Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Goal of this article is to document evolution of the Interface and its Symposia, from their conception and birth when small data were analyzed with Statistics in the mid 20th Century until Big Data are now analyzed with Data Science in the early 21st Century. Wilfrid Dixon's 1961 BMD Statistical Program Package was a pioneer predictor of Computing in Statistics, and Arthur Samuel's 1965 presentation on using game‐branch probabilities in teaching ILLIAC I to play checkers was a pioneer predictor of Statistics in Computing. Such predictors produced a perception that future interactions of Computing and Statistics might constitute a significant and productive Interface of Computing and Statistics. Another perception included Computing and Statistics with Computing in Statistics and Statistics in Computing. This presented the challenge of organizing an Interface Symposium, to introduce the Interface to a vibrant environment for Computing and Statistics in Southern California. Presentations at the Symposia reveal that small data are in the process of becoming Big Data, while Computing in Statistics and Machine Learning are becoming the Interface, and the Interface is becoming Data Science. Data Science, the first comprehensive Journal on Data Science, another 1 of the 15 ASA Journals as well as 3 of 21 ASA Sections constitute a proud heritage for Interface and its Symposia. Perspective of the article is shaped by 60 years of pioneering and continuously contributing to the Interface and its Symposia, which few can match. WIREs Comput Stat 2014, 6:367–377. doi: 10.1002/wics.1316This article is categorized under: Applications of Computational Statistics > Organizations and Publications

Financial data by nature are inter‐related and should be analyzed using multivariate methods. Many models exist for the joint analysis of multiple financial instruments. Early models often assumed some type of constant behavior between the instruments over the time period of analysis. But today, time‐varying covariance models are a key component of financial time series analysis leading to a deeper understanding of changing market conditions. Models for covolatility of financial data quickly grow in their complexity and parameters, and 20 years of research offers a variety of solutions to this complexity. After a short introduction of univariate volatility models, this article begins with the basic multivariate formulation for time series covariance modeling and moves to leading time series tools that address this complexity. Coupling these models with regime switching via a Markov process extends the features that can be understood from market behavior. We ground this review in an example of modeling the covariance of securities within sectors and sectors within markets, with dynamics that allow for two different market regimes. Specifically, we simultaneously model individual daily stock data that belong to one of three market sectors and examine the behavior of the market as a whole as well as the behavior of the market sectors over time. A motivation for this characterization concerns portfolio diversification and stock anomalies, and we capture the changing comovement of stocks within and between sectors as market conditions change. For example, some of these market conditions include market crashes or collapses and common external influences. WIREs Comput Stat 2014, 6:326–340. doi: 10.1002/wics.1323This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

High‐dimensional data analysis emerges in many different areas of scientific research and social practice. Variable selection is an important task in statistical analysis for high‐dimensional data. The traditional all‐subset‐selection method can be ideal for variable selection, but it is computationally intractable in the high‐dimensional setting. In both regression and classification contexts, sparsity penalties are commonly used for the purpose of defining the complexity of the resulting model so as to achieve variable selection. The current article reviews a few important milestones and some recent works in the area of variable selection, especially those methods which useLqnorm and their variants as the penalty term. In particular, we review theLqpenalty, nonconvex penalties, among others. In ultrahigh‐dimensional data analysis, independence learning is often used for the purpose of dimension reduction. Theoretical results, methodological developments and computational innovations in regard to these methods are discussed. These variable selection techniques can be easily extended to problems beyond linear regression, such as classification, quantile regression, etc. Lastly, an interesting and promising research trend is the combination of multiple methods and we review several successful methods which fall into this category.This article is categorized under:Statistical and Graphical Methods of Data Analysis > Modeling Methods and AlgorithmsStatistical Models > Model SelectionStatistical Models > Linear Models

