arXiv subjects

Paul A. Parker

Publications and source records attributed to Paul A. Parker.

At least 19 recordsLinked to original sources

arXiv2026

Mixtures of Neural Network Experts with Application to Phytoplankton Flow Cytometry Data

Flow cytometry is a valuable technique that measures the optical properties of particles at a single-cell resolution. When deployed in the ocean, flow cytometry allows oceanographers to study different types of photosynthetic microbes called phytoplankton. It is of great interest to study how phytoplankton properties change in response to environmental conditions. In our work, we develop a nonlinear mixture of experts model to estimate separate regression functions for each subpopulation utilizing random-weight neural networks. Our model allows one to flexibly estimate how cell properties and relative abundances depend on environmental covariates in each segment of a heterogeneous sample, without the computational burden of backpropagation. We show that the proposed model provides superior predictive performance in simulated examples compared to a mixture of linear experts. Also, applying our model to real data, we show that our model has (1) comparable out-of-sample prediction performance, and (2) more realistic estimates of phytoplankton behavior.

stat.ME↗

arXiv2026

Prediction-Powered Smoothing and Validation for Disaggregated AI Evaluation

Evaluating an AI system requires disaggregated assessment, as performance varies across domains such as benchmark task types or conversation types in deployed agents. Exhaustive testing is expensive, so evaluation rests on a sample of labeled units. We treat the evaluation set as a finite population and seek accurate point and interval estimates of each domain mean. Direct estimators, including prediction-powered inference (PPI), use only a domain's own labels and are imprecise where labels are few. Small area estimation addresses this problem, and we build on it to develop an integrated workflow for estimation and validation. For estimation, we propose prediction-powered smoothing (PP-S), a Bayesian model fit to each domain's prediction-powered estimate, with an extension that borrows strength across a reporting taxonomy (PP-TS). For validation, we derive a new, approximately unbiased design-based cross-validation score for choosing among direct and smoothed estimators. We study a curated benchmark with verifiable grading and deployed agent traffic graded by humans, each with every outcome observed. In both, the proposed estimators improve on the direct estimators in point and interval estimation, with near-nominal coverage. At the same sampling budget, our score selects as well as an independent validation sample does and estimates the selected estimator's error far more accurately.

stat.ML↗

arXiv2026

Nonprobability Samples for Small Area Estimation: A Review and Comparative Simulation Study

Nonprobability samples (NPS) are attractive because they are less costly to collect, can provide substantially larger sample sizes, and may reach populations that traditional probability surveys do not. As response rates for traditional surveys fall, interest in NPS has grown rapidly within the field of survey statistics. These methods are especially relevant for small area estimation (SAE), where there is ever-present demand for estimates at fine geographic scales and detailed demographic domains. Despite rapid methodological development, there remains limited understanding of which approaches perform best under different conditions. In this paper, we review recent developments in NPS methodology, including the concept of data defect correlation (DDC) as a measure of data quality and as a tool for categorizing the various NPS methods. We then present a comprehensive simulation study that evaluates a range of NPS approaches under varying levels of DDC and extend several existing methods to the SAE setting.

stat.ME↗

arXiv2026

Scalable Joint Modeling of Dependent Multi-Type Survey Data for Small Area Estimation

We develop a Bayesian area-level small area estimation framework that jointly models binomial and Gaussian survey responses through shared spatial random effects. This work is motivated by the American Community Survey (ACS), which provides useful information that contributes to federal funding and policy making decisions, and often yields direct estimates with large standard errors in small domains. The proposed Multi-type model borrows strength across outcomes and spatial neighbors to improve the precision of the associated estimates. For the binomial component, Polya-Gamma data augmentation yields a conditionally Gaussian representation, while spatial basis functions provide dimension reduction for high-dimensional spatial data. Together, these features lead to closed-form conditional posteriors and, thus, an efficient Gibbs sampler. Through empirical simulations, we show that the proposed joint model improves estimation precision relative to independent Univariate models. Applying the method to ACS median income and poverty rate data, we find that the proposed Multi-type model yields similar point estimates but smaller posterior variances than the corresponding Univariate models.

