior summarization technique, which identifies a subset of covariates that retains nearly the predictive accuracy of the full model. Our approach is broadly applicable for Bayesian functional regression models, and unlike existing methods provides joint rather than marginal selection of important predictor variables.Computationally scalable posterior inference is achieved using a Gibbs sampler with linear time complexity in the number of predictors. The resulting algorithm is empirically faster than existing frequentist and Bayesian techniques, and provides joint estimation of model parameters, prediction and imputation of functional trajectories, and uncertainty quantification via the posterior distribution. A simulation study demonstrates improvements in estimation accuracy, uncertainty quantification, and variable selection relative to existing alternatives. The methodology is applied to actigraphy data to investigate the association between intraday physical activity and responses to a sleep questionnaire.

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Section: Shrinkage Priorsmentioning

confidence: 99%

Bayesian Function-on-Scalars Regression for High-Dimensional Data

Kowal

Bourgeois

2020

Journal of Computational and Graphical Statistics

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“…Following Kowal et al . (), the distribution for

{θ_{i} (τ) - \log r}

is equivalent to the distribution for

θ_{i} (τ)

under the model

Z_{i}^{P G} (τ) = θ_{i} (τ) + ν_{i} (τ)

, where

Z_{i}^{P G} (τ) \equiv {Z_{i} (τ) - r} ∕ {2 ξ_{i} (τ)} + \log r, [ν_{i} (τ) ∣ ξ_{i} (τ)] \overset{i n d e p}{\sim} N (0, ξ_{i}^{- 1} (τ))

, and

ξ_{i} (τ) \overset{i i d}{\sim} normalP normalG (Z_{i} (τ) + r, 0)

is a Pólya‐Gamma random variable.…”

Section: Mcmc Sampling Algorithmmentioning

confidence: 99%

Integer-Valued Functional Data Analysis for Measles Forecasting

Kowal

2019

Biometrics

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Measles presents a unique and imminent challenge for epidemiologists and public health officials: the disease is highly contagious, yet vaccination rates are declining precipitously in many localities. Consequently, the risk of a measles outbreak continues to rise. To improve preparedness, we study historical measles data both prevaccine and postvaccine, and design new methodology to forecast measles counts with uncertainty quantification. We propose to model the disease counts as an integer-valued functional time series: measles counts are a function of time-ofyear and time-ordered by year. The counts are modeled using a negative-binomial distribution conditional on a real-valued latent process, which accounts for the overdispersion observed in the data. The latent process is decomposed using an unknown basis expansion, which is learned from the data, with dynamic basis coefficients. The resulting framework provides enhanced capability to model complex seasonality, which varies dynamically from year-to-year, and offers improved multimonth-ahead point forecasts and substantially tighter forecast intervals (with correct coverage) compared to existing forecasting models. Importantly, the fully Bayesian approach provides well-calibrated and precise uncertainty quantification for epi-relevant features, such as the future value and time of the peak measles count in a given year. An R package is available online. K E Y W O R D S Bayesian modeling, disease, MCMC, prediction, public health, time series 2 | KOWAL SUPPORTING INFORMATION Additional supporting information may be found online in the Supporting Information section.

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“…However, their methods are more demanding than the Kalman filter methods used in our paper since they require stochastic optimization and the evaluation of the stochastic volatility likelihood using a particle filter. We use a much simpler (albeit approximate) approach based on the transformed stochastic volatility model given in (20) and (21). This state-space model has measurement variance log (ǫ 2 t )…”

Section: (B22)mentioning

confidence: 99%

Variational Bayes Inference in High-Dimensional Time-Varying Parameter Models

Koop

Korobilis

2018

SSRN Journal

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This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.

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Dynamic Shrinkage Processes

Cited by 73 publications

References 68 publications

Bayesian Function-on-Scalars Regression for High-Dimensional Data

Bayesian Function-on-Scalars Regression for High-Dimensional Data

Integer-Valued Functional Data Analysis for Measles Forecasting

Variational Bayes Inference in High-Dimensional Time-Varying Parameter Models

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