Sohan Seth, Iain Murray, Christopher K. I. Williams.

Source: Bayesian Analysis, Volume 14, Number 3, 703--725.

Abstract:
Model criticism is usually carried out by assessing if replicated data generated under the fitted model looks similar to the observed data, see e.g. Gelman, Carlin, Stern, and Rubin (2004, p. 165). This paper presents a method for latent variable models by pulling back the data into the space of latent variables, and carrying out model criticism in that space. Making use of a model's structure enables a more direct assessment of the assumptions made in the prior and likelihood. We demonstrate the method with examples of model criticism in latent space applied to factor analysis, linear dynamical systems and Gaussian processes.

Yushu Shi, Michael Martens, Anjishnu Banerjee, Purushottam Laud.

Source: Bayesian Analysis, Volume 14, Number 3, 677--702.

Abstract:
Dirichlet process mixture (DPM) models provide flexible modeling for distributions of data as an infinite mixture of distributions from a chosen collection. Specifying priors for these models in individual data contexts can be challenging. In this paper, we introduce a scheme which requires the investigator to specify only simple scaling information. This is used to transform the data to a fixed scale on which a low information prior is constructed. Samples from the posterior with the rescaled data are transformed back for inference on the original scale. The low information prior is selected to provide a wide variety of components for the DPM to generate flexible distributions for the data on the fixed scale. The method can be applied to all DPM models with kernel functions closed under a suitable scaling transformation. Construction of the low information prior, however, is kernel dependent. Using DPM-of-Gaussians and DPM-of-Weibulls models as examples, we show that the method provides accurate estimates of a diverse collection of distributions that includes skewed, multimodal, and highly dispersed members. With the recommended priors, repeated data simulations show performance comparable to that of standard empirical estimates. Finally, we show weak convergence of posteriors with the proposed priors for both kernels considered.

Luis Gutiérrez, Andrés F. Barrientos, Jorge González, Daniel Taylor-Rodríguez.

Source: Bayesian Analysis, Volume 14, Number 2, 649--675.

Abstract:
We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.

Marcos Oliveira Prates, Renato Martins Assunção, Erica Castilho Rodrigues.

Source: Bayesian Analysis, Volume 14, Number 2, 623--647.

Abstract:
Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Techniques to alleviate this problem are based on decomposing the spatial random effect and fitting a restricted spatial regression. In this paper, we propose a different approach: a transformation of the geographic space to ensure that the unobserved spatial random effect added to the regression is orthogonal to the fixed effects covariates. Our approach, named SPOCK, has the additional benefit of providing a fast and simple computational method to estimate the parameters. Also, it does not constrain the distribution class assumed for the spatial error term. A simulation study and real data analyses are presented to better understand the advantages of the new method in comparison with the existing ones.

Marko Järvenpää, Michael U. Gutmann, Arijus Pleska, Aki Vehtari, Pekka Marttinen.

Source: Bayesian Analysis, Volume 14, Number 2, 595--622.

Abstract:
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.

Quan Zhou, Yongtao Guan.

Source: Bayesian Analysis, Volume 14, Number 2, 573--594.

Abstract:
Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special class of linear systems, which can increase the speed of the BVSR model-fitting tenfold. The iterative method hinges on the complex factorization of the sum of two matrices and the solution path resides in the complex domain (instead of the real domain). Compared to the Gauss-Seidel method, the complex factorization converges almost instantaneously and its error is several magnitude smaller than that of the Gauss-Seidel method. More importantly, the error is always within the pre-specified precision while the Gauss-Seidel method is not. For large problems with thousands of covariates, the complex factorization is 10–100 times faster than either the Gauss-Seidel method or the direct method via the Cholesky decomposition. In BVSR, one needs to repetitively solve large penalized regression systems whose design matrices only change slightly between adjacent MCMC steps. This slight change in design matrix enables the adaptation of the iterative complex factorization method. The computational innovation will facilitate the wide-spread use of BVSR in reanalyzing genome-wide association datasets.

Alberto Cassese, Weixuan Zhu, Michele Guindani, Marina Vannucci.

Source: Bayesian Analysis, Volume 14, Number 2, 553--572.

Abstract:
In many applications, investigators monitor processes that vary in space and time, with the goal of identifying temporally persistent and spatially localized departures from a baseline or “normal” behavior. In this manuscript, we consider the monitoring of pneumonia and influenza (P&I) mortality, to detect influenza outbreaks in the continental United States, and propose a Bayesian nonparametric model selection approach to take into account the spatio-temporal dependence of outbreaks. More specifically, we introduce a zero-inflated conditionally identically distributed species sampling prior which allows borrowing information across time and to assign data to clusters associated to either a null or an alternate process. Spatial dependences are accounted for by means of a Markov random field prior, which allows to inform the selection based on inferences conducted at nearby locations. We show how the proposed modeling framework performs in an application to the P&I mortality data and in a simulation study, and compare with common threshold methods for detecting outbreaks over time, with more recent Markov switching based models, and with spike-and-slab Bayesian nonparametric priors that do not take into account spatio-temporal dependence.

