Empirical Bayesian Methods Research Articles

Spatial extension of mixed models of the analysis of variance

ABSTRACT This study proposes a spatial extension of mixed models of the analysis of variance (MANOVA), called mixed spatial ANOVA (MS-ANOVA) models. MS-ANOVA models have been used to evaluate the spatial correlations between random effects in spatial multilevel data in which observations belong to nested clusters. Because the proposed model can be regarded as a Bayesian hierarchical model, we introduce empirical Bayesian estimation methods in which hyperparameters are estimated by quasi-maximum likelihood estimation methods in the first step, and posterior distributions for the parameters are evaluated with the estimated hyperparameters in the second step. Moreover, we justify the asymptotic properties of the first-step estimator. The proposed models were applied to happiness survey data collected in Japan. Empirical results show that social capital, which can be interpreted as ‘the beliefs and norms by which a community values collective action and pursues activities worthy for the entire community’, significantly increases people’s happiness, even after controlling for various individual characteristics and spatial correlations.

Finite sample inference for empirical Bayesian methods

AbstractIn recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real‐life problems, especially in complex and high‐dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the Universal Inference framework, we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.

Reliability analysis of bathtub-shaped distribution using empirical Bayesian and E-Bayesian estimations under progressive Type-II censoring

This paper investigates the performance of empirical Bayesian and E-Bayesian estimation of the bathtub-shaped distribution based on the progressive Type-II censored samples. These two estimations overcome the selection of hyperparameters in the Bayesian method. The empirical Bayesian analysis employs the classical approach to determine the hyperparameters. The E-Bayesian estimation uses the prior distribution of hyperparameters to derive the expectation of Bayesian estimates. The estimates of parameters are derived under the squared error loss and LINEX loss functions. The extensive simulations show the results of the empirical Bayesian estimates and the E-Bayesain estimates. Further, the empirical Bayesian estimation is also presented to analyze the parameters of bathtub-shaped distribution based on the general progressive Type-II censored samples. The two datasets from the electromechanical field and medical survival analysis are analyzed using the empirical Bayesian and E-Bayesian methods.

Bayesian and influence function-based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests.

In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence/credible intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of coverage probability. A real dataset from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is used to illustrate the proposedmethods.

Analysis of Empirical Bayesian Kriging Methods for Optimization of Measured Resources Estimation of Laterite Nickel

Laterite nickel deposits are formed from the intense weathering of ultramafic igneous rocks. The distribution of Ni content in an area does not always have a stationary data. One method of resource estimation and precise geological modeling is the Empirical Bayesian Kriging (EBK) method which is known to be able to perform precise estimates for stationary and non-stationary data. The results of this study were found that thickness of the limonite layer will increase as the slope decreases, while in the saprolite zone the thickness will increase with increasing the degree of slope up to the limit of 16°-25° then the thickness will decrease when crossing that limit. In the limonite zone, the concentration of Ni is maximally concentrated at a high degree of slope (>16°), while in the saprolite zone, Ni content is maximally concentrated on a slope of 16°-25° and then decreases in Ni content when passing through a slope of 25°. Validation of the estimation results and geological modeling using RMSE, MAE, MAPE, and linear regression in the limonite and saprolite zones indicate that the EBK method is a precise method for resource estimation and geological modeling.

Interferometric SAR Coherence Magnitude Estimation by Machine Learning

Current interferometric wide area ground motion services require the estimation of the coherence magnitude as accurately and computationally effectively as possible. However, a precise and at the same time computationally efficient method is missing. Therefore, the objective of this article is to improve the empirical Bayesian coherence magnitude estimation in terms of accuracy and computational cost. Precisely, this article proposes the interferometric coherence magnitude estimation by Machine Learning (ML). It results in a non-parametric and automated statistical inference. However, applying ML in this estimation context is not straightforward. The number and the domain of possible input processes is infinite and it is not possible to train all possible input signals. It is shown that the expected channel amplitudes and the expected interferometric phase cause redundancies in the input signals allowing to solve this issue. Similar to the empirical Bayesian methods, a single parameter for the maximum underlaying coherence is used to model the prior. However, no prior or any shape of prior probability is easy to implement within the ML framework. The article reports on the bias, the standard deviation and the root mean square error (RMSE) of the developed estimators. It was found that ML estimators improve the coherence estimation RMSE from small samples ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2 N &lt; 30$</tex-math></inline-formula> ) and for small underlaying coherence compared to the conventional and empirical Bayes estimators. For three interferometric samples ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N = 3$</tex-math></inline-formula> ) and a zero coherence magnitude, the bias related to the sample estimator improves from 0.53 to 0.39 by 27.8%. Assuming the maximum underlaying coherence is 0.6, the bias is reduced by 33.0% to 0.36 for the less strict and by 45.5% to 0.29 for the strict prior. The developed ML coherence magnitude estimators are suitable and recommended for operational InSAR systems. For the estimation, the ML model is extremely fast evaluated because no iteration, numeric integration or Bootstrapping is needed.

