Empirical Bayes Approach Research Articles

Robust empirical Bayes approach for Markov chain modeling of air pollution index.

The online version contains supplementary material available at 10.1007/s40201-020-00607-4.

An Empirical Bayes approach for the identification of long-range chromosomal interaction from Hi-C data.

Hi-C experiments have become very popular for studying the 3D genome structure in recent years. Identification of long-range chromosomal interaction, i.e.,peak detection, is crucial for Hi-C data analysis. But it remains a challenging task due to the inherent high dimensionality, sparsity and the over-dispersion of the Hi-C count data matrix. We propose EBHiC, an empirical Bayes approach for peak detection from Hi-C data. The proposed framework provides flexible over-dispersion modeling by explicitly including the "true" interaction intensities as latent variables. To implement the proposed peak identification method (via the empirical Bayes test), we estimate the overall distributions of the observed counts semiparametrically using a Smoothed Expectation Maximization algorithm, and the empirical null based on the zero assumption. We conducted extensive simulations to validate and evaluate the performance of our proposed approach and applied it to real datasets. Our results suggest that EBHiC can identify better peaks in terms of accuracy, biological interpretability, and the consistency across biological replicates. The source code is available on Github (https://github.com/QiZhangStat/EBHiC).

Efficient Detection in Large-Scale Testing

Large-scale inference has become increasingly popular in financial economics. I explore an empirical Bayes approach to large-scale multiple testing. The proposed approach bases its inference on the posterior probability that the null is true given the observed data. It provides a convenient way to establish data-driven $t$-stat hurdles associated with a prespecified false discovery rate or a weighted combination of the false discovery rate and false nondiscovery rate. Applying the method to meta-analysis of market anomalies, the factor zoo that is characterized by both multiple testing and p-hacking, and fund performance evaluation, I show that appropriate t-hurdles need to be raised substantially.

Double Empirical Bayes Testing.

Analyzing data from large-scale, multi-experiment studies requires scientists to both analyze each experiment and to assess the results as a whole. In this article, we develop double empirical Bayes testing (DEBT), an empirical Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. DEBT is a two-stage method: in the first stage, it reports which experiments yielded significant outcomes; in the second stage, it hypothesizes which covariates drive the experimental significance. In both of its stages, DEBT builds on Efron (2008), which lays out an elegant empirical Bayes approach to testing. DEBT enhances this framework by learning a series of black box predictive models to boost power and control the false discovery rate (FDR). In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, it uses an empirical Bayes version of the knockoff filter (Candes et al., 2018) to select covariates that have significant predictive power of Stage-1 significance. In both simulated and real data, DEBT increases the proportion of discovered significant outcomes and selects more features when signals are weak. In a real study of cancer cell lines, DEBT selects a robust set of biologically-plausible genomic drivers of drug sensitivity and resistance in cancer.

GARPOS: Analysis Software for the GNSS‐A Seafloor Positioning With Simultaneous Estimation of Sound Speed Structure

Global Navigation Satellite System–Acoustic ranging combined seafloor geodetic technique (GNSS-A) has extended the geodetic observation network into the ocean. The key issue for analyzing the GNSS-A data is how to correct the effect of sound speed variation in the seawater. We constructed a generalized observation equation and developed a method to directly extract the gradient sound speed structure by introducing appropriate statistical properties in the observation equation, especially the data correlation term. In the proposed scheme, we calculate the posterior probability based on the empirical Bayes approach using the Akaike’s Bayesian Information Criterion for model selection. This approach enabled us to suppress the overfitting of sound speed variables and thus to extract simpler sound speed field and stable seafloor positions from the GNSS-A dataset. The proposed procedure is implemented in the Python-based software “GARPOS” (GNSS-Acoustic Ranging combined POsitioning Solver).

A nonparametric empirical Bayes approach to large-scale multivariate regression

Multivariate regression has many applications, ranging from time series prediction to genomics. Borrowing information across the outcomes can improve prediction error, even when outcomes are statistically independent. Many methods exist to implement this strategy, for example the multiresponse lasso, but choosing the optimal method for a given dataset is difficult. These issues are addressed by establishing a connection between multivariate linear regression and compound decision problems. A nonparametric empirical Bayes procedure that can learn the optimal regression method from the data itself is proposed. Furthermore, the proposed procedure is free of tuning parameters and performs well in simulations and in a multiple stock price prediction problem.

Joint modeling of time-varying HIV exposure and infection for estimation of per-act efficacy in HIV prevention trials.