Benjamin Letham, Brian Karrer, Guilherme Ottoni, Eytan Bakshy.

Source: Bayesian Analysis, Volume 14, Number 2, 495--519.

Abstract:
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error. Bayesian optimization is a promising technique for efficiently optimizing multiple continuous parameters, but existing approaches degrade in performance when the noise level is high, limiting its applicability to many randomized experiments. We derive an expression for expected improvement under greedy batch optimization with noisy observations and noisy constraints, and develop a quasi-Monte Carlo approximation that allows it to be efficiently optimized. Simulations with synthetic functions show that optimization performance on noisy, constrained problems outperforms existing methods. We further demonstrate the effectiveness of the method with two real-world experiments conducted at Facebook: optimizing a ranking system, and optimizing server compiler flags.

Łukasz Rajkowski.

Source: Bayesian Analysis, Volume 14, Number 2, 477--494.

Abstract:
Mixture models are a natural choice in many applications, but it can be difficult to place an a priori upper bound on the number of components. To circumvent this, investigators are turning increasingly to Dirichlet process mixture models (DPMMs). It is therefore important to develop an understanding of the strengths and weaknesses of this approach. This work considers the MAP (maximum a posteriori) clustering for the Gaussian DPMM (where the cluster means have Gaussian distribution and, for each cluster, the observations within the cluster have Gaussian distribution). Some desirable properties of the MAP partition are proved: ‘almost disjointness’ of the convex hulls of clusters (they may have at most one point in common) and (with natural assumptions) the comparability of sizes of those clusters that intersect any fixed ball with the number of observations (as the latter goes to infinity). Consequently, the number of such clusters remains bounded. Furthermore, if the data arises from independent identically distributed sampling from a given distribution with bounded support then the asymptotic MAP partition of the observation space maximises a function which has a straightforward expression, which depends only on the within-group covariance parameter. As the operator norm of this covariance parameter decreases, the number of clusters in the MAP partition becomes arbitrarily large, which may lead to the overestimation of the number of mixture components.

Suprateek Kundu, Bani K. Mallick, Veera Baladandayuthapani.

Source: Bayesian Analysis, Volume 14, Number 2, 449--476.

Abstract:
There has been an intense development in the Bayesian graphical model literature over the past decade; however, most of the existing methods are restricted to moderate dimensions. We propose a novel graphical model selection approach for large dimensional settings where the dimension increases with the sample size, by decoupling model fitting and covariance selection. First, a full model based on a complete graph is fit under a novel class of mixtures of inverse–Wishart priors, which induce shrinkage on the precision matrix under an equivalence with Cholesky-based regularization, while enabling conjugate updates. Subsequently, a post-fitting model selection step uses penalized joint credible regions to perform model selection. This allows our methods to be computationally feasible for large dimensional settings using a combination of straightforward Gibbs samplers and efficient post-fitting inferences. Theoretical guarantees in terms of selection consistency are also established. Simulations show that the proposed approach compares favorably with competing methods, both in terms of accuracy metrics and computation times. We apply this approach to a cancer genomics data example.

Luis Gutiérrez, Eduardo Gutiérrez-Peña, Ramsés H. Mena.

Source: Bayesian Analysis, Volume 14, Number 2, 427--447.

Abstract:
This work presents a Bayesian predictive approach to statistical shape analysis. A modeling strategy that starts with a Gaussian distribution on the configuration space, and then removes the effects of location, rotation and scale, is studied. This boils down to an application of the projected normal distribution to model the configurations in the shape space, which together with certain identifiability constraints, facilitates parameter interpretation. Having better control over the parameters allows us to generalize the model to a regression setting where the effect of predictors on shapes can be considered. The methodology is illustrated and tested using both simulated scenarios and a real data set concerning eight anatomical landmarks on a sagittal plane of the corpus callosum in patients with autism and in a group of controls.

Haolun Shi, Guosheng Yin.

Source: Bayesian Analysis, Volume 14, Number 2, 399--425.

Abstract:
Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. To effectively maintain the overall type I error rate, we propose solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities. We present both theoretical and numerical methods for finding the optimal posterior probability boundaries with $alpha$ -spending functions that mimic those of the frequentist group sequential designs. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. We apply least-square fitting to find the $alpha$ -spending function closest to the target. We discuss the application of our method to single-arm and double-arm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.

