arXiv subjects

P. Richard Hahn

Publications and source records attributed to P. Richard Hahn.

36 records · Page 2Linked to original sources

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.

stat.ME↗

arXiv2019

An illustration of the risk of borrowing information via a shared likelihood

A concrete, stylized example illustrates that inferences may be degraded, rather than improved, by incorporating supplementary data via a joint likelihood. In the example, the likelihood is assumed to be correctly specified, as is the prior over the parameter of interest; all that is necessary for the joint modeling approach to suffer is misspecification of the prior over a nuisance parameter.

stat.OT↗

arXiv2019

XBART: Accelerated Bayesian Additive Regression Trees

Bayesian additive regression trees (BART) (Chipman et. al., 2010) is a powerful predictive model that often outperforms alternative models at out-of-sample prediction. BART is especially well-suited to settings with unstructured predictor variables and substantial sources of unmeasured variation as is typical in the social, behavioral and health sciences. This paper develops a modified version of BART that is amenable to fast posterior estimation. We present a stochastic hill climbing algorithm that matches the remarkable predictive accuracy of previous BART implementations, but is many times faster and less memory intensive. Simulation studies show that the new method is comparable in computation time and more accurate at function estimation than both random forests and gradient boosting.

stat.ML↗

arXiv2018

Efficient sampling for Gaussian linear regression with arbitrary priors

This paper develops a slice sampler for Bayesian linear regression models with arbitrary priors. The new sampler has two advantages over current approaches. One, it is faster than many custom implementations that rely on auxiliary latent variables, if the number of regressors is large. Two, it can be used with any prior with a density function that can be evaluated up to a normalizing constant, making it ideal for investigating the properties of new shrinkage priors without having to develop custom sampling algorithms. The new sampler takes advantage of the special structure of the linear regression likelihood, allowing it to produce better effective sample size per second than common alternative approaches.

stat.CO↗

arXiv2017

Regret-based Selection for Sparse Dynamic Portfolios

This paper considers portfolio construction in a dynamic setting. We specify a loss function comprised of utility and complexity components with an unknown tradeoff parameter. We develop a novel regret-based criterion for selecting the tradeoff parameter to construct optimal sparse portfolios over time.

q-fin.PM↗

arXiv2017

On recursive Bayesian predictive distributions

A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive. This paper shows that online Bayesian prediction is possible by characterizing the Bayesian predictive update in terms of a bivariate copula, making it unnecessary to pass through the posterior to update the predictive. In standard models, the Bayesian predictive update corresponds to familiar choices of copula but, in nonparametric problems, the appropriate copula may not have a closed-form expression. In such cases, our new perspective suggests a fast recursive approximation to the predictive density, in the spirit of Newton's predictive recursion algorithm, but without requiring evaluation of normalizing constants. Consistency of the new algorithm is shown, and numerical examples demonstrate its quality performance in finite-samples compared to fully Bayesian and kernel methods.

stat.ME↗

arXiv2017

A finite mixture model approach to regression under covariate misclassification

This paper considers the problem of mismeasured categorical covariates in the context of regression modeling; if unaccounted for, such misclassification is known to result in misestimation of model parameters. Here, we exploit the fact that explicitly modeling covariate misclassification leads to a mixture representation. Assuming common parametric families for the mixture components, and assuming that the misclassification occurrence is independent of the response variable, the mixture representation permits model parameters to be identified even when misclassification probabilities are unknown. Previous approaches to covariate misclassification use multiple surrogate covariates and/or validation data on the magnitude of errors. Based on this mixture structure, we demonstrate that valid inference can be performed on all the parameters even when no such additional information is available. Using Bayesian inference, the method allows for learning from data combined with external information on the magnitude of errors when such information does become available. The method is applied to adjust for misclassification on self-reported cocaine use in the Longitudinal Studies of HIV-Associated Lung Infections and Complications (Lung HIV). We find a substantial and statistically significant effect of cocaine use on pulmonary complications measured by the relative area of emphysema, whereas a regression that does not adjust for misclassification yields a much smaller estimate.

math.ST↗

arXiv2016

Regularization and confounding in linear regression for treatment effect estimation

This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of regularization-induced confounding is introduced, which refers to the tendency of regularization priors to adversely bias treatment effect estimates by over-shrinking control variable regression coefficients. Then, a simultaneous regression model is presented which permits regularization priors to be specified in a way that avoids this unintentional re-confounding. The new model is illustrated on synthetic and empirical data.

stat.ME↗

arXiv2016

Sparse Mean-Variance Portfolios: A Penalized Utility Approach

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many potential assets while acknowledging uncertainty in asset returns and parameter estimates. We demonstrate the procedure using static and dynamic models for asset returns.

q-fin.ST↗

arXiv2016

Variable Selection in Seemingly Unrelated Regressions with Random Predictors

This paper considers linear model selection when the response is vector-valued and the predictors are randomly observed. We propose a new approach that decouples statistical inference from the selection step in a "post-inference model summarization" strategy. We study the impact of predictor uncertainty on the model selection procedure. The method is demonstrated through an application to asset pricing.