The history of Bayesian statistics is traced, from a personal perspective, through various strands and via its re‐genesis during the 1960s to the current day. Emphasis is placed on broad‐sense Bayesian methodology that can be used to meaningfully analyze observed datasets. Over 750 people in science, medicine, and socioeconomics, who have influenced the evolution of the Bayesian approach into the powerful paradigm that it is today, are highlighted. The frequentist/Bayesian controversy is addressed, together with the ways in which many Bayesians combine the two ideologies as a Bayes/non‐Bayes compromise, e.g., when drawing inferences about unknown parameters or when investigating the choice of sampling model in relation to its real‐life background. A number of fundamental issues are discussed and critically examined, and some elementary explanations for nontechnical readers and some personal reminiscences are included. Some of the Bayesian contributions of the 21st century are subjected to more detailed critique, so that readers may learn more about the quality and relevance of the ongoing research. A recent resolution of Lindley's paradox by Baskurt and Evans is reported. The axioms of subjective probability are reassessed, some state‐of‐the‐art alternatives to Leonard Savage's axioms of utility are discussed, and Deborah Mayo and Michael Evan's refutation of Allan Birnbaum's 1962 justification of the likelihood principle in terms of the sufficiency and conditionality principles is addressed.WIREs Comput Stat2014, 6:80–115. doi: 10.1002/wics.1293This article is categorized under:Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

As the number of sources and quantity of document information explodes, efficient and intuitive visualization tools are desperately needed to assist users in understanding the contents and features of a document, while discovering hidden information. This overview introduces fundamental concepts of and designs for document visualization, a number of representative methods in the field, and challenges as well as promising directions of future development. The focus is on explaining the rationale and characteristics of representative document visualization methods for each category. A discussion of the limitations of our classification and a comparison of reviewed methods are presented at the end. This overview also aims to point out theoretical and practical challenges in document visualization.WIREs Comput Stat2014, 6:19–36. doi: 10.1002/wics.1285This article is categorized under:Algorithms and Computational Methods > Computer GraphicsStatistical Learning and Exploratory Methods of the Data Sciences > Text Mining

Stochastic differential equations (SDEs) provide accessible mathematical models that combine deterministic and probabilistic components of dynamic behavior. This article is an overview of numerical solution methods for SDEs. The solutions are stochastic processes that represent diffusive dynamics, a common modeling assumption in many application areas. We include a description of fundamental numerical methods and the concepts of strong and weak convergence and order for SDE solvers. In addition, we briefly discuss the extension of SDE solvers to coupled systems driven by correlated noise. WIREs Comput Stat 2013. doi: 10.1002/wics.1272This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Algorithms and Computational Methods > Numerical Methods

While permutation tests and bootstraps have very wide‐ranging application, both share a common potential drawback: as data‐intensive resampling methods, both can be runtime prohibitive when applied to large‐ or even medium‐sized data samples drawn from large datasets. The data explosion over the past few decades has made this a common occurrence, and it highlights the increasing need for faster, and more efficient and scalable, permutation test and bootstrap algorithms. Seven bootstrap and six permutation test algorithms coded in SAS (the largest privately owned software firm globally) are compared herein. The fastest algorithms (‘OPDY’ for the bootstrap, ‘OPDN’ for permutation tests) are new, use no modules beyond Base SAS, and achieve speed increases orders of magnitude faster than the relevant ‘built‐in’ SAS procedures (OPDY is over 200× faster than Proc SurveySelect; OPDN is over 240× faster than Proc SurveySelect, over 350× faster than NPAR1WAY (which crashes on datasets less than a 10th the size OPDN can handle), and over 720× faster than Proc Multtest). OPDY also is much faster than hashing, which crashes on datasets smaller—sometimes by orders of magnitude—than OPDY can handle. OPDY is easily generalizable to multivariate regression models, and OPDN, which uses an extremely efficient draw‐by‐draw random‐sampling‐without‐replacement algorithm, can use virtually any permutation statistic, so both have a very wide range of application. And the time complexity of both OPDY and OPDN is sublinear, making them not only the fastest but also the only truly scalable bootstrap and permutation test algorithms, respectively, in SAS. WIREs Comput Stat 2013. doi: 10.1002/wics.1266This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Software for Computational Statistics > Software/Statistical Software