stat.ME↗

arXiv2026

On Data Thinning for Model Validation in Small Area Estimation

Small area estimation produces estimates of population parameters for geographic and demographic subgroups with limited sample sizes. Such estimates are critical for policy decisions, yet principled validation of these models remains a challenge. Unlike conventional predictive settings, validation data are rarely available. Data thinning splits a single observation into independent training and test components. It enables out-of-sample validation using only the area-level summary statistics routinely available, requiring only their Gaussianity and known sampling variances. However, the properties of thinning-based model comparison have not been formally studied. In this paper, we develop these properties. We construct an unbiased estimator of thinned-data mean squared error and show that it differs systematically from its full-data counterpart; for the standard Fay-Herriot model, the gap admits a closed-form expression that depends on the candidate model's shrinkage behavior. We further show that the estimator variance increases sharply as the training fraction approaches one, producing a bias-variance tradeoff with no universally optimal thinning parameter. Practical recommendations balancing these forces are informed by theory and verified empirically. Design-based simulations using American Community Survey microdata show that the recommended data thinning approach is competitive with information-criterion and simulation-based methods, and substantially more stable across heterogeneous sampling designs.

stat.ME↗

arXiv2026

A Bayesian Approach to Unit-level Dependent Multi-type Survey Data

The American Community Survey (ACS) Public Use Microdata Sample (PUMS) provides access to a wide range of unit-level survey data consisting of correlated Gaussian and binomial distributed survey responses along with associated survey weights. As such, we propose a Bayesian hierarchical framework for jointly modeling unit-level Gaussian and binomial survey data. The model introduces a shared area-level random effect to capture dependence across responses. Informative sampling is addressed using a pseudo-likelihood construction, and Polya-Gamma data augmentation provides an efficient conjugate Gibbs sampler, enabling scalable inference for large survey datasets. Through empirical simulations based on ACS PUMS data, we show that the joint model achieves notable reductions in mean squared error and improved interval scores compared to univariate and design-based estimators. Applying the method to the 2023 Illinois PUMS data, we find that the joint model yields small-area estimates similar to those from the univariate model and the Horvitz-Thompson estimator, but with smaller posterior variances. The computational cost associated with the joint model is also comparable to that of the univariate binomial model. Combined with the empirical simulation results, these findings demonstrate the practical advantages of the proposed approach.

stat.ME↗

arXiv2025

Variational Autoencoded Multivariate Spatial Fay-Herriot Models

Small area estimation models are essential for estimating population characteristics in regions with limited sample sizes, thereby supporting policy decisions, demographic studies, and resource allocation, among other use cases. The spatial Fay-Herriot model is one such approach that incorporates spatial dependence to improve estimation by borrowing strength from neighboring regions. However, this approach often requires substantial computational resources, limiting its scalability for high-dimensional datasets, especially when considering multiple (multivariate) responses. This paper proposes two methods that integrate the multivariate spatial Fay-Herriot model with spatial random effects, learned through variational autoencoders, to efficiently leverage spatial structure. Importantly, after training the variational autoencoder to represent spatial dependence for a given set of geographies, it may be used again in future modeling efforts, without the need for retraining. Additionally, the use of the variational autoencoder to represent spatial dependence results in extreme improvements in computational efficiency, even for massive datasets. We demonstrate the effectiveness of our approach using 5-year period estimates from the American Community Survey over all census tracts in California.

stat.ML↗

arXiv2025

Bayesian Unit-level Modeling of Categorical Survey Data with a Longitudinal Design