M. W. McLean, M. P. Wand.

Source: Bayesian Analysis, Volume 14, Number 2, 371--398.

Abstract:
We build on recent work concerning message passing approaches to approximate fitting and inference for arbitrarily large regression models. The focus is on regression models where the response variable is modeled to have an elaborate distribution, which is loosely defined to mean a distribution that is more complicated than common distributions such as those in the Bernoulli, Poisson and Normal families. Examples of elaborate response families considered here are the Negative Binomial and $t$ families. Variational message passing is more challenging due to some of the conjugate exponential families being non-standard and numerical integration being needed. Nevertheless, a factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family. Computer code can be compartmentalized, including that involving numerical integration. A major finding of this work is that the modularity of variational message passing extends to elaborate response regression models.

Daniela Pauger, Helga Wagner.

Source: Bayesian Analysis, Volume 14, Number 2, 341--369.

Abstract:
We propose a Bayesian approach to obtain a sparse representation of the effect of a categorical predictor in regression type models. As this effect is captured by a group of level effects, sparsity cannot only be achieved by excluding single irrelevant level effects or the whole group of effects associated to this predictor but also by fusing levels which have essentially the same effect on the response. To achieve this goal, we propose a prior which allows for almost perfect as well as almost zero dependence between level effects a priori. This prior can alternatively be obtained by specifying spike and slab prior distributions on all effect differences associated to this categorical predictor. We show how restricted fusion can be implemented and develop an efficient MCMC (Markov chain Monte Carlo) method for posterior computation. The performance of the proposed method is investigated on simulated data and we illustrate its application on real data from EU-SILC (European Union Statistics on Income and Living Conditions).

Lloyd T. Elliott, Maria De Iorio, Stefano Favaro, Kaustubh Adhikari, Yee Whye Teh.

Source: Bayesian Analysis, Volume 14, Number 2, 313--339.

Abstract:
We propose a Bayesian nonparametric model to infer population admixture, extending the hierarchical Dirichlet process to allow for correlation between loci due to linkage disequilibrium. Given multilocus genotype data from a sample of individuals, the proposed model allows inferring and classifying individuals as unadmixed or admixed, inferring the number of subpopulations ancestral to an admixed population and the population of origin of chromosomal regions. Our model does not assume any specific mutation process, and can be applied to most of the commonly used genetic markers. We present a Markov chain Monte Carlo (MCMC) algorithm to perform posterior inference from the model and we discuss some methods to summarize the MCMC output for the analysis of population admixture. Finally, we demonstrate the performance of the proposed model in a real application, using genetic data from the ectodysplasin-A receptor (EDAR) gene, which is considered to be ancestry-informative due to well-known variations in allele frequency as well as phenotypic effects across ancestry. The structure analysis of this dataset leads to the identification of a rare haplotype in Europeans. We also conduct a simulated experiment and show that our algorithm outperforms parametric methods.

Peter D. Hoff

Source: Bayesian Anal., Volume 6, Number 2, 179--196.

Abstract:
Modern datasets are often in the form of matrices or arrays, potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as well as correlation among the variables. A possible model for matrix-valued data is the class of matrix normal distributions, which is parametrized by two covariance matrices, one for each index set of the data. In this article we discuss an extension of the matrix normal model to accommodate multidimensional data arrays, or tensors. We show how a particular array-matrix product can be used to generate the class of array normal distributions having separable covariance structure. We derive some properties of these covariance structures and the corresponding array normal distributions, and show how the array-matrix product can be used to define a semi-conjugate prior distribution and calculate the corresponding posterior distribution. We illustrate the methodology in an analysis of multivariate longitudinal network data which take the form of a four-way array.

Ruosi Guo, Chunming Zhang, Zhengjun Zhang.

Source: Statistical Science, Volume 35, Number 1, 145--157.

Abstract:
In many scientific disciplines, finding hidden influential factors behind observational data is essential but challenging. The majority of existing approaches, such as the independent component analysis (${mathrm{ICA}}$), rely on linear transformation, that is, true signals are linear combinations of hidden components. Motivated from analyzing nonlinear temporal signals in neuroscience, genetics, and finance, this paper proposes the “maximum independent component analysis” (${mathrm{MaxICA}}$), based on max-linear combinations of components. In contrast to existing methods, ${mathrm{MaxICA}}$ benefits from focusing on significant major components while filtering out ignorable components. A major tool for parameter learning of ${mathrm{MaxICA}}$ is an augmented genetic algorithm, consisting of three schemes for the elite weighted sum selection, randomly combined crossover, and dynamic mutation. Extensive empirical evaluations demonstrate the effectiveness of ${mathrm{MaxICA}}$ in either extracting max-linearly combined essential sources in many applications or supplying a better approximation for nonlinearly combined source signals, such as $mathrm{EEG}$ recordings analyzed in this paper.

