arXiv subjects

Scott H. Holan

Publications and source records attributed to Scott H. Holan.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Look into the Problem of Preferential Sampling from the Lens of Survey Statistics

An evolving problem in the field of spatial and ecological statistics is that of preferential sampling, where biases may be present due to a relationship between sample data locations and a response of interest. This field of research bears a striking resemblance to the longstanding problem of informative sampling within survey methodology, although with some important distinctions. With the goal of promoting collaborative effort within and between these two problem domains, we make comparisons and contrasts between the two problem statements. Specifically, we review many of the solutions available to address each of these problems, noting the important differences in modeling techniques. Additionally, we construct a series of simulation studies to examine some of the methods available for preferential sampling, as well as a comparison analyzing heavy metal biomonitoring data.

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arXiv2021

Interpolating Population Distributions using Public-use Data: An Application to Income Segregation using American Community Survey Data

Income segregation measures the extent to which households choose to live near other households with similar incomes. Sociologists theorize that income segregation can exacerbate the impacts of income inequality, and have developed indices to measure it at the metro area level, including the information theory index introduced in \citet{reardon2011income}, and the divergence index presented in \citet{roberto2015divergence}. To study their differences, we construct both indices using recent American Community Survey (ACS) estimates of features of the income distribution. Since the elimination of the decennial census long form, methods of computing these estimates must be updated to use ACS estimates and account for survey error. We propose a model-based method to interpolate estimates of features of the income distribution that accounts for this error. This method improves on previous approaches by allowing for the use of more types of estimates, and by providing uncertainty quantification. We apply this method to estimate U.S. census tract-level income distributions using ACS tabulations, and in turn use these to construct both income segregation indices. We find major differences between the two indices in the relative ranking of metro areas, as well as differences in how both indices correlate with the Gini index.

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arXiv2020

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

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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arXiv2020

A General Bayesian Model for Heteroskedastic Data with Fully Conjugate Full-Conditional Distributions

Models for heteroskedastic data are relevant in a wide variety of applications ranging from financial time series to environmental statistics. However, the topic of modeling the variance function conditionally has not seen near as much attention as modeling the mean. Volatility models have been used in specific applications, but these models can be difficult to fit in a Bayesian setting due to posterior distributions that are challenging to sample from efficiently. In this work, we introduce a general model for heteroskedastic data. This approach models the conditional variance in a mixed model approach as a function of any desired covariates or random effects. We rely on new distribution theory in order to construct priors that yield fully conjugate full conditional distributions. Thus, our approach can easily be fit via Gibbs sampling. Furthermore, we extend the model to a deep learning approach that can provide highly accurate estimates for time dependent data. We also provide an extension for heavy-tailed data. We illustrate our methodology via three applications. The first application utilizes a high dimensional soil dataset with inherent spatial dependence. The second application involves modeling of asset volatility. The third application focuses on clinical trial data for creatinine.

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arXiv2020

Bayesian Nonparametric Multivariate Spatial Mixture Mixed Effects Models with Application to American Community Survey Special Tabulations

Leveraging multivariate spatial dependence to improve the precision of estimates using American Community Survey data and other sample survey data has been a topic of recent interest among data-users and federal statistical agencies. One strategy is to use a multivariate spatial mixed effects model with a Gaussian observation model and latent Gaussian process model. In practice, this works well for a wide range of tabulations. Nevertheless, in situations that exhibit heterogeneity among geographies and/or sparsity in the data, the Gaussian assumptions may be problematic and lead to underperformance. To remedy these situations, we propose a multivariate hierarchical Bayesian nonparametric mixed effects spatial mixture model to increase model flexibility. The number of clusters is chosen automatically in a data-driven manner. The effectiveness of our approach is demonstrated through a simulation study and motivating application of special tabulations for American Community Survey data.

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arXiv2020

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

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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arXiv2020

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

Statistical estimates from survey samples have traditionally been obtained via design-based estimators. In many cases, these estimators tend to work well for quantities such as population totals or means, but can fall short as sample sizes become small. In today's "information age," there is a strong demand for more granular estimates. To meet this demand, using a Bayesian pseudo-likelihood, we propose a computationally efficient unit-level modeling approach for non-Gaussian data collected under informative sampling designs. Specifically, we focus on binary and multinomial data. Our approach is both multivariate and multiscale, incorporating spatial dependence at the area-level. We illustrate our approach through an empirical simulation study and through a motivating application to health insurance estimates using the American Community Survey.

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arXiv2020

Spatio-Temporal Change of Support Modeling with R

Spatio-temporal change of support methods are designed for statistical analysis on spatial and temporal domains which can differ from those of the observed data. Previous work introduced a parsimonious class of Bayesian hierarchical spatio-temporal models, which we refer to as STCOS, for the case of Gaussian outcomes. Application of STCOS methodology from this literature requires a level of proficiency with spatio-temporal methods and statistical computing which may be a hurdle for potential users. The present work seeks to bridge this gap by guiding readers through STCOS computations. We focus on the R computing environment because of its popularity, free availability, and high quality contributed packages. The stcos package is introduced to facilitate computations for the STCOS model. A motivating application is the American Community Survey (ACS), an ongoing survey administered by the U.S. Census Bureau that measures key socioeconomic and demographic variables for various populations in the United States. The STCOS methodology offers a principled approach to compute model-based estimates and associated measures of uncertainty for ACS variables on customized geographies and/or time periods. We present a detailed case study with ACS data as a guide for change of support analysis in R, and as a foundation which can be customized to other applications.

