Showing papers in "Journal of the American Statistical Association in 2017"
TL;DR: For instance, mean-field variational inference as discussed by the authors approximates probability densities through optimization, which is used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling.
Abstract: One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this article, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization. VI has been used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling. The idea behind VI is to first posit a family of densities and then to find a member of that family which is close to the target density. Closeness is measured by Kullback–Leibler divergence. We review the ideas behind mean-field variational inference, discuss the special case of VI applied to exponential family models, present a full example with a Bayesian mixture of Gaussians, and derive a variant that uses stochastic optimization to scale up to massive data...
3,421 citations
TL;DR: In this paper, a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space is proposed, which can capture spatial structure from very fine to very large scales.
Abstract: Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelize...
219 citations
TL;DR: In this article, the authors proposed a residual weighted learning (RWL) framework to improve the finite sample performance of OWL, which is a general framework that can be applied to individualized medicine.
Abstract: Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. (1) The estimated ITR of OWL is affected by a simple shift of the outcome. (2) The rule from OWL tries to keep treatment assignments that subjects actually received. (3) There is no variable selection mechanism with OWL. All of them weaken the finite sample performance of OWL. In this article, we propose a general framework, called residual weighted learning (RWL), to alleviate these problems, and hence to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcom...
158 citations
TL;DR: In this article, the authors proposed parsimonious tensor response regression with a generalized sparsity principle, which reduces the number of free parameters and leads to a feasible computation and improved interpretation.
Abstract: Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient...
153 citations
TL;DR: In this paper, a penalized approach for subgroup analysis based on a regression model is proposed, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts.
Abstract: An important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup. This article considers the problem using samples drawn from a population consisting of subgroups with different mean values, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts. We apply concave penalty functions to pairwise differences of the intercepts. This procedure automatically divides the observations into subgroups. To implement the proposed approach, we develop an alternating direction method of multipliers algorithm with concave penalties and demonstrate its convergence. We also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between g...
140 citations
TL;DR: In this article, the authors developed scalable methods for fitting penalized regression spline based generalized additive models with of the order of 104 coefficients to up to 108 data, with efficient scalable method for computing required crossproducts directly from the discrete representation.
Abstract: We develop scalable methods for fitting penalized regression spline based generalized additive models with of the order of 104 coefficients to up to 108 data. Computational feasibility rests on: (i) a new iteration scheme for estimation of model coefficients and smoothing parameters, avoiding poorly scaling matrix operations; (ii) parallelization of the iteration’s pivoted block Cholesky and basic matrix operations; (iii) the marginal discretization of model covariates to reduce memory footprint, with efficient scalable methods for computing required crossproducts directly from the discrete representation. Marginal discretization enables much finer discretization than joint discretization would permit. We were motivated by the need to model four decades worth of daily particulate data from the U.K. Black Smoke and Sulphur Dioxide Monitoring Network. Although reduced in size recently, over 2000 stations have at some time been part of the network, resulting in some 10 million measurements. Modeling ...
138 citations
TL;DR: The results of this reanalysis provide a compelling argument for both increasing the threshold required for declaring scientific discoveries and for adopting statistical summaries of evidence that account for the high proportion of tested hypotheses that are false.
Abstract: Investigators from a large consortium of scientists recently performed a multi-year study in which they replicated 100 psychology experiments. Although statistically significant results were reported in 97% of the original studies, statistical significance was achieved in only 36% of the replicated studies. This article presents a reanalysis of these data based on a formal statistical model that accounts for publication bias by treating outcomes from unpublished studies as missing data, while simultaneously estimating the distribution of effect sizes for those studies that tested nonnull effects. The resulting model suggests that more than 90% of tests performed in eligible psychology experiments tested negligible effects, and that publication biases based on p-values caused the observed rates of nonreproducibility. The results of this reanalysis provide a compelling argument for both increasing the threshold required for declaring scientific discoveries and for adopting statistical summaries of e...
131 citations
TL;DR: In this article, the ASA issued a Statement on Statistical Significance and p-values aimed at those who are not primarily statisticians, and showed that statisticians tend to interpret evidence dichotomously based on whether or not a p-value crosses the conventional 0.05 threshold for statistical significance.