stat.ME↗

arXiv2015

Optimal ETF Selection for Passive Investing

This paper considers the problem of isolating a small number of exchange traded funds (ETFs) that suffice to capture the fundamental dimensions of variation in U.S. financial markets. First, the data is fit to a vector-valued Bayesian regression model, which is a matrix-variate generalization of the well known stochastic search variable selection (SSVS) of George and McCulloch (1993). ETF selection is then performed using the decoupled shrinkage and selection (DSS) procedure described in Hahn and Carvalho (2015), adapted in two ways: to the vector-response setting and to incorporate stochastic covariates. The selected set of ETFs is obtained under a number of different penalty and modeling choices. Optimal portfolios are constructed from selected ETFs by maximizing the Sharpe ratio posterior mean, and they are compared to the (unknown) optimal portfolio based on the full Bayesian model. We compare our selection results to popular ETF advisor Wealthfront.com. Additionally, we consider selecting ETFs by modeling a large set of mutual funds.

q-fin.ST↗

arXiv2015

A Bayesian partial identification approach to inferring the prevalence of accounting misconduct

This paper describes the use of flexible Bayesian regression models for estimating a partially identified probability function. Our approach permits efficient sensitivity analysis concerning the posterior impact of priors on the partially identified component of the regression model. The new methodology is illustrated on an important problem where only partially observed data is available - inferring the prevalence of accounting misconduct among publicly traded U.S. businesses.

stat.ME↗

arXiv2015

Model specification via sequential coherence and backward induction

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new approach is applied to a kernel density estimator, which leads to a novel method for computing point-wise credible intervals in nonparametric density estimation. The new approach has two additional advantages; 1) the posterior mean density can be accurately approximated without resorting to Monte Carlo simulation and 2) concentration bounds are easily established as a function of sample size.

stat.ME↗

arXiv2014

A Bayesian hierarchical model for inferring player strategy types in a number guessing game

This paper presents an in-depth statistical analysis of an experiment designed to measure the extent to which players in a simple game behave according to a popular behavioral economic model. The p-beauty contest is a multi-player number guessing game that has been widely used to study strategic behavior. This paper describes beauty contest experiments for an audience of data analysts, with a special focus on a class of models for game play called k-step thinking models, which allow each player in the game to employ an idiosyncratic strategy. We fit a Bayesian statistical model to estimate the proportion of our player population whose game play is compatible with a k-step thinking model. Our findings put this number at approximately 25%.

stat.AP↗

arXiv2014

Shrinkage priors for linear instrumental variable models with many instruments

This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many instruments setting. The prior is constructed based on a factor model decomposition of the matrix of observed instruments, allowing many instruments to be incorporated into the analysis in a robust way. Second, the new prior is implemented via an importance sampling scheme, which utilizes posterior Monte Carlo samples from a first-stage Bayesian regression analysis. This modular computation makes sensitivity analyses straightforward. Two simulation studies are provided to demonstrate the advantages of the new method. As an empirical illustration, the new method is used to estimate a key parameter in macro-economic models: the elasticity of inter-temporal substitution. The empirical analysis produces substantive conclusions in line with previous studies, but certain inconsistencies of earlier analyses are resolved.

stat.ME↗

arXiv2014

Decoupling shrinkage and selection in Bayesian linear models: a posterior summary perspective

Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

stat.ME↗

arXiv2014

A Structural Approach to Coordinate-Free Statistics

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, we construct a version of the Ordinary Least Squares estimator in absolute generality. Our Gauss-Markov theorem demonstrates that OLS is a "best linear unbiased estimator", extending the classical result. We construct a stochastic version of the OLS estimator, which is a continuous disintegration exactly for the class of "uncorrelated implies independent" (UII) measures. As a consequence, Gaussian measures always exhibit continuous disintegrations through continuous linear maps, extending a theorem of the first author. Applying this framework to some problems in machine learning, we prove a useful representation theorem for covariance tensors, and show that OLS defines a good kriging predictor for vector-valued arrays on general index spaces. We also construct a support-vector machine classifier in this setting. We hope that our article shines light on some deeper connections between probability theory, statistics and machine learning, and may serve as a point of intersection for these three communities.

math.PR↗

arXiv2010

Predictor-dependent shrinkage for linear regression via partial factor modeling

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $π(Y,X)$, rather than a purely conditional model, $π(Y \mid X)$, where $Y$ is a scalar response variable and $X$ is a vector of predictors. This approach is motivated by the fact that in many situations the marginal predictor distribution $π(X)$ can provide useful information about the parameter values governing the conditional regression. However, under very mild misspecification, this marginal distribution can also lead conditional inferences astray. Here, we explore these ideas in the context of linear factor models, to understand how they play out in a familiar setting. The resulting Bayesian model performs well across a wide range of covariance structures, on real and simulated data.

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