Multifidelity Model Calibration in Structural Dynamics Using Stochastic Variational Inference on Manifolds.

Bayesian techniques for engineering problems, which rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian process based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

Bayesian estimation for the Tukey GH distribution with an application

Tukey GH is a transformed normal distribution, having two parameters (g,h). The g parameter represents skew measuring, and the h represents kurtosis measuring. Our motivation is to affect these parameters on the behavior for a simulation data and real data, such as the Iraqi stock market Index (ISX60) and the Standard and Poor’s (SP500) index using the Bayesian framework. Then, our aim is to find the estimation for the parameters in this distribution using empirical and parametric Bayesian methods, and study the effective on the simulation and real data. The simulation study will be shown the behavior of the parameters with a different number of sampling and prior distributions. We will use the real data from ISX60 and SP500 index.

Spatial and temporal distribution and influencing factor analysis of the malignant tumor mortality rate around the mining area.

Mining activities can threaten residents' health even lives. Integrating spatial empirical Bayesian smoothing, joinpoint regression and spatiotemporal scanning methods, we analyzed aggregations and possible factors of four tumor mortality rates at township and village scales from 2012 to 2016 in Suxian district of Hunan Province, China. Results indicate: (1) Mortality rates were ranked: lung cancer > liver cancer > gastric cancer > colorectal cancer. (2) Lung cancer had a higher five-year mortality rate in the middle; relative risk (RR) of death from lung cancer from 2012 to 2015 in Xujiadong Village was 7.48. Liver cancer had a higher five-year mortality rate in the Middle West; RR in areas centered on Nanta Street with a radius of 9.87km from 2015 to 2016, was 1.83. Gastric cancer had a higher five-year mortality rate in the east; RR in Xujiadong Village from 2012 to 2014 was 6.9. Five-year mortality rate of colorectal cancer was higher in the northwest; RR in regions centered on Huangcao Village with a radius of 12.11km in 2016, was 2.88. (3) Pollution from ore mining and smelting, heavy metal and non-metallic, and mine transportation were the main possible factors. This research provides a method reference for studying spatiotemporal patterns of disease in China even the world.

Revisiting Empirical Bayes Methods and Applications to Special Types of Data

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of the empirical Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider Tweedie's formula and show how it can be applied to analyze a microarray dataset. The application of the formula is simplified with the Pearson system of distributions. Saddlepoint approximations enable us to generalize several results in this direction. The results show that the proposed methods perform well in applications to real data sets.

Adverse events reported to the U.S. Food and Drug Administration Adverse Event Reporting System for tisagenlecleucel.

The U.S. Food and Drug Administration (FDA) approved the first chimeric antigen receptor T-cell therapy, tisagenlecleucel, in August 2017. We sought to describe adverse events (AEs) reported to the FDA Adverse Event Reporting System (FAERS) for tisagenlecleucel in the post-marketing period. We searched FAERS reports to identify U.S. patients treated with tisagenlecleucel between August 30, 2017-August 31, 2019. We reviewed individual reports, calculated AE frequencies and reporting rates (RRs), and used Empirical Bayesian Geometric Mean methods to identify disproportionate reporting. We identified 646 de-duplicated reports with a median age at AE of 18 (interquartile range: 11-56) years. The overall RR was 81.0%, and more than 95% of reports described a serious outcome. Cytokine release syndrome (CRS) was the most frequently reported AE (51.1%) with a RR of 41.4%; neurotoxicity was reported less frequently (21.2%), with a RR of 17.2%. Most disproportionately reported AEs were listed on the package insert or confounded by indication. We identified 13 subsequent neoplasms (SPN), the majority occurring within 6 months of tisagenlecleucel administration, and none reporting evidence of insertional mutagenesis. A total of 165 reports (26%) described a death outcome; most deaths occurred >30 days after treatment. The majority of deaths (64%) were due to progression of the underlying lymphoid neoplasm, and few (<5%) were attributed to CRS or neurotoxicity. We did not identify new safety concerns reported for tisagenlecleucel in the post-marketing period. Reporting rates for CRS and neurotoxicity were lower than identified in the prelicensure clinical trials.