Abstract: In light of recent concerns about reproducibility and replicability, the ASA issued a Statement on Statistical Significance and p-values aimed at those who are not primarily statisticians. While the ASA Statement notes that statistical significance and p-values are “commonly misused and misinterpreted,” it does not discuss and document broader implications of these errors for the interpretation of evidence. In this article, we review research on how applied researchers who are not primarily statisticians misuse and misinterpret p-values in practice and how this can lead to errors in the interpretation of evidence. We also present new data showing, perhaps surprisingly, that researchers who are primarily statisticians are also prone to misuse and misinterpret p-values thus resulting in similar errors. In particular, we show that statisticians tend to interpret evidence dichotomously based on whether or not a p-value crosses the conventional 0.05 threshold for statistical significance. We discuss im...
130 citations
TL;DR: In this paper, the prior distribution on the bias is orthogonal to the gradient of the computer model, which results in an issue where the posterior of the parameter is suboptimally broad.
Abstract: Bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias. The parameter in the predominant methodology is left undefined. This results in an issue, where the posterior of the parameter is suboptimally broad. There has been no generally accepted alternatives to date. This article proposes using Bayesian calibration, where the prior distribution on the bias is orthogonal to the gradient of the computer model. Problems associated with Bayesian calibration are shown to be mitigated through analytic results in addition to examples. Supplementary materials for this article are available online.
120 citations
TL;DR: The ASA Biopharmaceutical Section Work Group as discussed by the authors summarized, analyzed, and monitored of adverse experiences and proposed two treatment crossover designs for Rodent Carcinogenicity Studies and two active control equivalence studies for Dosing in the Elderly.
Abstract: 1. ASA Biopharmaceutical Section Work Groups 2. Summarization, Analysis, and Monitoring of Adverse Experiences 3. Two Treatment Crossover Designs 4. Active Control Equivalence Studies 5. Optimization in Clinical Trials and Combination Drug Development 6. Dosing in the Elderly 7. Intention to Treat in Clinical Trials 8. Dual Control Groups in Rodent Carcinogenicity Studies
118 citations
TL;DR: The authors used central limit theorems for randomization-based causal analyses of experimental data, where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment.
Abstract: Frequentists’ inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central limit theorems. Although previous literature has established various forms of central limit theorems for statistical inference in super population models, we still need general and convenient forms of central limit theorems for some randomization-based causal analyses of experimental data, where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment. We use central limit theorems for sample surveys and rank statistics to establish general forms of the finite population central limit theorems that are particularly useful for proving asymptotic distributions of randomization tests under th...
TL;DR: In this paper, the authors proposed a two-sample test statistic based on a similarity graph constructed on the pooled observations from the two samples, which can be applied to multivariate data and non-Euclidean data.
Abstract: Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This article presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can be applied to multivariate data and non-Euclidean data as long as a dissimilarity measure on the sample space can be defined, which can usually be provided by domain experts. Existing tests based on a similarity graph lack power either for location or for scale alternatives. The new test uses a common pattern that was overlooked previously, and works for both types of alternatives. The test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large datasets. The new test is illustrated on two applications: The assessment of covariate balance in a matched observational study, and the comparison of network data under different co...
TL;DR: The synthetic control method is applied to a neighborhood-specific crime intervention in Roanoke, VA, and several novel contributions are made to the synthetic control toolkit, illustrating the importance of adjusting the estimated effect of treatment for the design effect implicit within the weights.
Abstract: The synthetic control method is an increasingly popular tool for analysis of program efficacy. Here, it is applied to a neighborhood-specific crime intervention in Roanoke, VA, and several novel contributions are made to the synthetic control toolkit. We examine high-dimensional data at a granular level (the treated area has several cases, a large number of untreated comparison cases, and multiple outcome measures). Calibration is used to develop weights that exactly match the synthetic control to the treated region across several outcomes and time periods. Further, we illustrate the importance of adjusting the estimated effect of treatment for the design effect implicit within the weights. A permutation procedure is proposed wherein countless placebo areas can be constructed, enabling estimation of p-values under a robust set of assumptions. An omnibus statistic is introduced that is used to jointly test for the presence of an intervention effect across multiple outcomes and post-intervention tim...
