arXiv subjects

Jared S. Murray

Publications and source records attributed to Jared S. Murray.

At least 19 recordsLinked to original sources

arXiv2022

Bayesian inference for treatment effects under nested subsets of controls

When constructing a model to estimate the causal effect of a treatment, it is necessary to control for other factors which may have confounding effects. Because the ignorability assumption is not testable, however, it is usually unclear which minimal set of controls is appropriate -- as is their appropriate functional form in the model -- and effect estimation can be sensitive to these choices. A common approach in this case is to fit several models, each with a different control specification (under the assumption that the available controls are sufficient but possibly not all necessary to deconfound the treatment effect), but it is difficult to reconcile inference for the treatment effect under the multiple resulting posterior distributions. Therefore we propose a two-stage approach to measure the sensitivity of effect estimation with respect to control specification. In the first stage, a model is fit with all available controls using a prior carefully selected to adjust for confounding. In the second stage, posterior distributions are calculated for the treatment effect under submodels of nested sets of controls using projected posteriors under the full model, providing valid Bayesian inference. We demonstrate how our approach can be used to detect influential confounders in a dataset, and apply it in a sensitivity analysis of an observational study measuring the effect of legalized abortion on crime rates.

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arXiv2022

Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in the BART model we propose, we further introduce an approach to targeted smoothing which is possibly of independent interest for BART models. We study the proposed model theoretically and provide sufficient conditions for the posterior distribution to concentrate at close to the minimax optimal rate adaptively over smoothness classes in the high-dimensional regime in which many predictors are irrelevant. To fit our model we propose a data augmentation algorithm which allows for existing BART samplers to be extended with minimal effort. We illustrate the performance of our methodology on simulated data and use it to study the relationship between education and body mass index using data from the medical expenditure panel survey (MEPS).

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arXiv2021

Decoupling Shrinkage and Selection in Gaussian Linear Factor Analysis

Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a three-step approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of sparse point-estimates, with a decreasing number of factors, is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with applications in classical data from the Factor Analysis literature. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method.

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arXiv2020

Invited Discussion of "A Unified Framework for De-Duplication and Population Size Estimation"

Invited Discussion of "A Unified Framework for De-Duplication and Population Size Estimation", published in Bayesian Analysis. My discussion focuses on two main themes: Providing a more nuanced picture of the costs and benefits of joint models for record linkage and the "downstream task" (i.e. whatever we might want to do with the linked and de-duplicated files), and how we should measure performance.

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arXiv2020

Estimating heterogeneous effects of continuous exposures using Bayesian tree ensembles: revisiting the impact of abortion rates on crime

In estimating the causal effect of a continuous exposure or treatment, it is important to control for all confounding factors. However, most existing methods require parametric specification for how control variables influence the outcome or generalized propensity score, and inference on treatment effects is usually sensitive to this choice. Additionally, it is often the goal to estimate how the treatment effect varies across observed units. To address this gap, we propose a semiparametric model using Bayesian tree ensembles for estimating the causal effect of a continuous treatment of exposure which (i) does not require a priori parametric specification of the influence of control variables, and (ii) allows for identification of effect modification by pre-specified moderators. The main parametric assumption we make is that the effect of the exposure on the outcome is linear, with the steepness of this relationship determined by a nonparametric function of the moderators, and we provide heuristics to diagnose the validity of this assumption. We apply our methods to revisit a 2001 study of how abortion rates affect incidence of crime.

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arXiv2020

Model interpretation through lower-dimensional posterior summarization

Nonparametric regression models have recently surged in their power and popularity, accompanying the trend of increasing dataset size and complexity. While these models have proven their predictive ability in empirical settings, they are often difficult to interpret and do not address the underlying inferential goals of the analyst or decision maker. In this paper, we propose a modular two-stage approach for creating parsimonious, interpretable summaries of complex models which allow freedom in the choice of modeling technique and the inferential target. In the first stage a flexible model is fit which is believed to be as accurate as possible. In the second stage, lower-dimensional summaries are constructed by projecting draws from the distribution onto simpler structures. These summaries naturally come with valid Bayesian uncertainty estimates. Further, since we use the data only once to move from prior to posterior, these uncertainty estimates remain valid across multiple summaries and after iteratively refining a summary. We apply our method and demonstrate its strengths across a range of simulated and real datasets. Code to reproduce the examples shown is avaiable at github.com/spencerwoody/ghost

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arXiv2020

A Bayesian Hierarchical Model for Evaluating Forensic Footwear Evidence

When a latent shoeprint is discovered at a crime scene, forensic analysts inspect it for distinctive patterns of wear such as scratches and holes (known as accidentals) on the source shoe's sole. If its accidentals correspond to those of a suspect's shoe, the print can be used as forensic evidence to place the suspect at the crime scene. The strength of this evidence depends on the random match probability---the chance that a shoe chosen at random would match the crime scene print's accidentals. Evaluating random match probabilities requires an accurate model for the spatial distribution of accidentals on shoe soles. A recent report by the President's Council of Advisors in Science and Technology criticized existing models in the literature, calling for new empirically validated techniques. We respond to this request with a new spatial point process model for accidental locations, developed within a hierarchical Bayesian framework. We treat the tread pattern of each shoe as a covariate, allowing us to pool information across large heterogeneous databases of shoes. Existing models ignore this information; our results show that including it leads to significantly better model fit. We demonstrate this by fitting our model to one such database.

