Leo Breiman was a highly creative, influential researcher with a down-to-earth personal style and an insistence on working on important real world problems and producing useful solutions. This paper is a short review of Breiman’s extensive contributions to the field of applied statistics.

Large-scale statistical analysis of data sets associated with genome sequences plays an important role in modern biology. A key component of such statistical analyses is the computation of p-values and confidence bounds for statistics defined on the genome. Currently such computation is commonly achieved through ad hoc simulation measures. The method of randomization, which is at the heart of these simulation procedures, can significantly affect the resulting statistical conclusions. Most simulation schemes introduce a variety of hidden assumptions regarding the nature of the randomness in the data, resulting in a failure to capture biologically meaningful relationships. To address the need for a method of assessing the significance of observations within large scale genomic studies, where there often exists a complex dependency structure between observations, we propose a unified solution built upon a data subsampling approach. We propose a piecewise stationary model for genome sequences and show that the subsampling approach gives correct answers under this model. We illustrate the method on three simulation studies and two real data examples.

In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories and an excess of predictors over training cases. The current paper explores an elaboration of VDA that conducts classification and variable selection simultaneously. Adding lasso (ℓ₁-norm) and Euclidean penalties to the VDA loss function eliminates unnecessary predictors. Lasso penalties apply to each predictor coefficient separately; Euclidean penalties group the collective coefficients of a single predictor. With these penalties in place, cyclic coordinate descent accelerates estimation of all coefficients. Our tests on simulated and benchmark real data demonstrate the virtues of penalized VDA in model building and prediction in high-dimensional settings.

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework.

Recent advances in genomics have underscored the surprising ubiquity of DNA copy number variation (CNV). Fortunately, modern genotyping platforms also detect CNVs with fairly high reliability. Hidden Markov models and algorithms have played a dominant role in the interpretation of CNV data. Here we explore CNV reconstruction via estimation with a fused-lasso penalty as suggested by Tibshirani and Wang [Biostatistics 9 (2008) 18–29]. We mount a fresh attack on this difficult optimization problem by the following: (a) changing the penalty terms slightly by substituting a smooth approximation to the absolute value function, (b) designing and implementing a new MM (majorization–minimization) algorithm, and (c) applying a fast version of Newton’s method to jointly update all model parameters. Together these changes enable us to minimize the fused-lasso criterion in a highly effective way.

We also reframe the reconstruction problem in terms of imputation via discrete optimization. This approach is easier and more accurate than parameter estimation because it relies on the fact that only a handful of possible copy number states exist at each SNP. The dynamic programming framework has the added bonus of exploiting information that the current fused-lasso approach ignores. The accuracy of our imputations is comparable to that of hidden Markov models at a substantially lower computational cost.

Despite its shortcomings, cross-level or ecological inference remains a necessary part of some areas of quantitative inference, including in United States voting rights litigation. Ecological inference suffers from a lack of identification that, most agree, is best addressed by incorporating individual-level data into the model. In this paper we test the limits of such an incorporation by attempting it in the context of drawing inferences about racial voting patterns using a combination of an exit poll and precinct-level ecological data; accurate information about racial voting patterns is needed to assess triggers in voting rights laws that can determine the composition of United States legislative bodies. Specifically, we extend and study a hybrid model that addresses two-way tables of arbitrary dimension. We apply the hybrid model to an exit poll we administered in the City of Boston in 2008. Using the resulting data as well as simulation, we compare the performance of a pure ecological estimator, pure survey estimators using various sampling schemes and our hybrid. We conclude that the hybrid estimator offers substantial benefits by enabling substantive inferences about voting patterns not practicably available without its use.

Mass spectrometry-based proteomics has become the tool of choice for identifying and quantifying the proteome of an organism. Though recent years have seen a tremendous improvement in instrument performance and the computational tools used, significant challenges remain, and there are many opportunities for statisticians to make important contributions. In the most widely used “bottom-up” approach to proteomics, complex mixtures of proteins are first subjected to enzymatic cleavage, the resulting peptide products are separated based on chemical or physical properties and analyzed using a mass spectrometer. The two fundamental challenges in the analysis of bottom-up MS-based proteomics are as follows: (1) Identifying the proteins that are present in a sample, and (2) Quantifying the abundance levels of the identified proteins. Both of these challenges require knowledge of the biological and technological context that gives rise to observed data, as well as the application of sound statistical principles for estimation and inference. We present an overview of bottom-up proteomics and outline the key statistical issues that arise in protein identification and quantification.