TL;DR: In this article, independent components are estimated by combining a nonparametric probability integral transformation with a generalized non-parametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components.
Abstract: This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components. We prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification, all while placing assumptions on the observations directly, not on the latent components. U statistics of certain Euclidean distances between sample elements are combined to construct a test statistic for mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for...
TL;DR: This work derives asymptotic theory for this estimator for density level sets under Hausdorff loss, and based on this theory, two bootstrap confidence regions for level sets are developed.
Abstract: We study the plug-in estimator for density level sets under Hausdorff loss. We derive asymptotic theory for this estimator, and based on this theory, we develop two bootstrap confidence regions for level sets. We introduce a new technique for visualizing density level sets, even in multidimensions, which is easy to interpret and efficient to compute. Supplementary materials for this article are available online.
TL;DR: A bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional sparse linear models based on the recent desparsifying Lasso estimator that asymptotically achieves the prespecified significance level, and enjoys certain optimality in terms of its power even when the model errors are non-Gaussian.
Abstract: This article proposes a bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional sparse linear models based on the recent desparsifying Lasso estimator. Our procedure allows the dimension of the parameter vector of interest to be exponentially larger than sample size, and it automatically accounts for the dependence within the desparsifying Lasso estimator. Moreover, our simultaneous testing method can be naturally coupled with the margin screening to enhance its power in sparse testing with a reduced computational cost, or with the step-down method to provide a strong control for the family-wise error rate. In theory, we prove that our simultaneous testing procedure asymptotically achieves the prespecified significance level, and enjoys certain optimality in terms of its power even when the model errors are non-Gaussian. Our general theory is also useful in studying the support recovery problem. To broaden the applicability, we further extend our main results to general...
TL;DR: A new procedure for clustering a large number of financial time series based on high-dimensional panel data with grouped factor structures is introduced and nominal classifications based on either listed market, industry, country or region are found to be insufficient to characterize the heterogeneity of the global financial markets.
Abstract: This article introduces a new procedure for clustering a large number of financial time series based on high-dimensional panel data with grouped factor structures. The proposed method attempts to capture the level of similarity of each of the time series based on sensitivity to observable factors as well as to the unobservable factor structure. The proposed method allows for correlations between observable and unobservable factors and also allows for cross-sectional and serial dependence and heteroscedasticities in the error structure, which are common in financial markets. In addition, theoretical properties are established for the procedure. We apply the method to analyze the returns for over 6000 international stocks from over 100 financial markets. The empirical analysis quantifies the extent to which the U.S. subprime crisis spilled over to the global financial markets. Furthermore, we find that nominal classifications based on either listed market, industry, country or region are insufficien...
TL;DR: In this paper, a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data is proposed, where the joint distribution of the edges is defined via a mixture model that reduces dimensionality and efficiently incorporates network information within each mixture component.
Abstract: Replicated network data are increasingly available in many research fields. For example, in connectomic applications, interconnections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model that reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and c...
TL;DR: The constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals are outlined, showing that selection priors may actually be desirable for high-dimensional estimation.
Abstract: Jointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Nonlocal priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size n increases, while nonspurious parameter estimates are not shrunk. We extend some results to linear models with dimension p growing with n. Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models with p > >n at low computational cost. NLPs provided lower estimation error than benchmark and hyper-g priors, SCAD and LASSO in simulations, and in gene expression data ...
TL;DR: A new class of transGaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data, which have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and have a wide range of applications.
Abstract: We propose a new class of transGaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters. Asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the TGH random fields are investigated. An efficient estimation procedure, based on maximum approximated likelihood, is proposed and an extreme spatial outlier detection algorithm is formulated. Kriging and probabilistic prediction with TGH random fields are developed along with prediction confidence intervals. The predictive performance of TGH random fields is demonstrated through extensive simulation studies and an application to a dataset...
TL;DR: In this paper, an offline, iterated particle filter is presented to facilitate statistical inference in general state space hidden Markov models, given a model and a sequence of observations, the associated margina...
Abstract: We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated margina...