Divyansh Agarwal, Jingshu Wang, Nancy R. Zhang.

Source: Statistical Science, Volume 35, Number 1, 112--128.

Abstract:
Single cell sequencing technologies are transforming biomedical research. However, due to the inherent nature of the data, single cell RNA sequencing analysis poses new computational and statistical challenges. We begin with a survey of a selection of topics in this field, with a gentle introduction to the biology and a more detailed exploration of the technical noise. We consider in detail the problem of single cell data denoising, sometimes referred to as “imputation” in the relevant literature. We discuss why this is not a typical statistical imputation problem, and review current approaches to this problem. We then explore why the use of denoised values in downstream analyses invites novel statistical insights, and how denoising uncertainty should be accounted for to yield valid statistical inference. The utilization of denoised or imputed matrices in statistical inference is not unique to single cell genomics, and arises in many other fields. We describe the challenges in this type of analysis, discuss some preliminary solutions, and highlight unresolved issues.

Thomas Staudt, Timo Aspelmeier, Oskar Laitenberger, Claudia Geisler, Alexander Egner, Axel Munk.

Source: Statistical Science, Volume 35, Number 1, 92--111.

Abstract:
Super-resolution microscopy is rapidly gaining importance as an analytical tool in the life sciences. A compelling feature is the ability to label biological units of interest with fluorescent markers in (living) cells and to observe them with considerably higher resolution than conventional microscopy permits. The images obtained this way, however, lack an absolute intensity scale in terms of numbers of fluorophores observed. In this article, we discuss state of the art methods to count such fluorophores and statistical challenges that come along with it. In particular, we suggest a modeling scheme for time series generated by single-marker-switching (SMS) microscopy that makes it possible to quantify the number of markers in a statistically meaningful manner from the raw data. To this end, we model the entire process of photon generation in the fluorophore, their passage through the microscope, detection and photoelectron amplification in the camera, and extraction of time series from the microscopic images. At the heart of these modeling steps is a careful description of the fluorophore dynamics by a novel hidden Markov model that operates on two timescales (HTMM). Besides the fluorophore number, information about the kinetic transition rates of the fluorophore’s internal states is also inferred during estimation. We comment on computational issues that arise when applying our model to simulated or measured fluorescence traces and illustrate our methodology on simulated data.

Chao Du, S. C. Kou.

Source: Statistical Science, Volume 35, Number 1, 75--91.

Abstract:
Toward the last quarter of the 20th century, the emergence of single-molecule experiments enabled scientists to track and study individual molecules’ dynamic properties in real time. Unlike macroscopic systems’ dynamics, those of single molecules can only be properly described by stochastic models even in the absence of external noise. Consequently, statistical methods have played a key role in extracting hidden information about molecular dynamics from data obtained through single-molecule experiments. In this article, we survey the major statistical methodologies used to analyze single-molecule experimental data. Our discussion is organized according to the types of stochastic models used to describe single-molecule systems as well as major experimental data collection techniques. We also highlight challenges and future directions in the application of statistical methodologies to single-molecule experiments.

Yazhen Wang, Xinyu Song.

Source: Statistical Science, Volume 35, Number 1, 51--74.

Abstract:
Quantum science and quantum technology are of great current interest in multiple frontiers of many scientific fields ranging from computer science to physics and chemistry, and from engineering to mathematics and statistics. Their developments will likely lead to a new wave of scientific revolutions and technological innovations in a wide range of scientific studies and applications. This paper provides a brief review on quantum communication, quantum information, quantum computation, quantum simulation, and quantum metrology. We present essential quantum properties, illustrate relevant concepts of quantum science and quantum technology, and discuss their scientific developments. We point out the need for statistical analysis in their developments, as well as their potential applications to and impacts on statistics and data science.

Peter J. Diggle, Emanuele Giorgi, Julienne Atsame, Sylvie Ntsame Ella, Kisito Ogoussan, Katherine Gass.

Source: Statistical Science, Volume 35, Number 1, 42--50.