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arXiv2020

Nonlinear Time Series Classification Using Bispectrum-based Deep Convolutional Neural Networks

Time series classification using novel techniques has experienced a recent resurgence and growing interest from statisticians, subject-domain scientists, and decision makers in business and industry. This is primarily due to the ever increasing amount of big and complex data produced as a result of technological advances. A motivating example is that of Google trends data, which exhibit highly nonlinear behavior. Although a rich literature exists for addressing this problem, existing approaches mostly rely on first and second order properties of the time series, since they typically assume linearity of the underlying process. Often, these are inadequate for effective classification of nonlinear time series data such as Google Trends data. Given these methodological deficiencies and the abundance of nonlinear time series that persist among real-world phenomena, we introduce an approach that merges higher order spectral analysis (HOSA) with deep convolutional neural networks (CNNs) for classifying time series. The effectiveness of our approach is illustrated using simulated data and two motivating industry examples that involve Google trends data and electronic device energy consumption data.

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arXiv2020

Unit Level Modeling of Survey Data for Small Area Estimation Under Informative Sampling: A Comprehensive Overview with Extensions

Model-based small area estimation is frequently used in conjunction with survey data in order to establish estimates for under-sampled or unsampled geographies. These models can be specified at either the area-level, or the unit-level, but unit-level models often offer potential advantages such as more precise estimates and easy spatial aggregation. Nevertheless, relative to area-level models, literature on unit-level models is less prevalent. In modeling small areas at the unit level, challenges often arise as a consequence of the informative sampling mechanism used to collect the survey data. This paper provides a comprehensive methodological review for unit-level models under informative sampling, with an emphasis on Bayesian approaches. To provide insight into the differences between methods, we conduct a simulation study that compares several of the described approaches. In addition, the methods used for simulation are further illustrated through an application to the American Community Survey. Finally, we present several extensions and areas for future research.

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arXiv2019

Conjugate Bayesian Unit-level Modeling of Count Data Under Informative Sampling Designs

Unit-level models for survey data offer many advantages over their area-level counterparts, such as potential for more precise estimates and a natural benchmarking property. However two main challenges occur in this context: accounting for an informative survey design and handling non-Gaussian data types. The pseudo-likelihood approach is one solution to the former, and conjugate multivariate distribution theory offers a solution to the latter. By combining these approaches, we attain a unit-level model for count data that accounts for informative sampling designs and includes fully Bayesian model uncertainty propagation. Importantly, conjugate full conditional distributions hold under the pseudo-likelihood, yielding an extremely computationally efficient approach. Our method is illustrated via an empirical simulation study using count data from the American Community Survey public-use microdata sample.

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arXiv2019

Bayesian Hierarchical Models with Conjugate Full-Conditional Distributions for Dependent Data from the Natural Exponential Family

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce the "conjugate multivariate distribution," which is motivated by the univariate distribution introduced in Diaconis and Ylvisaker (1979). Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively.

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arXiv2018

Spatio-Temporal Models for Big Multinomial Data using the Conditional Multivariate Logit-Beta Distribution

We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio-temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit-beta distribution into the dependent multinomial data setting, which leads to conjugate full-conditional distributions for use in a collapsed Gibbs sampler. We refer to this model as the multinomial spatio-temporal mixed effects model (MN-STM). Additionally, we provide methodological developments including: the derivation of the associated full-conditional distributions, a relationship with a latent Gaussian process model, and the stability of the non-stationary vector autoregressive model. We illustrate the MN-STM through simulations and through a demonstration with public-use Quarterly Workforce Indicators (QWI) data from the Longitudinal Employer Household Dynamics (LEHD) program of the U.S. Census Bureau.

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arXiv2018

A Bayesian Semiparametric Jolly-Seber Model with Individual Heterogeneity: An Application to Migratory Mallards at Stopover

We propose a Bayesian hierarchical Jolly-Seber model that can account for individual heterogeneity in departure and the dependence of arrival time on covariates. Additionally, our model provides a semiparametric functional form for modeling capture probabilities. The model is flexible and can be used to estimate the stopover duration and stopover population size, which are key to stopover duration analysis. From the modeling perspective, our model allows for individual heterogeneity in departure due to a continuous intrinsic factor that varies with time and individual. A stochastic process is considered to model the change of this intrinsic factor over time. Moreover, our model links extrinsic factors to capture probabilities and arrival time. Consequently, our proposed model enables us to draw inference about the impacts of the intrinsic factor on departure, and extrinsic factors on both capture outcome and arrival time. Through the use of a semiparametric model for capture probabilities, we allow the data to suggest the functional relationship between extrinsic factors and capture probabilities rather than relying on an imposed parametric model. By using data augmentation, we develop a well customized Markov chain Monte Carlo algorithm that is free of tuning. We demonstrate the effectiveness of our model through a motivating example of stopover duration analysis for mallards (Anas platyrhynchos) studied during fall migration in Sweden.