Using the MTN-020/ASPIRE HIV prevention trial as a motivating example, our objective is to construct a joint model for the HIV exposure process through vaginal intercourse and the time to HIV infection in a population of sexually active women. By modeling participants' HIV infection in terms of exposures, rather than time exposed, our aim is to obtain a valid estimate of the per-act efficacy of a preventive intervention. Within the context of HIV prevention trials, in which the frequency of sex acts is self-reported periodically by the participants, we model the exposure process of the trial participants with a non-homogeneous Poisson process. This approach allows for variability in the rate of sexual contacts between participants as well as variability in the rate of sexual contacts over time. The time to HIV infection for each participant is modeled as the time to the exposure that results in HIV infection, based on the modeled sexual contact rate. We propose an empirical Bayes approach for estimation. We report the results of a simulation study where we evaluate the performance of our proposed approachandcompareittothetraditionalapproachofestimatingtheoverallreductioninHIVincidenceusing a Proportional Hazards Cox model. The proposed approach is also illustrated with data from the MTN-020/ASPIRE trial. The proposed joint modeling, along with the proposed empirical Bayes estimation approach, can provide valid estimation of the per-exposure efficacy of a preventive intervention.

Incorporating prior knowledge into regularized regression.

Associated with genomic features like gene expression, methylation and genotypes, used in statistical modeling of health outcomes, there is a rich set of meta-features like functional annotations, pathway information and knowledge from previous studies, that can be used post hoc to facilitate the interpretation of a model. However, using this meta-feature information a priori rather than post hoc can yield improved prediction performance as well as enhanced model interpretation. We propose a new penalized regression approach that allows a priori integration of external meta-features. The method extends LASSO regression by incorporating individualized penalty parameters for each regression coefficient. The penalty parameters are, in turn, modeled as a log-linear function of the meta-features and are estimated from the data using an approximate empirical Bayes approach. Optimization of the marginal likelihood on which the empirical Bayes estimation is performed using a fast and stable majorization-minimization procedure. Through simulations, we show that the proposed regression with individualized penalties can outperform the standard LASSO in terms of both parameters estimation and prediction performance when the external data is informative. We further demonstrate our approach with applications to gene expression studies of bone density and breast cancer. The methods have been implemented in the R package xtune freely available for download from https://cran.r-project.org/web/packages/xtune/index.html.

Improving Access to Treatment for Opioid Use Disorder in High-Need Areas: The Role of HRSA Health Centers.

IntroductionDespite the opioid epidemic adversely affecting areas across the U.S. for more than two decades and increasing evidence that medication-assisted treatment (MAT) is effective for patients with opioid use disorder (OUD), access to treatment is still limited. The limited access to treatment holds true in the Appalachia region despite being disproportionately affected by the crisis, particularly in rural, central Appalachia.PurposeThis research identifies opportunities for health centers located in high-need areas based on drug poisoning mortality to better meet MAT care gaps. We also provide an in-depth look at health center MAT capacity relative to need in the Appalachia region.MethodsThe analysis included county-level drug poisoning mortality data (2013–2015) from the National Center for Health Statistics (NCHS) and Health Center Program Awardee and Look-Alike data (2017) on the number of providers with a DATA waiver to provide medication-assisted treatment (MAT) and the number of patients receiving MAT for the U.S. Several geospatial methods were used including an Empirical Bayes approach to estimate drug poisoning mortality, excess risk maps to identify outliers, and the Local Moran’s I tool to identify clusters of high drug poisoning mortality counties.ResultsHigh-need counties were disproportionately located in the Appalachia region. More than 6 in 10 health centers in high-need counties have the potential to expand MAT delivery to patients.ImplicationsThe results indicate an opportunity to increase health center capacity for providing treatment for opioid use disorder in high-need areas, particularly in central and northern Appalachia.

Irrational Exuberance: Correcting Bias in Probability Estimates

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach “excess certainty adjusted probabilities” (ECAP), using a variant of Tweedie’s formula, which updates probability estimates to correct for selection bias. ECAP is a flexible nonparametric method, which directly estimates the score function associated with the probability estimates, so it does not need to make any restrictive assumptions about the prior on the true probabilities. ECAP also works well in settings where the probability estimates are biased. We demonstrate through theoretical results, simulations, and an analysis of two real world datasets, that ECAP can provide significant improvements over the original probability estimates. Supplementary materials for this article are available online.

