Supplementary Material Online Research Articles

Multi-Domain Sampling With Applications to Structural Inference of Bayesian Networks

When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditional expectations on domains of attraction, which are much more informative than the mean and other unconditional expectations. A computational method, the multi-domain sampler, is developed to construct domain-based representations for an arbitrary multimodal distribution. The multi-domain sampler is applied to structural learning of protein-signaling networks from high-throughput single-cell data, where a signaling network is modeled as a causal Bayesian network. Not only does our method provide a detailed landscape of the posterior distribution but also improves the accuracy and the predictive power of estimated networks. This article has supplementary material online.

Multivariate Spatial Analysis of Climate Change Projections

The goal of this work is to characterize the annual temperature for regional climate models. Of interest for impacts studies, these profiles and the potential change in these profiles are a new way to describe climate change and the inherent uncertainty. To that end, we propose a Bayesian hierarchical spatial model to simultaneously model the temperature profile for the four seasons of the year, current and future. These profiles are then analyzed focusing on understanding how they change over time, how they vary spatially, and how they vary between five different regional climate models. The results show that for temperature, the regional models have different profile shapes depending on a number of factors including spatial location, driving climate model, and regional climate model. This article has supplementary material online.

Quantifying Simulator Discrepancy in Discrete-Time Dynamical Simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum-likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall-runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules. This article has supplementary material online.

Flexible Bivariate Count Data Regression Models

The paper develops a semiparametric estimation method for the bivariate count data regression model. We develop a series expansion approach in which dependence between count variables is introduced by means of stochastically related unobserved heterogeneity components, and in which, unlike existing commonly used models, positive as well as negative correlations are allowed. Extensions that accommodate excess zeros, censored data and multivariate generalizations are also given. Monte Carlo experiments and an empirical application to tobacco use confirms that the model performs well relative to existing bivariate models, in terms of various statistical criteria and in capturing the range of correlation among dependent variables. This article has supplementary materials online.

Statistical Accuracy of Spreadsheet Software

As the use of spreadsheet packages for statistical analysis increases, so does the need for assessing the reliability of these packages. This study compares the accuracy of six spreadsheet packages: Excel, Google Docs, Gnumeric, Numbers, OpenOffice Calc, and Quattro Pro. The National Institute of Standards and Technology (NIST) compiled sets of data specifically to test for computational accuracy. Certified statistically accurate computations for standard statistical procedures accompany these datasets. This study analyzes the accuracy of summary statistics such as the mean, standard deviation, and autocorrelation as well as the F statistics for a one-way ANOVA, and the coefficients and R2statistics in regression analysis using the Statistical Reference Datasets (StRD) provided by NIST. Wilkinson’s Tests are also examined to document a package’s ability to perform rounding, univariate statistics, scatterplots, and regression/correlation with particularly challenging data. The final analysis reports the accuracy of probability and percentile computations involving statistical distributions. The results suggest that Gnumeric is the most reliable both in performing statistical analysis and for calculations involving statistical distributions. Google Docs spreadsheet, while convenient, has deficiencies and should not be used for scientific statistical analysis. This article has supplementary material online.

On Nonparametric Statistical Process Control of Univariate Processes

This article considers statistical process control (SPC) of univariate processes when the parametric form of the process distribution is unavailable. Most existing SPC procedures are based on the assumption that a parametric form (e.g., normal) of the process distribution can be specified beforehand. In the literature, it has been demonstrated that their performance is unreliable in cases when the prespecified process distribution is invalid. To overcome this limitation, some nonparametric (or distribution-free) SPC charts have been proposed, most of which are based on the ordering information of the observed data. This article tries to make two contributions to the nonparametric SPC literature. First, we propose an alternative framework for constructing nonparametric control charts, by first categorizing observed data and then applying categorical data analysis methods to SPC. Under this framework, some new nonparametric control charts are proposed. Second, we compare our proposed control charts with several representative existing control charts in various cases. Some empirical guidelines are provided for users to choose a proper nonparametric control chart for a specific application. This article has supplementary materials online.

Two-Way MANOVA With Unequal Cell Sizes and Unequal Cell Covariance Matrices

In this article, we propose and study an approximate Hotelling T2 (AHT) test for heteroscedastic two-way MANOVA. The AHT test is shown to be invariant under affine-transformations, different choices of the contrast matrix used to define the same hypothesis, and different labeling schemes of the cell mean vectors. We demonstrate via intensive simulations that the AHT test generally performs well and outperforms two existing approaches in terms of size and power. An extension of the AHT test for heteroscedastic multi-way MANOVA is briefly described. A dataset from a smoking cessation trial is analyzed to illustrate the methodologies. This article has supplementary material online in a single archive.