Response time models separate single- and dual-process accounts of memory-based decisions

Human decisions often deviate from economic rationality and are influenced by cognitive biases. One such bias is the memory bias according to which people prefer choice options they have a better memory of—even when the options’ utilities are comparatively low. Although this phenomenon is well supported empirically, its cognitive foundation remains elusive. Here we test two conceivable computational accounts of the memory bias against each other. On the one hand, a single-process account explains the memory bias by assuming a single biased evidence-accumulation process in favor of remembered options. On the contrary, a dual-process account posits that some decisions are driven by a purely memory-driven process and others by a utility-maximizing one. We show that both accounts are indistinguishable based on choices alone as they make similar predictions with respect to the memory bias. However, they make qualitatively different predictions about response times. We tested the qualitative and quantitative predictions of both accounts on behavioral data from a memory-based decision-making task. Our results show that a single-process account provides a better account of the data, both qualitatively and quantitatively. In addition to deepening our understanding of memory-based decision-making, our study provides an example of how to rigorously compare single- versus dual-process models using empirical data and hierarchical Bayesian parameter estimation methods.

Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model

We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes over n=500, there has been much attention for alternative approaches like approximate algorithms (Gibbs sampling, variational Bayes, etc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO) or empirical Bayesian methods. However, by introducing algorithmic ideas from online sequential prediction, we show that exact calculations are feasible for much larger sample sizes: for general model selection priors we reach n=25000, and for certain spike-and-slab priors we can easily reach n=100000. We further prove a de Finetti-like result for finite sample sizes that characterizes exactly which model selection priors can be expressed as spike-and-slab priors. The computational speed and numerical accuracy of the proposed methods are demonstrated in experiments on simulated data, on a differential gene expression data set, and to compare the effect of multiple hyper-parameter settings in the beta-binomial prior. In our experimental evaluation we compute guaranteed bounds on the numerical accuracy of all new algorithms, which shows that the proposed methods are numerically reliable whereas an alternative based on long division is not.

A general Bayesian approach to meet different inferential goals in poverty research for small areas

Abstract Poverty mapping that displays spatial distribution of various poverty indices is most useful to policymakers and researchers when they are disaggregated into small geographic units, such as cities, municipalities or other administrative partitions of a country. Typically, national household surveys that contain welfare variables such as income and expenditures provide limited or no data for small areas. It is well-known that while direct survey-weighted estimates are quite reliable for national or large geographical areas they are unreliable for small geographic areas. If the objective is to find areas with extreme poverty, these direct estimates will often select small areas due to the high variability in the estimates. Empirical best prediction and Bayesian methods have been proposed to improve on the direct point estimates. These estimates are, however, not appropriate for different inferential purposes. For example, for identifying areas with extreme poverty, these estimates would often select areas with large sample sizes. In this paper, using real life data, we illustrate how appropriate Bayesian methodology can be developed to address different inferential problems.

Assessing Interpolation Methods for Accuracy of Design Groundwater Levels for Civil Projects

This research compared natural neighbor interpolation with other interpolation methods commonly implemented in ArcGIS. It evaluated the relative performance of interpolation methods for various spatial data distributions, including line transects. It characterized locations which are associated with large prediction errors. To assess the relative performance of interpolation methods, a validation procedure was used consisting of 75% training data and 25% test data. Statistical error measures were used to measure the predictive performance of the interpolation methods, and the spatial distribution of errors was used to characterize areas where interpolation methods performed poorly. Results showed that Topo to Raster, natural neighbor, ordinary kriging, and empirical Bayesian kriging methods consistently outperformed other interpolation methods for a variety of spatial distributions of the data. However, natural neighbor interpolation was unsuitable for linear transects. In general, the accuracy of most of the interpolation methods increased with narrow spatial data distributions. Spatial distribution of large prediction errors was predominantly similar, regardless of the interpolation method used, and was related to changes in physical characteristics.