A graphical approach to assess the goodness-of-fit of random-effects linear models when the goal is to measure individual benefits of medical treatments in severely ill patients

BackgroundTwo-dimensional personalized medicine (2-PM) models are tools for measuring individual benefits of medical treatments for chronic diseases which have potential applications in personalized medicine. These models assume normality for the distribution of random effects. It is necessary to examine the appropriateness of this assumption. Here, we propose a graphical approach to assessing the goodness-of-fit of 2-PM models with continuous responses.MethodsWe propose benefit quantile-quantile (BQQ) plots which compare the empirical quantiles of individual benefits from a patient sample predicted through an empirical Bayes (EB) approach versus the quantiles of the theoretical distribution of individual benefits derived from the assumption of normality for the random effects. We examine the performance of the approach by conducting a simulation study that compared 2-PM models with non-normal distributions for the random effects versus models with comparable normal distributions. Cramer-von Mises discrepancies were used to quantify the performance of the approach. The approach was illustrated with data from a clinical trial of imipramine for patients with depression.ResultsSimulations showed that BQQ plots were able to capture deviations from the normality assumption for the random effects and did not show any asymmetric deviations from the y = x line when the random effects were normally distributed. For the depression data, the points of the BQQ plot were scattered around closely to the y = x line, without presenting any asymmetric deviations. This implied the adequacy of the normality assumption for the random effects and the goodness-of-fit of the 2-PM model for the imipramine data.ConclusionBQQ plots are sensitive to violations of the normality assumption for the random effects, suggesting that the approach is a useful tool for examining the goodness-of-fit of random-effects linear models when the goal is to measure individual treatment benefits.

A comparative analysis of intersection hotspot identification: Fixed vs. varying dispersion parameters in negative binomial models

Network screening for crash hotspots is the first step in roadway safety management. The empirical Bayes (EB) method has been widely used for ranking sites. In the EB process, the most frequently used model for developing safety performance functions (SPFs) is the negative binomial (NB) regression model, in which the dispersion parameter plays a critical role. There are primarily two forms of the dispersion parameter: fixed and varying. Previous studies showed that SPFs with varying dispersion parameters had better performance in modeling crash estimations, and the Highway Safety Manual has adopted the varying form for segment SPFs. However, a comparative analysis of hotspot identification with fixed and varying dispersion parameters for intersections has not yet been well studied. Moreover, this paper includes a thorough exploration of the varying dispersion parameters with five different functional forms at 1,943 unsignalized intersections in Texas. To evaluate the intersection SPFs, the authors implement three hotspot identification tests in addition to model statistical fit. Two EB approaches with proposed varying dispersion parameters were found superior to the EB approach with a fixed dispersion parameter in hotspot identification. Safety analysts and practitioners are encouraged to consider varying forms of dispersion parameter when analyzing intersection crashes.

An empirical Bayes approach to normalization and differential abundance testing for microbiome data

BackgroundAdvances in DNA sequencing have offered researchers an unprecedented opportunity to better study the variety of species living in and on the human body. However, the analysis of microbiome data is complicated by several challenges. First, the sequencing depth may vary by orders of magnitude across samples. Second, species are rare and the data often contain many zeros. Third, the specimen is a fraction of the microbial ecosystem, and so the data are compositional carrying only relative information. Other characteristics of microbiome data include pronounced over-dispersion in taxon abundances, and the existence of a phylogenetic tree that relates all bacterial species. To address some of these challenges, microbiome analysis workflows often normalize the read counts prior to downstream analysis. However, there are limitations in the current literature on the normalization of microbiome data.ResultsUnder the multinomial distribution for the read counts and a prior for the unknown proportions, we propose an empirical Bayes approach to microbiome data normalization. Using a tree-based extension of the Dirichlet prior, we further extend our method by incorporating the phylogenetic tree into the normalization process. We study the impact of normalization on differential abundance analysis. In the presence of tree structure, we propose a phylogeny-aware detection procedure.ConclusionsExtensive simulations and gut microbiome data applications are conducted to demonstrate the superior performance of our empirical Bayes method over other normalization methods, and over commonly-used methods for differential abundance testing. Original R scripts are available at GitHub (https://github.com/liudoubletian/eBay).

Optimal Stopping and Worker Selection in Crowdsourcing: an Adaptive Sequential Probability Ratio Test Framework

In this study, we solve a class of multiple testing problems under a Bayesian sequential decision framework. Our work is motivated by binary labeling tasks in crowdsourcing, where a requestor needs to simultaneously choose a worker to provide a label and decide when to stop collecting labels, under a certain budget constraint. We begin by using a binary hypothesis testing problem to determine the true label of a single object, and provide an optimal solution by casting it under an adaptive sequential probability ratio test framework. Then, we characterize the structure of the optimal solution, that is, the optimal adaptive sequential design, which minimizes the Bayes risk using a log-likelihood ratio statistic. We also develop a dynamic programming algorithm to efficiently compute the optimal solution. For the multiple testing problem, we propose an empirical Bayes approach for estimating the class priors, and show that the average loss of our method converges to the minimal Bayes risk under the true model. Experiments on both simulated and real data show the robustness of our method, as well as its superiority over existing methods in terms of its labeling accuracy.