Abstract:
Vector-borne diseases have long presented major challenges to the health of rural communities in the wet tropical regions of the world, but especially in sub-Saharan Africa. In this paper, we describe the contribution that statistical modelling has made to the global elimination programme for one vector-borne disease, onchocerciasis. We explain why information on the spatial distribution of a second vector-borne disease, Loa loa, is needed before communities at high risk of onchocerciasis can be treated safely with mass distribution of ivermectin, an antifiarial medication. We show how a model-based geostatistical analysis of Loa loa prevalence survey data can be used to map the predictive probability that each location in the region of interest meets a WHO policy guideline for safe mass distribution of ivermectin and describe two applications: one is to data from Cameroon that assesses prevalence using traditional blood-smear microscopy; the other is to Africa-wide data that uses a low-cost questionnaire-based method. We describe how a recent technological development in image-based microscopy has resulted in a change of emphasis from prevalence alone to the bivariate spatial distribution of prevalence and the intensity of infection among infected individuals. We discuss how statistical modelling of the kind described here can contribute to health policy guidelines and decision-making in two ways. One is to ensure that, in a resource-limited setting, prevalence surveys are designed, and the resulting data analysed, as efficiently as possible. The other is to provide an honest quantification of the uncertainty attached to any binary decision by reporting predictive probabilities that a policy-defined condition for action is or is not met.

Adam R. Brentnall, Jack Cuzick.

Source: Statistical Science, Volume 35, Number 1, 14--30.

Abstract:
Strategies to prevent cancer and diagnose it early when it is most treatable are needed to reduce the public health burden from rising disease incidence. Risk assessment is playing an increasingly important role in targeting individuals in need of such interventions. For breast cancer many individual risk factors have been well understood for a long time, but the development of a fully comprehensive risk model has not been straightforward, in part because there have been limited data where joint effects of an extensive set of risk factors may be estimated with precision. In this article we first review the approach taken to develop the IBIS (Tyrer–Cuzick) model, and describe recent updates. We then review and develop methods to assess calibration of models such as this one, where the risk of disease allowing for competing mortality over a long follow-up time or lifetime is estimated. The breast cancer risk model model and calibration assessment methods are demonstrated using a cohort of 132,139 women attending mammography screening in the State of Washington, USA.

Zhixiang Lin, Mahdi Zamanighomi, Timothy Daley, Shining Ma, Wing Hung Wong.

Source: Statistical Science, Volume 35, Number 1, 2--13.

Abstract:
Unsupervised methods, including clustering methods, are essential to the analysis of single-cell genomic data. Model-based clustering methods are under-explored in the area of single-cell genomics, and have the advantage of quantifying the uncertainty of the clustering result. Here we develop a model-based approach for the integrative analysis of single-cell chromatin accessibility and gene expression data. We show that combining these two types of data, we can achieve a better separation of the underlying cell types. An efficient Markov chain Monte Carlo algorithm is also developed.

Source: Statistical Science, Volume 35, Number 1, 1--1.

Junhui Cai, Avishai Mandelbaum, Chaitra H. Nagaraja, Haipeng Shen, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 669--691.

Abstract:
Statisticians are finding their place in the emerging field of data science. However, many issues considered “new” in data science have long histories in statistics. Examples of using statistical thinking are illustrated, which range from exploratory data analysis to measuring uncertainty to accommodating nonrandom samples. These examples are then applied to service networks, baseball predictions and official statistics.

Iain M. Johnstone.

Source: Statistical Science, Volume 34, Number 4, 657--668.

Abstract:
Many papers in the early part of Brown’s career focused on the admissibility or otherwise of estimators of a vector parameter. He established that inadmissibility of invariant estimators in three and higher dimensions is a general phenomenon, and found deep and beautiful connections between admissibility and other areas of mathematics. This review touches on several of his major contributions, with a focus on his celebrated 1971 paper connecting admissibility, recurrence and elliptic partial differential equations.

T. Tony Cai.

Source: Statistical Science, Volume 34, Number 4, 635--656.

Abstract:
A wide range of nonparametric function estimation models have been studied individually in the literature. Among them the homoscedastic nonparametric Gaussian regression is arguably the best known and understood. Inspired by the asymptotic equivalence theory, Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046) and Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433) developed a unified approach to turn a collection of non-Gaussian function estimation models into a standard Gaussian regression and any good Gaussian nonparametric regression method can then be used. These Gaussianization Machines have two key components, binning and transformation. When combined with BlockJS, a wavelet thresholding procedure for Gaussian regression, the procedures are computationally efficient with strong theoretical guarantees. Technical analysis given in Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046) and Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433) shows that the estimators attain the optimal rate of convergence adaptively over a large set of Besov spaces and across a collection of non-Gaussian function estimation models, including robust nonparametric regression, density estimation, and nonparametric regression in exponential families. The estimators are also spatially adaptive. The Gaussianization Machines significantly extend the flexibility and scope of the theories and methodologies originally developed for the conventional nonparametric Gaussian regression. This article aims to provide a concise account of the Gaussianization Machines developed in Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046), Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433).