TL;DR: The generalized higher criticism (GHC) is proposed to test for the association between an SNP set and a disease outcome, allowing for arbitrary correlation structures among the SNPs in an SNP-set, while performing accurate analytic p-value calculations for any finite number ofSNPs in the SNP- set.
Abstract: It is of substantial interest to study the effects of genes, genetic pathways, and networks on the risk of complex diseases. These genetic constructs each contain multiple SNPs, which are often correlated and function jointly, and might be large in number. However, only a sparse subset of SNPs in a genetic construct is generally associated with the disease of interest. In this article, we propose the generalized higher criticism (GHC) to test for the association between an SNP set and a disease outcome. The higher criticism is a test traditionally used in high-dimensional signal detection settings when marginal test statistics are independent and the number of parameters is very large. However, these assumptions do not always hold in genetic association studies, due to linkage disequilibrium among SNPs and the finite number of SNPs in an SNP set in each genetic construct. The proposed GHC overcomes the limitations of the higher criticism by allowing for arbitrary correlation structures among the S...
TL;DR: A class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates with superior performance against many existing approaches is developed.
Abstract: The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this article is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtain...
TL;DR: This paper argues that this independence assumption in the matching statuses of record pairs is unreasonable and proposes partial Bayes estimates that allow uncertain parts of the bipartite matching to be left unresolved and demonstrates the advantages of these methods merging two datafiles on casualties from the civil war of El Salvador.
Abstract: The bipartite record linkage task consists of merging two disparate datafiles containing information on two overlapping sets of entities. This is nontrivial in the absence of unique identifiers and it is important for a wide variety of applications given that it needs to be solved whenever we have to combine information from different sources. Most statistical techniques currently used for record linkage are derived from a seminal article by Fellegi and Sunter in 1969. These techniques usually assume independence in the matching statuses of record pairs to derive estimation procedures and optimal point estimators. We argue that this independence assumption is unreasonable and instead target a bipartite matching between the two datafiles as our parameter of interest. Bayesian implementations allow us to quantify uncertainty on the matching decisions and derive a variety of point estimators using different loss functions. We propose partial Bayes estimates that allow uncertain parts of the bipartite...
TL;DR: In this article, a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed, which provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed.
Abstract: Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are ...
TL;DR: In this article, it was shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of Type 1 (or Type 3) errors.
Abstract: Given a sample from a bivariate distribution, consider the problem of testing independence. A permutation test based on the sample correlation is known to be an exact level α test. However, when used to test the null hypothesis that the samples are uncorrelated, the permutation test can have rejection probability that is far from the nominal level. Further, the permutation test can have a large Type 3 (directional) error rate, whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value, when in fact the true correlation is negative. It will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of Type 1 (or Type 3) errors. These conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution. We will also present asymptotically robust randomization tests for regression coeffi...
TL;DR: The proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response.
Abstract: In quantile linear regression with ultra-high dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response. Theoretical results show that the proposed algorithm can yield the sure screening set. By controlling the false selection rate, model selection consistency can be achieved theoretically. In practice, we proposed using EBIC for best subset selection so that the resulting model is screening consistent. Simulation studies demonstrate that the proposed algorithm performs well, and an empirical example is presented.
TL;DR: The leverage effect is examined under a general setup that allows the log-price and volatility processes to be Itô semimartingales and the asymptotic properties of these estimators are established.
Abstract: This article examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Ito semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one. Supplementary materials for this article are available online.
TL;DR: This article develops a family of “accumulation tests” to choose a cutoff k that adapts to the amount of signal at the top of the ranked list, and introduces a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques.
Abstract: Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this article, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list to increase the number of discoveries. Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR). Generalizing several existing methods, we develop a family of “accumulation tests” to choose a cutoff k that adapts to the amount of signal at the top of the ranked list. We introduce a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques. Our theoretical results prove that these metho...
TL;DR: It is well known that even experienced scientists routinely misinterpret p-values in all sorts of ways, including confusion of statistical and practical significance, treating nonrejection as accep...
Abstract: It is well known that even experienced scientists routinely misinterpret p-values in all sorts of ways, including confusion of statistical and practical significance, treating nonrejection as accep...