Optimization of Designed Experiments Based on Multiple Criteria Utilizing a Pareto Frontier

Balancing competing objectives to select an optimal design of experiments involves flexibly combining measures to select a winner. The Pareto front approach for simultaneously considering multiple responses is adapted to design of experiments. The Pareto approach identifies a suite of potential best designs based on different emphases of the objectives. We propose a new algorithm, the Pareto Aggregating Point Exchange (PAPE) algorithm, to more efficiently explore candidate designs by populating the Pareto frontier with all possible contending designs identified during the search. The connection between the Pareto and the Derringer–Suich (1980) desirability function approaches is established and graphical methods are given which enable the user to easily explore design robustness to different weightings of the competing objectives as well as trade-offs between criteria among competing designs. The method is illustrated with two examples: a screening design setting in which it is of interest to simultaneously consider D-efficiency and protect against model misspecification, and a robust parameter design example where simultaneous consideration of Ds-mean, Ds-variance, and design size is of interest. This article has supplementary material online.

Inference on Partially Observed Quasi-stationary Markov Chains With Applications to Multistate Population Models

If the full capture histories of captured individuals are available, inferences on multistate open population models may be conducted using the well known Arnason–Schwarz model. However, data of this detail is not always available. It is well known that inference on the transition probabilities of a Markov chain may be conducted using aggregate data and we extend this approach to aggregate data on multistate open population models. We show that for parameters to be identifiable we need to augment the aggregate data and we achieve this by batch marking a cohort of individuals according to their initial state, so that the batch marking augments the aggregate data. Model performance is examined by conducting several simulation studies and the model is applied to a real data set where full capture histories are available so it may be compared with the Arnason–Schwarz estimates. This article has supplementary material online.

Homogenous and Heterogenous Contestants in Piece Rate Tournaments: Theory and Empirical Analysis

In this article we show that sorting different ability contestants in piece rate tournaments into more homogenous groups alters agents’ incentives to exert effort. We propose a method for structurally estimating the piece rate tournament game with heterogenous players and apply it to the payroll data from a broiler production contract. Our counterfactual analysis shows that under reasonable assumptions, both the principal and the growers can gain when the tournament groups are heterogenized. This business strategy could be difficult to implement in real-life settings, however. This article has supplementary material online.

Score Tests for Hyperbolic GARCH Models

Davidson (2004) recently proposed the hyperbolic GARCH model to capture the phenomenon of long-range dependence in volatility, with the extent of such dependence measured by the geometric or hyperbolic decay of the coefficients in an ARCH(∞) model. In this article, we reinterpret the hyperbolic GARCH model by building a link with the common GARCH model, and construct a simplified score test to check the presence of the hyperbolic decay. We derive the asymptotic of the test statistic under the null hypothesis and the local alternatives. We conduct Monte Carlo simulation experiments to study the performance of this test, and report an illustration on two log return sequences. This article has supplementary material online.

Can cor triatriatum hide mitral valve pathology?

A 40-year-old man was admitted to our Department for paroxysmal atrial fibrillation. A transthoracic echocardiographic examination revealed a membrane attached laterally to the junction between the left upper pulmonary vein and left atrial appendage, dividing the left atrium into two chambers: the former communicating with the mitral valve and the latter with pulmonary veins. One fenestration of ∼10 mm connected the two chambers and an echo colour-Doppler demonstrated a flow through this fenestration ( Panel A ; see Supplementary material online, Video S1 ). The mean pressure gradient across the membrane was 5 mmHg, while the maximum gradient was 12 mmHg. The echocardiogram also showed a dilation of the left atrial chamber (volume 59 mL/m2), a slight dilation of the pulmonary veins, a reduced mitral flow, and a mild mitral valve regurgitation due to mitral valve prolapse. …

Measurement Error in Earnings Data: Using a Mixture Model Approach to Combine Survey and Register Data

Survey data on earnings tend to contain measurement error. Administrative data are superior in principle, but are worthless in case of a mismatch. We develop methods for prediction in mixture factor analysis models that combine both data sources to arrive at a single earnings figure. We apply the methods to a Swedish data set. Our results show that register earnings data perform poorly if there is a (small) probability of a mismatch. Survey earnings data are more reliable, despite their measurement error. Predictors that combine both and take conditional class probabilities into account outperform all other predictors. This article has supplementary material online.

Adaptive Confidence Intervals for the Test Error in Classification

The estimated test error of a learned classifier is the most commonly reported measure of classifier performance. However, constructing a high-quality point estimator of the test error has proved to be very difficult. Furthermore, common interval estimators (e.g., confidence intervals) are based on the point estimator of the test error and thus inherit all the difficulties associated with the point estimation problem. As a result, these confidence intervals do not reliably deliver nominal coverage. In contrast, we directly construct the confidence interval by using smooth data-dependent upper and lower bounds on the test error. We prove that, for linear classifiers, the proposed confidence interval automatically adapts to the nonsmoothness of the test error, is consistent under fixed and local alternatives, and does not require that the Bayes classifier be linear. Moreover, the method provides nominal coverage on a suite of test problems using a range of classification algorithms and sample sizes. This article has supplementary material online.

