Bayesian models and streaming samplers for complex data with application to network regression and record linkage
Date
2023
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Abstract
Real-world statistical problems often feature complex data due to either the structure of the data itself or the methods used to collect the data. In this dissertation, we present three methods for the analysis of specific complex data: Restricted Network Regression, Streaming Record Linkage, and Generative Filtering. Network data contain observations about the relationships between entities. Applying mixed models to network data can be problematic when the primary interest is estimating unconditional regression coefficients and some covariates are exactly or nearly in the vector space of node-level effects. We introduce the Restricted Network Regression model that removes the collinearity between fixed and random effects in network regression by orthogonalizing the random effects against the covariates. We discuss the change in the interpretation of the regression coefficients in Restricted Network Regression and analytically characterize the effect of Restricted Network Regression on the regression coefficients for continuous response data. We show through simulation on continuous and binary data that Restricted Network Regression mitigates, but does not alleviate, network confounding. We apply the Restricted Network Regression model in an analysis of 2015 Eurovision Song Contest voting data and show how the choice of regression model affects inference. Data that are collected from multiple noisy sources pose challenges to analysis due to potential errors and duplicates. Record linkage is the task of combining records from multiple files which refer to overlapping sets of entities when there is no unique identifying field. In streaming record linkage, files arrive sequentially in time and estimates of links are updated after the arrival of each file. We approach streaming record linkage from a Bayesian perspective with estimates calculated from posterior samples of parameters, and present methods for updating link estimates after the arrival of a new file that are faster than fitting a joint model with each new data file. We generalize a two-file Bayesian Fellegi-Sunter model to the multi-file case and propose two methods to perform streaming updates. We examine the effect of prior distribution on the resulting linkage accuracy as well as the computational trade-offs between the methods when compared to a Gibbs sampler through simulated and real-world survey panel data. We achieve near-equivalent posterior inference at a small fraction of the compute time. Motivated by the streaming data setting and streaming record linkage, we propose a more general sampling method for Bayesian models for streaming data. In the streaming data setting, Bayesian models can employ recursive updates, incorporating each new batch of data into the model parameters' posterior distribution. Filtering methods are currently used to perform these updates efficiently, however, they suffer from eventual degradation as the number of unique values within the filtered samples decreases. We propose Generative Filtering, a method for efficiently performing recursive Bayesian updates in the streaming setting. Generative Filtering retains the speed of a filtering method while using parallel updates to avoid degenerate distributions after repeated applications. We derive rates of convergence for Generative Filtering and conditions for the use of sufficient statistics instead of storing all past data. We investigate properties of Generative Filtering through simulation and ecological species count data.
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Subject
MCMC
record linkage
streaming data
network regression
confounding
recursive Bayes