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arXiv2016

Multivariate spatio-temporal models for high-dimensional areal data with application to Longitudinal Employer-Household Dynamics

Many data sources report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate spatio-temporal dependencies. Additionally, many multivariate spatio-temporal areal data sets are extremely high dimensional, which leads to practical issues when formulating statistical models. For example, we analyze Quarterly Workforce Indicators (QWI) published by the US Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) program. QWIs are available by different variables, regions, and time points, resulting in millions of tabulations. Despite their already expansive coverage, by adopting a fully Bayesian framework, the scope of the QWIs can be extended to provide estimates of missing values along with associated measures of uncertainty. Motivated by the LEHD, and other applications in federal statistics, we introduce the multivariate spatio-temporal mixed effects model (MSTM), which can be used to efficiently model high-dimensional multivariate spatio-temporal areal data sets. The proposed MSTM extends the notion of Moran's I basis functions to the multivariate spatio-temporal setting. This extension leads to several methodological contributions, including extremely effective dimension reduction, a dynamic linear model for multivariate spatio-temporal areal processes, and the reduction of a high-dimensional parameter space using a novel parameter model.

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arXiv2015

Computationally Efficient Distribution Theory for Bayesian Inference of High-Dimensional Dependent Count-Valued Data

We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic regions, and times. This problem requires extensive methodological advancements, as jointly modeling correlated data of this size leads to the so-called "big n problem." The computational complexity of prediction in this setting is further exacerbated by acknowledging that count-valued data are naturally non-Gaussian. Thus, we develop a new computationally efficient distribution theory for this setting. In particular, we introduce a multivariate log-gamma distribution and provide substantial theoretical development including: results regarding conditional distributions, marginal distributions, an asymptotic relationship with the multivariate normal distribution, and full-conditional distributions for a Gibbs sampler. To incorporate dependence between variables, regions, and time points, a multivariate spatio-temporal mixed effects model (MSTM) is used. The results in this manuscript are extremely general, and can be used for data that exhibit fewer sources of dependency than what we consider (e.g., multivariate, spatial-only, or spatio-temporal-only data). Hence, the implications of our modeling framework may have a large impact on the general problem of jointly modeling correlated count-valued data. We show the effectiveness of our approach through a simulation study. Additionally, we demonstrate our proposed methodology with an important application analyzing data obtained from the Longitudinal Employer-Household Dynamics (LEHD) program, which is administered by the U.S. Census Bureau.

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arXiv2015

Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error

The modifiable areal unit problem and the ecological fallacy are known problems that occur when modeling multiscale spatial processes. We investigate how these forms of spatial aggregation error can guide a regionalization over a spatial domain of interest. By "regionalization" we mean a specification of geographies that define the spatial support for areal data. This topic has been studied vigorously by geographers, but has been given less attention by spatial statisticians. Thus, we propose a criterion for spatial aggregation error (CAGE), which we minimize to obtain an optimal regionalization. To define CAGE we draw a connection between spatial aggregation error and a new multiscale representation of the Karhunen-Loeve (K-L) expansion. This relationship between CAGE and the multiscale K-L expansion leads to illuminating theoretical developments including: connections between spatial aggregation error, squared prediction error, spatial variance, and a novel extension of Obled-Creutin eigenfunctions. The effectiveness of our approach is demonstrated through an analysis of two datasets, one using the American Community Survey and one related to environmental ocean winds.

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arXiv2015

Spatio-Temporal Change of Support with Application to American Community Survey Multi-Year Period Estimates

We present hierarchical Bayesian methodology to perform spatio-temporal change of support (COS) for survey data with Gaussian sampling errors. This methodology is motivated by the American Community Survey (ACS), which is an ongoing survey administered by the U.S. Census Bureau that provides timely information on several key demographic variables. The ACS has published 1-year, 3-year, and 5-year period-estimates, and margins of errors, for demographic and socio-economic variables recorded over predefined geographies. The spatio-temporal COS methodology considered here provides data users with a way to estimate ACS variables on customized geographies and time periods, while accounting for sampling errors. Additionally, 3-year ACS period estimates are to be discontinued, and this methodology can provide predictions of ACS variables for 3-year periods given the available period estimates. The methodology is based on a spatio-temporal mixed effects model with a low-dimensional spatio-temporal basis function representation, which provides multi-resolution estimates through basis function aggregation in space and time. This methodology includes a novel parameterization that uses a target dynamical process and recently proposed parsimonious Moran's I propagator structures. Our approach is demonstrated through two applications using public-use ACS estimates, and is shown to produce good predictions on a holdout set of 3-year period estimates.

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