Statistical inference of Type-I progressively censored step-stress accelerated life test with dependent competing risks

This paper considers a step-stress accelerated dependent competing risks model under progressively Type-I censoring schemes. The dependence structure between competing risks is modeled by a general bivariate function, the cumulative exposure model is assumed and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability under normal usage level at mission time are obtained by using the maximum likelihood method and the asymptotic normal theory. We also consider the Bayesian estimators and the highest posterior density credible intervals based on conjugate priors, E-Bayesian, hierarchical Bayesian and empirical Bayesian methods. To illustrate the proposed methodology, the Marshall-Olkin bivariate exponential distribution is used to model the dependence structure between competing risks. A Monte Carlo simulation study and a real data analysis are presented to study the performance of different estimation methods.

Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests.

In medical diagnostic studies, a diagnostic test can be evaluated based on its sensitivity under a desired specificity. Existing methods for inference on sensitivity include normal approximation-based approaches and empirical likelihood (EL)-based approaches. These methods generally have poor performance when the specificity is high, and some require choosing smoothing parameters. We propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to overcome such problems. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. The proposed methods are shown to perform better in terms of both coverage probability and interval length. A real data set from Alzheimer's Disease Neuroimaging Initiative (ANDI) is analyzed.

Zeroing in on the Expected Returns of Anomalies

We zero in on the expected returns of long-short portfolios based on 120 stock market anomalies by accounting for (1) effective bid-ask spreads, (2) post-publication effects, and (3) the modern era of trading technology that began in the early 2000s. Net of these effects, the average anomaly&amp;amp;amp;#x27;s expected return is a measly 8 bps per month. The strongest anomalies return only 10-20 bps after accounting for data-mining with either out-of-sample tests or empirical Bayesian methods. Expected returns are negligible despite cost optimizations that produce impressive net returns in-sample and the omission of additional trading costs like price impact.

Multivariate estimation of Poisson parameters

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and also the sum (or equivalently the mean) of the parameters is introduced. Under this loss function, a class of minimax estimators that uniformly dominate the maximum likelihood estimator is derived. Crucially, these methods have the property that for estimating a given component parameter, the full data vector is utilised. Estimators in this class can be fine-tuned to limit shrinkage away from the maximum likelihood estimator, thereby avoiding implausible estimates of the sum of the parameters. Further light is shed on this new class of estimators by showing that it can be derived by Bayesian and empirical Bayesian methods. In particular, we exhibit a generalisation of the Clevenson–Zidek estimator, and prove its admissibility. Moreover, a class of prior distributions for which the Bayes estimators uniformly dominate the maximum likelihood estimator under the new loss function is derived. A section is included involving weighted loss functions, notably also leading to a procedure improving uniformly on the maximum likelihood method in an infinite-dimensional setup. Importantly, some of our methods lead to constructions of new multivariate models for both rate parameters and count observations. Finally, estimators that shrink the usual estimators towards a data based point in the parameter space are derived and compared.

Comparative Analysis of Empirical Bayes and Bayesian Hierarchical Models in Hotspot Identification

Hotspot identification is an important step in the highway safety management process. Errors in hotspot identification (HSID) may result in an inefficient use of limited resources for safety improvements. The empirical Bayesian (EB) HSID has been widely applied as an effective approach in identifying hotspots. However, there are some limitations with the EB approach. It assumes that the parameter estimates of the safety performance function (SPF) are correct without any uncertainty, and does not consider temporal instability in crashes, which has been reported in recent studies. The Bayesian hierarchical model is an emerging technique that addresses the limitations of the EB method. Thus, the objective of this study is to compare the performance of the standard EB method and the Bayesian hierarchical model in identifying hotspots. Three methods (crash rate, EB, and the Bayesian hierarchical model) were applied to identify risky intersections with different significance levels. Four evaluation tests (site consistency, method consistency, total rank differences, and Poisson mean differences tests) were conducted to assess the performance of these three methods. The testing results suggest that: (1) the Bayesian hierarchical model outperforms the crash rate and the EB methods in most cases, and the Bayesian hierarchical model improves the accuracy of HSID significantly; and (2) hotspots identified with crash rates are generally unreliable. This is significant for roadway agencies and practitioners trying to accurately rank sites in the roadway network to effectively manage safety investments. Roadway agencies and practitioners are encouraged to consider the Bayesian hierarchical model in identifying hotspots.