James O. Berger, Anirban DasGupta.

Source: Statistical Science, Volume 34, Number 4, 621--634.

Abstract:
This article gives a panoramic survey of the general area of parametric statistical inference, decision theory and foundations of statistics for the period 1965–2010 through the lens of Larry Brown’s contributions to varied aspects of this massive area. The article goes over sufficiency, shrinkage estimation, admissibility, minimaxity, complete class theorems, estimated confidence, conditional confidence procedures, Edgeworth and higher order asymptotic expansions, variational Bayes, Stein’s SURE, differential inequalities, geometrization of convergence rates, asymptotic equivalence, aspects of empirical process theory, inference after model selection, unified frequentist and Bayesian testing, and Wald’s sequential theory. A reasonably comprehensive bibliography is provided.

Andreas Buja, Arun Kumar Kuchibhotla, Richard Berk, Edward George, Eric Tchetgen Tchetgen, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 606--620.

Abstract:
We respond to the discussants of our articles emphasizing the importance of inference under misspecification in the context of the reproducibility/replicability crisis. Along the way, we discuss the roles of diagnostics and model building in regression as well as connections between our well-specification framework and semiparametric theory.

Dalia Ghanem, Todd A. Kuffner.

Source: Statistical Science, Volume 34, Number 4, 604--605.

Alessandro Rinaldo, Ryan J. Tibshirani, Larry Wasserman.

Source: Statistical Science, Volume 34, Number 4, 599--603.

Abstract:
What is the meaning of a regression parameter? Why is this the de facto standard object of interest for statistical inference? These are delicate issues, especially when the model is misspecified. We argue that focusing on predictive quantities may be a desirable alternative.

David Whitney, Ali Shojaie, Marco Carone.

Source: Statistical Science, Volume 34, Number 4, 591--598.

Anthony C. Davison, Erwan Koch, Jonathan Koh.

Source: Statistical Science, Volume 34, Number 4, 584--590.

Abstract:
This discussion focuses on areas of disagreement with the papers, particularly the target of inference and the case for using the robust ‘sandwich’ variance estimator in the presence of moderate mis-specification. We also suggest that existing procedures may be appreciably more powerful for detecting mis-specification than the authors’ RAV statistic, and comment on the use of the pairs bootstrap in balanced situations.

Roderick J. Little.

Source: Statistical Science, Volume 34, Number 4, 580--583.

Dag Tjøstheim.

Source: Statistical Science, Volume 34, Number 4, 575--579.

Nikki L. B. Freeman, Xiaotong Jiang, Owen E. Leete, Daniel J. Luckett, Teeranan Pokaprakarn, Michael R. Kosorok.

Source: Statistical Science, Volume 34, Number 4, 572--574.

Jerald F. Lawless.

Source: Statistical Science, Volume 34, Number 4, 569--571.

Abstract:
I comment on the papers Models as Approximations I and II, by A. Buja, R. Berk, L. Brown, E. George, E. Pitkin, M. Traskin, L. Zhao and K. Zhang.

Sara van de Geer.

Source: Statistical Science, Volume 34, Number 4, 566--568.

Abstract:
We discuss the papers “Models as Approximations” I & II, by A. Buja, R. Berk, L. Brown, E. George, E. Pitkin, M. Traskin, L. Zao and K. Zhang (Part I) and A. Buja, L. Brown, A. K. Kuchibhota, R. Berk, E. George and L. Zhao (Part II). We present a summary with some details for the generalized linear model.

Andreas Buja, Lawrence Brown, Arun Kumar Kuchibhotla, Richard Berk, Edward George, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 545--565.

Abstract:
We develop a model-free theory of general types of parametric regression for i.i.d. observations. The theory replaces the parameters of parametric models with statistical functionals, to be called “regression functionals,” defined on large nonparametric classes of joint ${x extrm{-}y}$ distributions, without assuming a correct model. Parametric models are reduced to heuristics to suggest plausible objective functions. An example of a regression functional is the vector of slopes of linear equations fitted by OLS to largely arbitrary ${x extrm{-}y}$ distributions, without assuming a linear model (see Part I). More generally, regression functionals can be defined by minimizing objective functions, solving estimating equations, or with ad hoc constructions. In this framework, it is possible to achieve the following: (1) define a notion of “well-specification” for regression functionals that replaces the notion of correct specification of models, (2) propose a well-specification diagnostic for regression functionals based on reweighting distributions and data, (3) decompose sampling variability of regression functionals into two sources, one due to the conditional response distribution and another due to the regressor distribution interacting with misspecification, both of order $N^{-1/2}$, (4) exhibit plug-in/sandwich estimators of standard error as limit cases of ${x extrm{-}y}$ bootstrap estimators, and (5) provide theoretical heuristics to indicate that ${x extrm{-}y}$ bootstrap standard errors may generally be preferred over sandwich estimators.