Categorical response data are ubiquitous in complex survey applications, yet few methods model the dependence across different outcome categories when the response is ordinal. Likewise, few methods exist for the common combination of a longitudinal design and categorical data. By modeling individual survey responses at the unit-level, it is possible to capture both ordering information in ordinal responses and any longitudinal correlation. However, accounting for a complex survey design becomes more challenging in the unit-level setting. We propose a Bayesian hierarchical, unit-level, model-based approach for categorical data that is able to capture ordering among response categories, can incorporate longitudinal dependence, and accounts for the survey design. To handle computational scalability, we develop efficient Gibbs samplers with appropriate data augmentation as well as variational Bayes algorithms. Using public-use microdata from the Household Pulse Survey, we provide an analysis of an ordinal response that asks about the frequency of anxiety symptoms at the beginning of the COVID-19 pandemic. We compare both design-based and model-based estimators and demonstrate superior performance for the proposed approaches.

stat.ME↗

arXiv2025

Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollments

Poisson autoregressive count models have evolved into a time series staple for correlated count data. This paper proposes an alternative to Poisson autoregressions: count echo state networks. Echo state networks can be statistically analyzed in frequentist manners via optimizing penalized likelihoods, or in Bayesian manners via MCMC sampling. This paper develops Poisson echo state techniques for count data and applies them to a massive count data set containing the number of graduate students from 1,758 United States universities during the years 1972-2021 inclusive. Negative binomial models are also implemented to better handle overdispersion in the counts. Performance of the proposed models are compared via their forecasting performance as judged by several methods. In the end, a hierarchical negative binomial based echo state network is judged as the superior model.

stat.ME↗

arXiv2025

Topic Modeling for Free-Response Text Data from a Complex Survey

Topic Modeling is a popular statistical tool commonly used on textual data to identify the hidden thematic structure in a document collection based on the distribution of words. Additionally, it can be used to cluster the documents, with clusters representing distinct topics. The Mixture of Unigrams (MoU) is a standard topic model for clustering document-term data and can be particularly useful for analyzing open-ended survey responses to extract meaningful information from the underlying topics. However, with complex survey designs, where data is often collected on individual (document) characteristics, it is essential to account for the sample design in order to avoid biased estimates. To address this issue, we propose the MoU model under informative sampling using a pseudolikelihood to account for the sample design in the model by incorporating survey weights. We evaluate the effectiveness of this approach through a simulation study and illustrate its application using two datasets from the American National Election Studies (ANES). We compare our pseudolikelihood-based MoU model to the traditional MoU and assess its effectiveness in extracting meaningful topics from survey data. Additionally, we introduce a hierarchical Mixture of Unigrams (hMoU) accounting for informative sampling where topic proportions are defined as functions of document-level fixed and random effects. We demonstrate the effectiveness of the proposed model through an application to ANES data comparing topic proportions across respondent-level factors such as gender, race, age group, and state.

stat.AP↗

arXiv2024

Spatial Deep Convolutional Neural Networks

Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities exist. Recent work has shown that pre-computed spatial basis functions and a feed-forward neural network can capture complex spatial dependence structures while remaining computationally efficient. This paper builds on this literature by tailoring spatial basis functions for use in convolutional neural networks. Through both simulated and real data, we demonstrate that this approach yields more accurate spatial predictions than existing methods. Uncertainty quantification is also considered.

stat.ME↗

arXiv2024

Spatially Selected and Dependent Random Effects for Small Area Estimation with Application to Rent Burden

Area-level models for small area estimation typically rely on areal random effects to shrink design-based direct estimates towards a model-based predictor. Incorporating the spatial dependence of the random effects into these models can further improve the estimates when there are not enough covariates to fully account for spatial dependence of the areal means. A number of recent works have investigated models that include random effects for only a subset of areas, in order to improve the precision of estimates. However, such models do not readily handle spatial dependence. In this paper, we introduce a model that accounts for spatial dependence in both the random effects as well as the latent process that selects the effects. We show how this model can significantly improve predictive accuracy via an empirical simulation study based on data from the American Community Survey, and illustrate its properties via an application to estimate county-level median rent burden.

stat.ME↗

arXiv2023

A Heterogeneous Spatial Model for Soil Carbon Mapping of the Contiguous United States Using VNIR Spectra