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arXiv2020

Targeted Smooth Bayesian Causal Forests: An analysis of heterogeneous treatment effects for simultaneous versus interval medical abortion regimens over gestation

We introduce Targeted Smooth Bayesian Causal Forests (tsBCF), a nonparametric Bayesian approach for estimating heterogeneous treatment effects which vary smoothly over a single covariate in the observational data setting. The tsBCF method induces smoothness by parameterizing terminal tree nodes with smooth functions, and allows for separate regularization of treatment effects versus prognostic effect of control covariates. Smoothing parameters for prognostic and treatment effects can be chosen to reflect prior knowledge or tuned in a data-dependent way. We use tsBCF to analyze a new clinical protocol for early medical abortion. Our aim is to assess relative effectiveness of simultaneous versus interval administration of mifepristone and misoprostol over the first nine weeks of gestation. The model reflects our expectation that the relative effectiveness varies smoothly over gestation, but not necessarily over other covariates. We demonstrate the performance of the tsBCF method on benchmarking experiments. Software for tsBCF is available at https://github.com/jestarling/tsbcf/.

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arXiv2020

Scaling Bayesian Probabilistic Record Linkage with Post-Hoc Blocking: An Application to the California Great Registers

Probabilistic record linkage (PRL) is the process of determining which records in two databases correspond to the same underlying entity in the absence of a unique identifier. Bayesian solutions to this problem provide a powerful mechanism for propagating uncertainty due to uncertain links between records (via the posterior distribution). However, computational considerations severely limit the practical applicability of existing Bayesian approaches. We propose a new computational approach, providing both a fast algorithm for deriving point estimates of the linkage structure that properly account for one-to-one matching and a restricted MCMC algorithm that samples from an approximate posterior distribution. Our advances make it possible to perform Bayesian PRL for larger problems, and to assess the sensitivity of results to varying prior specifications. We demonstrate the methods on a subset of an OCR'd dataset, the California Great Registers, a collection of 57 million voter registrations from 1900 to 1968 that comprise the only panel data set of party registration collected before the advent of scientific surveys.

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arXiv2019

Monotone function estimation in the presence of extreme data coarsening: Analysis of preeclampsia and birth weight in urban Uganda

This paper proposes a Bayesian hierarchical model to characterize the relationship between birth weight and maternal pre-eclampsia across gestation at a large maternity hospital in urban Uganda. Key scientific questions we investigate include: 1) how pre-eclampsia compares to other maternal-fetal covariates as a predictor of birth weight; and 2) whether the impact of pre-eclampsia on birthweight varies across gestation. Our model addresses several key statistical challenges: it correctly encodes the prior medical knowledge that birth weight should vary smoothly and monotonically with gestational age, yet it also avoids assumptions about functional form along with assumptions about how birth weight varies with other covariates. Our model also accounts for the fact that a high proportion (83%) of birth weights in our data set are rounded to the nearest 100 grams. Such extreme data coarsening is rare in maternity hospitals in high resource obstetrics settings but common for data sets collected in low and middle-income countries (LMICs); this introduces a substantial extra layer of uncertainty into the problem and is a major reason why we adopt a Bayesian approach. Our proposed non-parametric regression model, which we call Projective Smooth BART (psBART), builds upon the highly successful Bayesian Additive Regression Tree (BART) framework. This model captures complex nonlinear relationships and interactions, induces smoothness and monotonicity in a single target covariate, and provides a full posterior for uncertainty quantification. The results of our analysis show that pre-eclampsia is a dominant predictor of birth weight in this urban Ugandan setting, and therefore an important risk factor for perinatal mortality.

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arXiv2019

Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects

This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

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arXiv2019

Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models

We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been limited to models for Gaussian "data", either observed or latent. This is primarily because efficient MCMC algorithms are available for Gaussian likelihoods. But while many useful models are naturally cast in terms of latent Gaussian variables, many others are not -- including models considered in this paper. We develop new data augmentation strategies and carefully specified prior distributions for these new models. Like the original BART prior, the new prior distributions are carefully constructed and calibrated to be flexible while guarding against overfitting. Together the new priors and data augmentation schemes allow us to implement an efficient MCMC sampler outside the context of Gaussian models. The utility of these new methods is illustrated with examples and an application to a previously published dataset.

