Computationally Efficient Bayesian Unit-Level Models for Non-Gaussian Data Under Informative Sampling

Parker, Paul A.; Holan, Scott H.; Janicki, Ryan

doi:10.48550/arxiv.2009.05642

Cited by 2 publications

(5 citation statements)

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“…For the linear predictor ψ = x β, if we use a Gaussian prior on β, the full conditional distribution for β will also be Gaussian. Furthermore, Parker et al (2020a) show that under a PL setup, conjugacy is still retained. They develop both a Gibbs sampling algorithm as well as a variational Bayes algorithm for PL-based mixed effects models with Binomial data.…”

Section: Logistic Modelsmentioning

confidence: 91%

“…This allows for the use of generlized linear model fitting procedures rather than custom techniques. Specifically, we use the variational Bayes procedure from Parker et al (2020a) for all model fitting.…”

Section: Proposed Modelmentioning

confidence: 99%

“…Dependent data models typically rely on Gaussian prior distributions for model parameters (Bradley et al, 2015); however, most survey variables tend to be non-Gaussian, leading to non-conjugate conditional distributions that can be difficult to sample from. This problem is addressed by Parker et al (2020b) and Parker et al (2020a) for count data and Binomial data, although they do not consider the further problem of modeling complex data types in a computationally efficient manner.…”

Section: Introductionmentioning

confidence: 99%

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Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation

Parker¹,

Holan²

2020

Preprint

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The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when compared to linear or generalized linear models. However, one of the main challenges with deep modeling approaches is quantification of uncertainty. The use of random weight models, such as the popularized Extreme Learning Machine, offer a potential solution in this regard. In addition to uncertainty quantification, these models are extremely computationally efficient as they do not require optimization through stochastic gradient descent, which is what is typically done for deep learning. We show how the use of random weights in a deep model can fit into a likelihood based framework to allow for uncertainty quantification of the model parameters and any desired estimates. Furthermore, we show how this approach can be used to account for informative sampling of survey data through the use of a pseudo-likelihood. We illustrate the effectiveness of this methodology through simulation and with a real survey data application involving American National Election Studies data.

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Section: Logistic Modelsmentioning

confidence: 91%

Section: Proposed Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation

Parker¹,

Holan²

2020

Preprint

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“…Modeling non-Gaussian data types in a Bayesian setting can be computationally burdensome, especially while accounting for informative sampling. Parker et al (2020) utilize a data augmentation approach to construct a flexible mixed model for Binomial and Multinomial data under informative sampling. Their model for Binomial data is given by,…”

Section: Non-gaussian Datamentioning

confidence: 99%

“…The modeling framework of Parker et al (2020) is useful for fitting Binomial data under informative sampling, such as the NHANES mortality data of interest; however, the approach must be extended in order to consider functional covariates.…”

Section: Non-gaussian Datamentioning

confidence: 99%

A Bayesian Functional Data Model for Surveys Collected under Informative Sampling with Application to Mortality Estimation using NHANES

Parker¹,

Holan²

2020

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Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through an empirical simulation study as well as an example of mortality estimation using NHANES data.

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Computationally Efficient Bayesian Unit-Level Models for Non-Gaussian Data Under Informative Sampling

Cited by 2 publications

References 0 publications

Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation

Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation

A Bayesian Functional Data Model for Surveys Collected under Informative Sampling with Application to Mortality Estimation using NHANES

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