Extreme value data with a high clump-at-zero occur in many domains. Moreover, it might happen that the observed data are either truncated below a given threshold and/or might not be reliable enough below that threshold because of the recording devices. These situations occur, in particular, with radio audience data measured using personal meters that record environmental noise every minute, that is then matched to one of the several radio programs. There are therefore genuine zeros for respondents not listening to the radio, but also zeros corresponding to real listeners for whom the match between the recorded noise and the radio program could not be achieved. Since radio audiences are important for radio broadcasters in order, for example, to determine advertisement price policies, possibly according to the type of audience at different time points, it is essential to be able to explain not only the probability of listening to a radio but also the average time spent listening to the radio by means of the characteristics of the listeners. In this paper we propose a generalized linear model for zero-inflated truncated Pareto distribution (ZITPo) that we use to fit audience radio data. Because it is based on the generalized Pareto distribution, the ZITPo model has nice properties such as model invariance to the choice of the threshold and from which a natural residual measure can be derived to assess the model fit to the data. From a general formulation of the most popular models for zero-inflated data, we derive our model by considering successively the truncated case, the generalized Pareto distribution and then the inclusion of covariates to explain the nonzero proportion of listeners and their average listening time. By means of simulations, we study the performance of the maximum likelihood estimator (and derived inference) and use the model to fully analyze the audience data of a radio station in a certain area of Switzerland.

During primary HIV infection, the kinetics of plasma virus concentrations and CD4+ cell counts is very complex. Parametric and nonparametric models have been suggested for fitting repeated measurements of these markers. Alternatively, mechanistic approaches based on ordinary differential equations have also been proposed. These latter models are constructed according to biological knowledge and take into account the complex nonlinear interactions between viruses and cells. However, estimating the parameters of these models is difficult. A main difficulty in the context of primary HIV infection is that the date of infection is generally unknown. For some patients, the date of last negative HIV test is available in addition to the date of first positive HIV test (seroconverters). In this paper we propose a likelihood-based method for estimating the parameters of dynamical models using a population approach and taking into account the uncertainty of the infection date. We applied this method to a sample of 761 HIV-infected patients from the Concerted Action on SeroConversion to AIDS and Death in Europe (CASCADE).

A method for estimating the axis of reflectional symmetry of an image f(x, y) on the unit disc D={(x, y) : x²+y²≤1} is proposed, given that noisy data of f(x, y) are observed on a discrete grid of edge width Δ. Our estimation procedure is based on minimizing over β∈[0, π) the L₂ distance between empirical versions of f and τ_βf, the image of f after reflection at the axis along (cos β, sin β). Here, f and τ_βf are estimated using truncated radial series of the Zernike type. The inherent symmetry properties of the Zernike functions result in a particularly simple estimation procedure for β. It is shown that the estimate β̂ converges at the parametric rate Δ⁻¹ for images f of bounded variation. Further, we establish asymptotic normality of β̂ if f is Lipschitz continuous. The method is applied to calibrating the point spread function (PSF) for the deconvolution of images from confocal microscopy. For various reasons the PSF characterizing the problem may not be rotationally invariant but rather only reflection symmetric with respect to two orthogonal axes. For an image of a bead acquired by a confocal laser scanning microscope (Leica TCS), these axes are estimated and corresponding confidence intervals are constructed. They turn out to be close to the coordinate axes of the imaging device. As cause for deviation from rotational invariance, this indicates some slight misalignment of the optical system or anisotropy of the immersion medium rather than some irregular shape of the bead. In an extensive simulation study, we show that using a symmetrized version of the observed PSF significantly improves the subsequent reconstruction process of the target image.

