This article is a review article on the optimal Markov chain Monte Carlo (MCMC) sampling. The focus is on homogeneous Markov chains. This article first reviews the problem of finding the optimal transition matrix, which is defined to minimize the asymptotic variance of MCMC estimators. The article later reviews the locally optimal sampler (LOS), an MCMC sampling that performs local updates based on the optimal transition matrix. We conducted a simulation study to compare the LOS with the Metropolis–Hastings and the Gibbs Sampler. The LOS was shown to provide an improved rate of convergence over these two most popular sampling schemes. The implementation of the LOS requires only minor modifications in existing Gibbs sampling code. WIREs Comput Stat 2013. doi: 10.1002/wics.1265

An important aspect of statistical modeling of spatial or spatiotemporal data is to determine the covariance function. It is a key part of spatial prediction (kriging). The classical geostatistical approach uses an assumption of isotropy, which yields circular isocorrelation curves. However, this is inappropriate for many applications, and several nonstationary approaches have been developed. Adding the temporal aspect, there is often interaction between time and space, requiring classes of nonseparable covariance structures. WIREs Comput Stat 2013, 5:279–287. doi: 10.1002/wics.1259

Face recognition involves at least three major concepts from statistics: dimension reduction, feature extraction, and prediction. A selective review of algorithms, from seminal to state-of-the-art, explores how these concepts persist as organizing principles in the field. Algorithms based directly upon classical statistical techniques include linear methods like principal component analysis and linear discriminant analysis. Nonlinear manifold methods, such as Laplacianfaces and Stiefel quotients, offer considerable performance improvements. Other noteworthy ideas include three-dimensional morphable models, methods using local regions and/or alternative feature spaces (e.g., elastic bunch graph matching and local binary patterns) and sparse representation approaches. Opportunities for innovative statistical and collaborative research in face recognition are expanding in tandem with the growing complexity and diversity of applications. WIREs Comput Stat 2013, 5:288–308. doi: 10.1002/wics.1262

DNA microarrays are a relatively new technology that can simultaneously measure the expression level of thousands of genes. They have become an important tool for a wide variety of biological experiments. One of the most common goals of DNA microarray experiments is to identify genes associated with biological processes of interest. Conventional statistical tests often produce poor results when applied to microarray data owing to small sample sizes, noisy data, and correlation among the expression levels of the genes. Thus, novel statistical methods are needed to identify significant genes in DNA microarray experiments. This article discusses the challenges inherent in DNA microarray analysis and describes a series of statistical techniques that can be used to overcome these challenges. The problem of multiple hypothesis testing and its relation to microarray studies are also considered, along with several possible solutions. WIREs Comput Stat 2013, 5:309–325. doi: 10.1002/wics.1260

The study of sleep, and in particular electroencephalogram (EEG)-sleep recordings, is important in several areas of medicine. Next to pain, sleep anomalies are the most significant indicators of illness. During sleep the human brain goes through several physiological stages; therefore, the problem of automated detection of sleep stages using EEG data naturally arises in neurosciences. A two step procedure of computerized scoring of sleep stages is considered, with the first step involving features extractions via spectral and nonlinear dynamics characteristics and the second step in which sleep classifications can be accomplished. WIREs Comput Stat 2013, 5:326–333. doi: 10.1002/wics.1261

We focus on a timeline for stereoscopic visualization. The timeline can be conceived as three distinct eras. The first era was characterized by the full understanding of stereoscopic vision and the development of the stereoscope technology for viewing three dimensional images. The first era was greatly enabled by the simultaneous development of photographic technologies. The second era was characterized by the development of polarized light and anaglyph stereo technology and was mainly manifested with a dramatic outpouring of motion pictures. The third era, the digital era, was developed in connection with virtual reality and scientific data visualization. WIREs Comput Stat 2013, 5:334–340. doi: 10.1002/wics.1264