Efficient screening of predictive biomarkers for individual treatment selection.

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available treatments. However, due to the large number of candidate biomarkers in the large-scale genetic and molecular studies, and complex relationships among clinical outcome, biomarkers, and treatments, the ordinary statistical tests for the interactions between treatments and covariates have difficulties from their limited statistical powers. In this paper, we propose an efficient method for detecting predictive biomarkers. We employ weighted loss functions of Chen etal. to directly estimate individual treatment scores and propose synthetic posterior inference for effect sizes of biomarkers. We develop an empirical Bayes approach, namely, we estimate unknown hyperparameters in the prior distribution based on data. We then provide efficient screening methods for the candidate biomarkers via optimal discovery procedure with adequate control of false discovery rate. The proposed method is demonstrated in simulation studies and an application to a breast cancer clinical study in which the proposed method was shown to detect the much larger numbers of significant biomarkers than existing standardmethods.

A Nonparametric Bayesian Approach to the Rare Type Match Problem

The “rare type match problem” is the situation in which, in a criminal case, the suspect’s DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. Ideally, the evaluation of this observed match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) should be based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions and discards the information about the names of the different DNA profiles. This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation.

Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes

Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose MOdel Priors with Empirical Bayes using DNN (MOPED) method to choose informed weight priors in Bayesian neural networks. We formulate a two-stage hierarchical modeling, first find the maximum likelihood estimates of weights with DNN, and then set the weight priors using empirical Bayes approach to infer the posterior with variational inference. We empirically evaluate the proposed approach on real-world tasks including image classification, video activity recognition and audio classification with varying complex neural network architectures. We also evaluate our proposed approach on diabetic retinopathy diagnosis task and benchmark with the state-of-the-art Bayesian deep learning techniques. We demonstrate MOPED method enables scalable variational inference and provides reliable uncertainty quantification.

Development of crash modification factors for intersections in Toowoomba city

ABSTRACT This research outlines the analytical approaches that may be employed to recommend multiple treatments for application to improve safety level at hazardous intersections in regional areas. Data from 106 intersections in the regional city of Toowoomba, Queensland, Australia were used in modelling and subsequent analysis. Specifically, crash prediction models were developed to estimate crash modification factors that could be used to propose remedial measures. A total of sixteen geometric and operational conditions were used as explanatory variables including the number of legs at an intersection, the availability of entering and exiting via through lanes, the presence of left-turning lanes, right-turning lanes, slip lanes, median islands, traffic control, and speed limits on the feed roads. The Empirical Bayes approach was employed to identify five hazardous intersections in Toowoomba for further investigation. The four most suitable techniques for estimating combined crash modification factors were reviewed and then used to propose effective road safety measures for the five selected hazardous intersections. Finally, this research suggests four future areas worthy of further investigation. Highlights Estimated the number of road crashes at intersections using crash prediction models. Applied the Empirical Bayes method to identify the most hazardous intersections. Combined crash modifications factors were calculated using various techniques. Identified the effective countermeasures to reduce the road crashes at hazardous intersections.

Hierarchical Bayes Approach to Estimate the Treatment Effect for Randomized Controlled Trials.

One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.

Evaluation of Section Speed Enforcement System Using Empirical Bayes Approach and Turning Point Analysis

Speeding is a major risk factor for traffic-related injuries. As a countermeasure against speeding, automated speed enforcement systems (ASES) have been deployed in many countries. However, drivers’ awareness of enforcement locations allows themselves to adjust vehicle speeds in the vicinity of the enforcement locations. This enforcement avoidance behavior leads to a criticism of the effectiveness of ASES, in which the system promotes abrupt changes in vehicle speed near enforcement locations, increasing crash risk as a side effect. To address this issue, the section speed enforcement system (SSES), which enforces overspeeding vehicles by their average travel speed over a section, has been devised. In this study, we evaluate traffic speed and safety data that were collected from sections with SSES on Korean expressways. The speed analysis showed that the vehicles reduced their speeds inside the enforcement section, and this reduction in speed variations across vehicles was also noticeable, signifying that the risk of traffic crash should be lower. In view of this, we have performed before and after comparative analysis using the empirical Bayes method with the comparison group. The outcomes estimate 43% reduction in crash occurrence after installation of SSES. Furthermore, turning point analysis confirmed that the reduction in crash occurrence ensued immediately after installation of SSES.