This paper suggests a nonlinear mixed effects model for data points in SO(3), the set of 3×3 rotation matrices, collected according to a repeated measure design. Each sample individual contributes a sequence of rotation matrices giving the relative orientations of the right foot with respect to the right lower leg as its ankle moves. The random effects are the five angles characterizing the orientation of the two rotation axes of a subject’s right ankle. The fixed parameters are the average value of these angles and their variances within the population. The algorithms to fit nonlinear mixed effects models presented in Pinheiro and Bates (2000) are adapted to the new directional model. The estimation of the random effects are of interest since they give predictions of the rotation axes of an individual ankle. The performance of these algorithms is investigated in a Monte Carlo study. The analysis of two data sets is presented. In the biomechanical literature, there is no consensus on an in vivo method to estimate the two rotation axes of the ankle. The new model is promising. The estimates obtained from a sample of volunteers are shown to be in agreement with the clinically accepted results of Inman (1976), obtained by manipulating cadavers. The repeated measure directional model presented in this paper is developed for a particular application. The approach is, however, general and might be applied to other models provided that the random directional effects are clustered around their mean values.

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins’ conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins’ structure.

Ozone and particulate matter, PM_2.5, are co-pollutants that have long been associated with increased public health risks. Information on concentration levels for both pollutants comes from two sources: monitoring sites and output from complex numerical models that produce concentration surfaces over large spatial regions. In this paper, we offer a fully-model-based approach for fusing these two sources of information for the pair of co-pollutants which is computationally feasible over large spatial regions and long periods of time. Due to the association between concentration levels of the two environmental contaminants, it is expected that information regarding one will help to improve prediction of the other. Misalignment is an obvious issue since the monitoring networks for the two contaminants only partly intersect and because the collection rate for PM_2.5 is typically less frequent than that for ozone.

Extending previous work in Berrocal, Gelfand and Holland (2010), we introduce a bivariate downscaler that provides a flexible class of bivariate space–time assimilation models. We discuss computational issues for model fitting and analyze a dataset for ozone and PM_2.5 for the ozone season during year 2002. We show a modest improvement in predictive performance, not surprising in a setting where we can anticipate only a small gain.

This paper describes a novel approach based on “proportional imputation” when identical units produced in a batch have random but independent installation and failure times. The current problem is motivated by a real life industrial production–delivery supply chain where identical units are shipped after production to a third party warehouse and then sold at a future date for possible installation. Due to practical limitations, at any given time point, the exact installation as well as the failure times are known for only those units which have failed within that time frame after the installation. Hence, in-house reliability engineers are presented with a very limited, as well as partial, data to estimate different model parameters related to installation and failure distributions. In reality, other units in the batch are generally not utilized due to lack of proper statistical methodology, leading to gross misspecification. In this paper we have introduced a likelihood based parametric and computationally efficient solution to overcome this problem.

In the information system research, a question of particular interest is to interpret and to predict the probability of a firm to adopt a new technology such that market promotions are targeted to only those firms that were more likely to adopt the technology. Typically, there exists significant difference between the observed number of “adopters” and “nonadopters,” which is usually coded as binary response. A critical issue involved in modeling such binary response data is the appropriate choice of link functions in a regression model. In this paper we introduce a new flexible skewed link function for modeling binary response data based on the generalized extreme value (GEV) distribution. We show how the proposed GEV links provide more flexible and improved skewed link regression models than the existing skewed links, especially when dealing with imbalance between the observed number of 0’s and 1’s in a data. The flexibility of the proposed model is illustrated through simulated data sets and a billing data set of the electronic payments system adoption from a Fortune 100 company in 2005.

It has been estimated that about 30% of the genes in the human genome are regulated by microRNAs (miRNAs). These are short RNA sequences that can down-regulate the levels of mRNAs or proteins in animals and plants. Genes regulated by miRNAs are called targets. Typically, methods for target prediction are based solely on sequence data and on the structure information. In this paper we propose a Bayesian graphical modeling approach that infers the miRNA regulatory network by integrating expression levels of miRNAs with their potential mRNA targets and, via the prior probability model, with their sequence/structure information. We use a directed graphical model with a particular structure adapted to our data based on biological considerations. We then achieve network inference using stochastic search methods for variable selection that allow us to explore the huge model space via MCMC. A time-dependent coefficients model is also implemented. We consider experimental data from a study on a very well-known developmental toxicant causing neural tube defects, hyperthermia. Some of the pairs of target gene and miRNA we identify seem very plausible and warrant future investigation. Our proposed method is general and can be easily applied to other types of network inference by integrating multiple data sources.