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arXiv2019

BART with Targeted Smoothing: An analysis of patient-specific stillbirth risk

This article introduces BART with Targeted Smoothing, or tsBART, a new Bayesian tree-based model for nonparametric regression. The goal of tsBART is to introduce smoothness over a single target covariate t, while not necessarily requiring smoothness over other covariates x. TsBART is based on the Bayesian Additive Regression Trees (BART) model, an ensemble of regression trees. TsBART extends BART by parameterizing each tree's terminal nodes with smooth functions of t, rather than independent scalars. Like BART, tsBART captures complex nonlinear relationships and interactions among the predictors. But unlike BART, tsBART guarantees that the response surface will be smooth in the target covariate. This improves interpretability and helps regularize the estimate. After introducing and benchmarking the tsBART model, we apply it to our motivating example: pregnancy outcomes data from the National Center for Health Statistics. Our aim is to provide patient-specific estimates of stillbirth risk across gestational age (t), based on maternal and fetal risk factors (x). Obstetricians expect stillbirth risk to vary smoothly over gestational age, but not necessarily over other covariates, and tsBART has been designed precisely to reflect this structural knowledge. The results of our analysis show the clear superiority of the tsBART model for quantifying stillbirth risk, thereby providing patients and doctors with better information for managing the risk of perinatal mortality. All methods described here are implemented in the R package tsbart.

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arXiv2019

Atlantic Causal Inference Conference (ACIC) Data Analysis Challenge 2017

This brief note documents the data generating processes used in the 2017 Data Analysis Challenge associated with the Atlantic Causal Inference Conference (ACIC). The focus of the challenge was estimation and inference for conditional average treatment effects (CATEs) in the presence of targeted selection, which leads to strong confounding. The associated data files and further plots can be found on the first author's web page.

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arXiv2018

Multiple Imputation: A Review of Practical and Theoretical Findings

Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for generating and using multiple imputations. A review of strategies for generating imputations follows, including recent developments in flexible joint modeling and sequential regression/chained equations/fully conditional specification approaches. Finally, we compare and contrast different methods for generating imputations on a range of criteria before identifying promising avenues for future research.

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arXiv2017

Practical Bayesian Inference for Record Linkage

Probabilistic record linkage (PRL) is the process of determining which records in two databases correspond to the same underlying entity in the absence of a unique identifier. Bayesian solutions to this problem provide a powerful mechanism for propagating uncertainty due to uncertain links between records (via the posterior distribution). However, computational considerations severely limit the practical applicability of existing Bayesian approaches. We propose a new computational approach, providing both a fast algorithm for deriving point estimates of the linkage structure that properly account for one-to-one matching and a restricted MCMC algorithm that samples from an approximate posterior distribution. Our advances make it possible to perform Bayesian PRL for larger problems, and to assess the sensitivity of results to varying prior specifications. We demonstrate the methods on simulated data and an application to a post-enumeration survey for coverage estimation in the Italian census.

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arXiv2016

Probabilistic Record Linkage and Deduplication after Indexing, Blocking, and Filtering

Probabilistic record linkage, the task of merging two or more databases in the absence of a unique identifier, is a perennial and challenging problem. It is closely related to the problem of deduplicating a single database, which can be cast as linking a single database against itself. In both cases the number of possible links grows rapidly in the size of the databases under consideration, and in most applications it is necessary to first reduce the number of record pairs that will be compared. Spurred by practical considerations, a range of methods have been developed for this task. These methods go under a variety of names, including indexing and blocking, and have seen significant development. However, methods for inferring linkage structure that account for indexing, blocking, and additional filtering steps have not seen commensurate development. In this paper we review the implications of indexing, blocking and filtering within the popular Fellegi-Sunter framework, and propose a new model to account for particular forms of indexing and filtering.

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arXiv2015

Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependence

We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures of multinomial distributions for categorical variables with Dirichlet process mixtures of multivariate normal distributions for continuous variables. We incorporate dependence between the continuous and categorical variables by (i) modeling the means of the normal distributions as component-specific functions of the categorical variables and (ii) forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model. This structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst. We apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the Survey of Income and Program Participation (SIPP). The goal is to compare estimates from a field test with the new design to estimates from selected individuals from a panel collected under the old design. We show that accounting for the missing data changes some conclusions about the comparability of the distributions in the two datasets. We also perform an extensive repeated sampling simulation using similar data from complete cases in an existing SIPP panel, comparing our proposed model to a default application of multiple imputation by chained equations. Imputations based on the proposed model tend to have better repeated sampling properties than the default application of chained equations in this realistic setting.

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