The Rapid Carbon Assessment, conducted by the U.S. Department of Agriculture, was implemented in order to obtain a representative sample of soil organic carbon across the contiguous United States. In conjunction with a statistical model, the dataset allows for mapping of soil carbon prediction across the U.S., however there are two primary challenges to such an effort. First, there exists a large degree of heterogeneity in the data, whereby both the first and second moments of the data generating process seem to vary both spatially and for different land-use categories. Second, the majority of the sampled locations do not actually have lab measured values for soil organic carbon. Rather, visible and near-infrared (VNIR) spectra were measured at most locations, which act as a proxy to help predict carbon content. Thus, we develop a heterogeneous model to analyze this data that allows both the mean and the variance to vary as a function of space as well as land-use category, while incorporating VNIR spectra as covariates. After a cross-validation study that establishes the effectiveness of the model, we construct a complete map of soil organic carbon for the contiguous U.S. along with uncertainty quantification.

stat.AP↗

arXiv2023

The Link Between Health Insurance Coverage and Citizenship Among Immigrants: Bayesian Unit-Level Regression Modeling of Categorical Survey Data Observed with Measurement Error

Social scientists are interested in studying the impact that citizenship status has on health insurance coverage among immigrants in the United States. This can be done using data from the Survey of Income and Program Participation (SIPP); however, two primary challenges emerge. First, statistical models must account for the survey design in some fashion to reduce the risk of bias due to informative sampling. Second, it has been observed that survey respondents misreport citizenship status at nontrivial rates. This too can induce bias within a statistical model. Thus, we propose the use of a weighted pseudo-likelihood mixture of categorical distributions, where the mixture component is determined by the latent true response variable, in order to model the misreported data. We illustrate through an empirical simulation study that this approach can mitigate the two sources of bias attributable to the sample design and misreporting. Importantly, our misreporting model can be further used as a component in a deeper hierarchical model. With this in mind, we conduct an analysis of the relationship between health insurance coverage and citizenship status using data from the SIPP.

stat.ME↗

arXiv2023

Bayesian Unit-level Models for Longitudinal Survey Data under Informative Sampling: An Analysis of Expected Job Loss Using the Household Pulse Survey

The Household Pulse Survey (HPS), recently released by the U.S. Census Bureau, gathers timely information about the societal and economic impacts of coronavirus. The first phase of the survey was quickly launched one month after the beginning of the coronavirus pandemic and ran for 12 weeks. To track the immediate impact of the pandemic, individual respondents during this phase were re-sampled for up to three consecutive weeks. Motivated by expected job loss during the pandemic, using public-use microdata, this work proposes unit-level, model-based estimators that incorporate longitudinal dependence at both the response and domain level. In particular, using a pseudo-likelihood, we consider a Bayesian hierarchical unit-level, model-based approach for both Gaussian and binary response data under informative sampling. To facilitate construction of these model-based estimates, we develop an efficient Gibbs sampler. An empirical simulation study is conducted to compare the proposed approach to models that do not account for unit-level longitudinal correlation. Finally, using public-use HPS micro-data, we provide an analysis of "expected job loss" that compares both design-based and model-based estimators and demonstrates superior performance for the proposed model-based approaches.

stat.ME↗

arXiv2022

Conjugate Modeling Approaches for Small Area Estimation with Heteroscedastic Structure

Small area estimation has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression, where the variance for each domain is assumed to be known and plugged in following a design-based estimate. Recent work has considered hierarchical models for the variance, where the design-based estimates are used as an additional data point to model the latent true variance in each domain. These hierarchical models may incorporate covariate information, but can be difficult to sample from in high-dimensional settings. Utilizing recent distribution theory, we explore a class of Bayesian hierarchical models for small area estimation that smooth both the design-based estimate of the mean and the variance. In addition, we develop a class of unit-level models for heteroscedastic Gaussian response data. Importantly, we incorporate both covariate information as well as spatial dependence, while retaining a conjugate model structure that allows for efficient sampling. We illustrate our methodology through an empirical simulation study as well as an application using data from the American Community Survey.

stat.ME↗

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.

stat.ME↗

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.

stat.ME↗