Optimal Weight Choice for Frequentist Model Average Estimators

There has been increasing interest recently in model averaging within the frequentist paradigm. The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process. One of the most important, yet challenging, aspects of model averaging is how to optimally combine estimates from different models. In this work, we suggest a procedure of weight choice for frequentist model average estimators that exhibits optimality properties with respect to the estimator’s mean squared error (MSE). As a basis for demonstrating our idea, we consider averaging over a sequence of linear regression models. Building on this base, we develop a model weighting mechanism that involves minimizing the trace of an unbiased estimator of the model average estimator’s MSE. We further obtain results that reflect the finite sample as well as asymptotic optimality of the proposed mechanism. A Monte Carlo study based on simulated and real data evaluates and compares the finite sample properties of this mechanism with those of existing methods. The extension of the proposed weight selection scheme to general likelihood models is also considered. This article has supplementary material online.

Fast and Accurate Approximation to Significance Tests in Genome-Wide Association Studies

Genome-wide association studies commonly involve simultaneous tests of millions of single nucleotide polymorphisms (SNP) for disease association. The SNPs in nearby genomic regions, however, are often highly correlated due to linkage disequilibrium (LD, a genetic term for correlation). Simple Bonferonni correction for multiple comparisons is therefore too conservative. Permutation tests, which are often employed in practice, are both computationally expensive for genome-wide studies and limited in their scopes. We present an accurate and computationally efficient method, based on Poisson de-clumping heuristics, for approximating genome-wide significance of SNP associations. Compared with permutation tests and other multiple comparison adjustment approaches, our method computes the most accurate and robust p-value adjustments for millions of correlated comparisons within seconds. We demonstrate analytically that the accuracy and the efficiency of our method are nearly independent of the sample size, the number of SNPs, and the scale of p-values to be adjusted. In addition, our method can be easily adopted to estimate false discovery rate. When applied to genome-wide SNP datasets, we observed highly variable p-value adjustment results evaluated from different genomic regions. The variation in adjustments along the genome, however, are well conserved between the European and the African populations. The p-value adjustments are significantly correlated with LD among SNPs, recombination rates, and SNP densities. Given the large variability of sequence features in the genome, we further discuss a novel approach of using SNP-specific (local) thresholds to detect genome-wide significant associations. This article has supplementary material online.

Functional Principal Component Analysis of Density Families With Categorical and Continuous Data on Canadian Entrant Manufacturing Firms

This article investigates the evolution of firm distributions for entrant manufacturing firms in Canada using functional principal components analysis. This methodology describes the dynamics of firms by examining production variables, size, and labor productivity, and a financial variable, leverage (debt-to-asset ratio). We adapt the canonical functional principal components analysis to allow for the inclusion of qualitative information in the form of discrete variables, industry, and region, to capture market structure differences, which is shown to change the dynamics of firm size and labor productivity distributions only. We also perform various tests with the null hypothesis that the distributions are equal across time. When accounting for industry and regional categories, there is a substantial fall in the number of rejections of the null hypothesis of equality for size and labor productivity, which is not the case for leverage. These results show the importance of including qualitative information to account for potential heterogeneity when applying functional principal component analysis to firm-level data. Finally, the methodology finds a correlation between the evolution of variable distributions and macroeconomic factors. This article has supplementary material online.

Independent Component Analysis Involving Autocorrelated Sources With an Application to Functional Magnetic Resonance Imaging

Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated.In this article, we consider a novel approach to ICA that fully exploits the correlation structures within the source signals. Specifically, we propose to estimate the spectral density functions of the source signals instead of their marginal density functions. This is made possible by virtue of the intrinsic relationship between the (unobserved) sources and the (observed) mixed signals. Our methodology is described and implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. This article has supplementary material online.

Spatially Varying Autoregressive Processes

We develop a class of models for processes indexed in time and space that are based on autoregressive (AR) processes at each location. We use a Bayesian hierarchical structure to impose spatial coherence for the coefficients of the AR processes. The priors on such coefficients consist of spatial processes that guarantee time stationarity at each point in the spatial domain. The AR structures are coupled with a dynamic model for the mean of the process, which is expressed as a linear combination of time-varying parameters. We use satellite data on sea surface temperature for the North Pacific to illustrate how the model can be used to separate trends, cycles, and short-term variability for high-frequency environmental data. This article has supplementary material online.

Statistical Sleuthing by Leveraging Human Nature: A Study of Olympic Figure Skating

Analysis of figure skating scoring is notoriously difficult under the new Code of Points (CoP) scoring system, created following the judging scandal of the 2002 Olympic Winter Games. The CoP involves the selection of a random subpanel of judges; scores from other judges are reported but not used. An attempt to repeat the methods of previous studies establishing the presence of nationalistic bias in CoP scoring failed to recreate the competition scores from the raw scoring sheets. This raised the concern that different subpanels of judges were being selected for each skater (breaking ISU rules). However, it is also possible that the ISU was attempting to further reduce transparency in the system by permuting, separately for each skater, the order of the presentation of scores from the judging panel. Intuition suggests that it is impossible to tell the difference between accidental randomization and intentional permutation of the judges’ scores. Although the recent changes do successfully prevent the study of nationalistic bias, this article provides strong evidence against the hypothesis that a separate random subpanel is chosen for each competitor. It addresses the problem by applying Gleser’s extension of the Kolmogorov–Smirnov goodness-of-fit test. This article has supplementary material online.