Alex Lenkoski

Copula Gaussian graphical models and their application to modeling functional disability data

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses many studies from social science and economics. We illustrate the use of the copula Gaussian graphical models in the analysis of a 16-dimensional functional disability contingency table.

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.

Robust FDI Determinants: Bayesian Model Averaging In The Presence Of Selection Bias

The literature on Foreign Direct Investment (FDI) determinants is remarkably diverse in terms of competing theories and empirical results. We utilize Bayesian Model Averaging (BMA) to resolve the model uncertainty that surrounds the validity of the competing FDI theories. Since the structure of existing FDI data is well known to induce selection bias, we extend BMA theory to HeckitBMA in order to address model uncertainty in the presence of selection bias. We show that more than half of the previously suggested FDI determinants are not robust and highlight theories that do receive robust support from the data. Our selection approach allows us to identify the determinants of the margins of FDI (intensive and extensive), which are shown to differ profoundly. Our results suggest a new emphasis in FDI theories that explicitly identify the dynamics of the intensive and extensive FDI margins.

Multivariate probabilistic forecasting using ensemble Bayesian model averaging and copulas

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint distribution. To correct this, we propose the use of a Gaussian copula, which offers a simple procedure for recovering the dependence that is lost in the estimation of the ensemble BMA marginals. Our method is applied to 48 h forecasts of a set of five weather quantities using the eight-member University of Washington mesoscale ensemble. We show that our method recovers many well-understood dependencies between weather quantities and subsequently improves calibration and sharpness over both the raw ensemble and a method which does not incorporate joint distributional information. Copyright

Computational Aspects Related to Inference in Gaussian Graphical Models With the G-Wishart Prior

We describe a comprehensive framework for performing Bayesian inference for Gaussian graphical models based on the G-Wishart prior with a special focus on efficiently including nondecomposable graphs in the model space. We develop a new approximation method to the normalizing constant of a G-Wishart distribution based on the Laplace approximation. We review recent developments in stochastic search algorithms and propose a new method, the mode oriented stochastic search (MOSS), that extends these techniques and proves superior at quickly finding graphical models with high posterior probability. We then develop a novel stochastic search technique for multivariate regression models and conclude with a real-world example from the recent covariance estimation literature. Supplemental materials are available online.

Repeat surgery after lumbar decompression for herniated disc: the quality implications of hospital and surgeon variation.

BACKGROUND CONTEXT Repeat lumbar spine surgery is generally an undesirable outcome. Variation in repeat surgery rates may be because of patient characteristics, disease severity, or hospital- and surgeon-related factors. However, little is known about population-level variation in reoperation rates. PURPOSE To examine hospital- and surgeon-level variation in reoperation rates after lumbar herniated disc surgery and to relate these to published benchmarks. STUDY DESIGN/SETTING Retrospective analysis of a discharge registry including all nonfederal hospitals in Washington State. METHODS We identified adults who underwent an initial inpatient lumbar decompression for herniated disc from 1997 to 2007. We then performed generalized linear mixed-effect logistic regressions, controlling for patient characteristics and comorbidity, to examine the variation in reoperation rates within 90 days, 1 year, and 4 years. RESULTS Our cohort included 29,529 patients with a mean age of 47.5 years, 61% privately insured, and 15% having any comorbidity. The age-, sex-, insurance-, and comorbidity-adjusted mean rate of reoperation among hospitals was 1.9% at 90 days (95% confidence interval [CI], 1.2-3.1), with a range from 1.1% to 3.4%; 6.4% at 1 year (95% CI, 3.9-10.6), with a range from 2.8% to 12.5%; and 13.8% at 4 years (95% CI, 8.8-19.8), with a range from 8.1% to 24.5%. The adjusted mean reoperation rates of surgeons were 1.9% at 90 days (95% CI, 1.4-2.4) with a range from 1.2% to 4.6%, 6.1% at 1 year (95% CI, 4.8-7.7) with a range from 4.3% to 10.5%, and 13.2% at 4 years (95% CI, 11.3-15.5) with a range from 10.0% to 19.3%. Multilevel random-effect models suggested that variation across surgeons was greater than that of hospitals and that this effect increased with long-term outcomes. CONCLUSIONS Even after adjusting for patient demographics and comorbidity, we observed a large variation in reoperation rates across hospitals and surgeons after lumbar discectomy, a relatively simple spinal procedure. These findings suggest uncertainty about indications for repeat surgery, variations in perioperative care, or variations in quality of care.

Sparse covariance estimation in heterogeneous samples

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era.

Hierarchical Gaussian graphical models: Beyond reversible jump

The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in existence for over a decade. However, due to the lack of a direct sampler, its use has been limited in hierarchical Bayesian contexts, relegating mixing over the class of GGMs mostly to situations involving standard Gaussian likelihoods. Recent work has developed methods that couple model and parameter moves, first through reversible jump methods and later by direct evaluation of conditional Bayes factors and subsequent resampling. Further, methods for avoiding prior normalizing constant calculations-a serious bottleneck and source of numerical instability-have been proposed. We review and clarify these developments and then propose a new methodology for GGM comparison that blends many recent themes. Theoretical developments and computational timing experiments reveal an algorithm that has limited computational demands and dramatically improves on computing times of existing methods. We conclude by developing a parsimonious multivariate stochastic volatility model that embeds GGM uncertainty in a larger hierarchical framework. The method is shown to be capable of adapting to swings in market volatility, offering improved calibration of predictive distributions.

Bayesian motion estimation for dust aerosols

Dust storms in the earth’s major desert regions significantly influence microphysical weather processes, the CO2-cycle and the global climate in general. Recent increases in the spatio-temporal resolution of remote sensing instruments have created new opportunities to understand these phenomena. However, the scale of the data collected and the inherent stochasticity of the underlying process pose significant challenges, requiring a careful combination of image processing and statistical techniques. Using satellite imagery data, we develop a statistical model of atmospheric transport that relies on a latent Gaussian Markov random field (GMRF) for inference. In doing so, we make a link between the optical flow method of Horn and Schunck and the formulation of the transport process as a latent field in a generalized linear model. We critically extend this framework to satisfy the integrated continuity equation, thereby incorporating a flow field with nonzero divergence, and show that such an approach dramatically improves performance while remaining computationally feasible. Effects such as air compressibility and satellite column projection hence become intrinsic parts of this model. We conclude with a study of the dynamics of dust storms formed over Saharan Africa and show that our methodology is able to accurately and coherently track storm movement, a critical problem in this field.