When choosing a suitable technique for regression and classification with multivariate predictor variables, one is often faced with a tradeoff between interpretability and high predictive accuracy. To give a classical example, classification and regression trees are easy to understand and interpret. Tree ensembles like Random Forests provide usually more accurate predictions. Yet tree ensembles are also more difficult to analyze than single trees and are often criticized, perhaps unfairly, as ‘black box’ predictors.

Node harvest is trying to reconcile the two aims of interpretability and predictive accuracy by combining positive aspects of trees and tree ensembles. Results are very sparse and interpretable and predictive accuracy is extremely competitive, especially for low signal-to-noise data. The procedure is simple: an initial set of a few thousand nodes is generated randomly. If a new observation falls into just a single node, its prediction is the mean response of all training observation within this node, identical to a tree-like prediction. A new observation falls typically into several nodes and its prediction is then the weighted average of the mean responses across all these nodes. The only role of node harvest is to ‘pick’ the right nodes from the initial large ensemble of nodes by choosing node weights, which amounts in the proposed algorithm to a quadratic programming problem with linear inequality constraints. The solution is sparse in the sense that only very few nodes are selected with a nonzero weight. This sparsity is not explicitly enforced. Maybe surprisingly, it is not necessary to select a tuning parameter for optimal predictive accuracy. Node harvest can handle mixed data and missing values and is shown to be simple to interpret and competitive in predictive accuracy on a variety of data sets.

Within the private-values paradigm, we construct a tractable empirical model of equilibrium behavior at first-price auctions when bidders’ valuations are potentially dependent, but not necessarily affiliated. We develop a test of affiliation and apply our framework to data from low-price, sealed-bid auctions held by the Department of Transportation in the State of Michigan to procure road-resurfacing services: we do not reject the hypothesis of affiliation in cost signals.

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber–White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated when the data-generating mechanism is not linear. We demonstrate the applicability of our approach using a simulation study and health care cost data from an evaluation of the Washington State Basic Health Plan.

The statistical tests that are commonly used for detecting mean or median treatment effects suffer from low power when the two distribution functions differ only in the upper (or lower) tail, as in the assessment of the Total Sharp Score (TSS) under different treatments for rheumatoid arthritis. In this article, we propose a more powerful test that detects treatment effects through the expected shortfalls. We show how the expected shortfall can be adjusted for covariates, and demonstrate that the proposed test can achieve a substantial sample size reduction over the conventional tests on the mean effects.

Based on a data set obtained in a dental longitudinal study, conducted in Flanders (Belgium), the joint time to caries distribution of permanent first molars was modeled as a function of covariates. This involves an analysis of multivariate continuous doubly-interval-censored data since: (i) the emergence time of a tooth and the time it experiences caries were recorded yearly, and (ii) events on teeth of the same child are dependent. To model the joint distribution of the emergence times and the times to caries, we propose a dependent Bayesian semiparametric model. A major feature of the proposed approach is that survival curves can be estimated without imposing assumptions such as proportional hazards, additive hazards, proportional odds or accelerated failure time.

Shrinking methods in regression analysis are usually designed for metric predictors. In this article, however, shrinkage methods for categorial predictors are proposed. As an application we consider data from the Munich rent standard, where, for example, urban districts are treated as a categorial predictor. If independent variables are categorial, some modifications to usual shrinking procedures are necessary. Two L₁-penalty based methods for factor selection and clustering of categories are presented and investigated. The first approach is designed for nominal scale levels, the second one for ordinal predictors. Besides applying them to the Munich rent standard, methods are illustrated and compared in simulation studies.

This paper is motivated by a Eurobarometer survey on science knowledge. As part of the survey, respondents were asked to rank sources of science information in order of importance. The official statistical analysis of these data however failed to use the complete ranking information. We instead propose a method which treats ranked data as a set of paired comparisons which places the problem in the standard framework of generalized linear models and also allows respondent covariates to be incorporated.

An extension is proposed to allow for heterogeneity in the ranked responses. The resulting model uses a nonparametric formulation of the random effects structure, fitted using the EM algorithm. Each mass point is multivalued, with a parameter for each item. The resultant model is equivalent to a covariate latent class model, where the latent class profiles are provided by the mass point components and the covariates act on the class profiles. This provides an alternative interpretation of the fitted model. The approach is also suitable for paired comparison data.