Andreas Buja, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 523--544.

Abstract:
In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x extrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x extrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

Peter M. Atkinson, Jorge Mateu.

Source: Statistical Science, Volume 34, Number 3, 504--521.

Abstract:
Peter John Diggle was born on February 24, 1950, in Lancashire, England. Peter went to school in Scotland, and it was at the end of his school years that he found that he was good at maths and actually enjoyed it. Peter went to Edinburgh to do a maths degree, but transferred halfway through to Liverpool where he completed his degree. Peter studied for a year at Oxford and was then appointed in 1974 as a lecturer in statistics at the University of Newcastle-upon-Tyne where he gained his PhD, and was promoted to Reader in 1983. A sabbatical at the Swedish Royal College of Forestry gave him his first exposure to real scientific data and problems, prompting a move to CSIRO, Australia. After five years with CSIRO where he was Senior, then Principal, then Chief Research Scientist and Chief of the Division of Mathematics and Statistics, he returned to the UK in 1988, to a Chair at Lancaster University. Since 2011 Peter has held appointments at Lancaster and Liverpool, together with honorary appointments at Johns Hopkins, Columbia and Yale. At Lancaster, Peter was the founder and Director of the Medical Statistics Unit (1995–2001), University Dean for Research (1998–2001), EPSRC Senior Fellow (2004–2008), Associate Dean for Research at the School of Health and Medicine (2007–2011), Distinguished University Professor, and leader of the CHICAS Research Group (2007–2017). A Fellow of the Royal Statistical Society since 1974, he was a Member of Council (1983–1985), Joint Editor of JRSSB (1984–1987), Honorary Secretary (1990–1996), awarded the Guy Medal in Silver (1997) and the Barnett Award (2018), Associate Editor of Applied Statistics (1998–2000), Chair of the Research Section Committee (1998–2000), and President (2014–2016). Away from work, Peter enjoys music, playing folk-blues guitar and tenor recorder, and listening to jazz. His running days are behind him, but he can just about hold his own in mixed-doubles badminton with his family. His boyhoood hero was Stirling Moss, and he retains an enthusiasm for classic cars, not least his 1988 Porsche 924S. His favorite authors are George Orwell, Primo Levi and Nigel Slater. This interview was done prior to the fourth Spatial Statistics conference held in Lancaster, July 2017 where a session was dedicated to Peter celebrating his contributions to statistics.

Pantelis Samartsidis, Shaun R. Seaman, Anne M. Presanis, Matthew Hickman, Daniela De Angelis.

Source: Statistical Science, Volume 34, Number 3, 486--503.

Abstract:
Researchers are often challenged with assessing the impact of an intervention on an outcome of interest in situations where the intervention is nonrandomised, the intervention is only applied to one or few units, the intervention is binary, and outcome measurements are available at multiple time points. In this paper, we review existing methods for causal inference in these situations. We detail the assumptions underlying each method, emphasize connections between the different approaches and provide guidelines regarding their practical implementation. Several open problems are identified thus highlighting the need for future research.

Daniele Durante, Tommaso Rigon.

Source: Statistical Science, Volume 34, Number 3, 472--485.

Abstract:
Variational Bayes (VB) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions within an exponential family. Models with logit components are an apparently notable exception to this class, due to the absence of conjugacy among the logistic likelihood and the Gaussian priors for the coefficients in the linear predictor. To facilitate approximate inference within this widely used class of models, Jaakkola and Jordan ( Stat. Comput. 10 (2000) 25–37) proposed a simple variational approach which relies on a family of tangent quadratic lower bounds of the logistic log-likelihood, thus restoring conjugacy between these approximate bounds and the Gaussian priors. This strategy is still implemented successfully, but few attempts have been made to formally understand the reasons underlying its excellent performance. Following a review on VB for logistic models, we cover this gap by providing a formal connection between the above bound and a recent Pólya-gamma data augmentation for logistic regression. Such a result places the computational methods associated with the aforementioned bounds within the framework of variational inference for conditionally conjugate exponential family models, thereby allowing recent advances for this class to be inherited also by the methods relying on Jaakkola and Jordan ( Stat. Comput. 10 (2000) 25–37).

Yuan Ke, Stanislav Minsker, Zhao Ren, Qiang Sun, Wen-Xin Zhou.

Source: Statistical Science, Volume 34, Number 3, 454--471.

Abstract:
We provide a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce elementwise and spectrumwise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key insight is that estimators should adapt to the sample size, dimensionality and noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate practical implementation, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.

Anna L. Smith, Dena M. Asta, Catherine A. Calder.

Source: Statistical Science, Volume 34, Number 3, 428--453.

Abstract:
We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads’ unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.

Sijia Xiang, Weixin Yao, Guangren Yang.

Source: Statistical Science, Volume 34, Number 3, 391--404.

Abstract:
Finite mixture models have offered a very important tool for exploring complex data structures in many scientific areas, such as economics, epidemiology and finance. Semiparametric mixture models, which were introduced into traditional finite mixture models in the past decade, have brought forth exciting developments in their methodologies, theories, and applications. In this article, we not only provide a selective overview of the newly-developed semiparametric mixture models, but also discuss their estimation methodologies, theoretical properties if applicable, and some open questions. Recent developments are also discussed.

Nathan B. Cruze, Andreea L. Erciulescu, Balgobin Nandram, Wendy J. Barboza, Linda J. Young.

Source: Statistical Science, Volume 34, Number 2, 301--316.

Abstract:
In the United States, county-level estimates of crop yield, production, and acreage published by the United States Department of Agriculture’s National Agricultural Statistics Service (USDA NASS) play an important role in determining the value of payments allotted to farmers and ranchers enrolled in several federal programs. Given the importance of these official county-level crop estimates, NASS continually strives to improve its crops county estimates program in terms of accuracy, reliability and coverage. In 2015, NASS engaged a panel of experts convened under the auspices of the National Academies of Sciences, Engineering, and Medicine Committee on National Statistics (CNSTAT) for guidance on implementing models that may synthesize multiple sources of information into a single estimate, provide defensible measures of uncertainty, and potentially increase the number of publishable county estimates. The final report titled Improving Crop Estimates by Integrating Multiple Data Sources was released in 2017. This paper discusses several needs and requirements for NASS county-level crop estimates that were illuminated during the activities of the CNSTAT panel. A motivating example of planted acreage estimation in Illinois illustrates several challenges that NASS faces as it considers adopting any explicit model for official crops county estimates.

Laura Anderlucci, Angela Montanari, Cinzia Viroli.

Source: Statistical Science, Volume 34, Number 2, 280--300.

Abstract:
In this paper, we retrace the recent history of statistics by analyzing all the papers published in five prestigious statistical journals since 1970, namely: The Annals of Statistics , Biometrika , Journal of the American Statistical Association , Journal of the Royal Statistical Society, Series B and Statistical Science . The aim is to construct a kind of “taxonomy” of the statistical papers by organizing and clustering them in main themes. In this sense being identified in a cluster means being important enough to be uncluttered in the vast and interconnected world of the statistical research. Since the main statistical research topics naturally born, evolve or die during time, we will also develop a dynamic clustering strategy, where a group in a time period is allowed to migrate or to merge into different groups in the following one. Results show that statistics is a very dynamic and evolving science, stimulated by the rise of new research questions and types of data.

Lei Liu, Ya-Chen Tina Shih, Robert L. Strawderman, Daowen Zhang, Bankole A. Johnson, Haitao Chai.

Source: Statistical Science, Volume 34, Number 2, 253--279.

Abstract:
Zero-inflated nonnegative continuous (or semicontinuous) data arise frequently in biomedical, economical, and ecological studies. Examples include substance abuse, medical costs, medical care utilization, biomarkers (e.g., CD4 cell counts, coronary artery calcium scores), single cell gene expression rates, and (relative) abundance of microbiome. Such data are often characterized by the presence of a large portion of zero values and positive continuous values that are skewed to the right and heteroscedastic. Both of these features suggest that no simple parametric distribution may be suitable for modeling such type of outcomes. In this paper, we review statistical methods for analyzing zero-inflated nonnegative outcome data. We will start with the cross-sectional setting, discussing ways to separate zero and positive values and introducing flexible models to characterize right skewness and heteroscedasticity in the positive values. We will then present models of correlated zero-inflated nonnegative continuous data, using random effects to tackle the correlation on repeated measures from the same subject and that across different parts of the model. We will also discuss expansion to related topics, for example, zero-inflated count and survival data, nonlinear covariate effects, and joint models of longitudinal zero-inflated nonnegative continuous data and survival. Finally, we will present applications to three real datasets (i.e., microbiome, medical costs, and alcohol drinking) to illustrate these methods. Example code will be provided to facilitate applications of these methods.