Spike-and-slab priors are commonly used for Bayesian variable selection, due to their interpretability and favorable statistical properties. However, existing samplers for spike-and-slab posteriors incur prohibitive computational costs when the number of variables is large. In this article, we propose Scalable Spike-and-Slab (S^3), a scalable Gibbs sampling implementation for high-dimensional Bayesian regression with the continuous spike-and-slab prior of George & McCulloch (1993). For a dataset with n observations and p covariates, S^3 has order max{n^2 p_t, np} computational cost at iteration t where p_t never exceeds the number of covariates switching spike-and-slab states between iterations t and t-1 of the Markov chain. This improves upon the order n^2 p per-iteration cost of state-of-the-art implementations as, typically, p_t is substantially smaller than p. We apply S^3 on synthetic and real-world datasets, demonstrating orders of magnitude speed-ups over existing exact samplers and significant gains in inferential quality over approximate samplers with comparable cost.

Several months ago, Phil Bourne, the initiator and frequent author of the wildly successful and incredibly useful “Ten Simple Rules” series, suggested that some statisticians put together a Ten Simple Rules article related to statistics. (One of the rules for writing a PLOS Ten Simple Rules article is to be Phil Bourne [1]. In lieu of that, we hope effusive praise for Phil will suffice.) Implicit in the guidelines for writing Ten Simple Rules [1] is “know your audience.” We developed our list of rules with researchers in mind: researchers having some knowledge of statistics, possibly with one or more statisticians available in their building, or possibly with a healthy do-it-yourself attitude and a handful of statistical packages on their laptops. We drew on our experience in both collaborative research and teaching, and, it must be said, from our frustration at being asked, more than once, to “take a quick look at my student’s thesis/my grant application/my referee’s report: it needs some input on the stats, but it should be pretty straightforward.” There are some outstanding resources available that explain many of these concepts clearly and in much more detail than we have been able to do here: among our favorites are Cox and Donnelly [2], Leek [3], Peng [4], Kass et al. [5], Tukey [6], and Yu [7]. Every article on statistics requires at least one caveat. Here is ours: we refer in this article to “science” as a convenient shorthand for investigations using data to study questions of interest. This includes social science, engineering, digital humanities, finance, and so on. Statisticians are not shy about reminding administrators that statistical science has an impact on nearly every part of almost all organizations.

The structure of the motor and the pattern of windings have great influence on the electrical excitation flux-switching (EEFS) motor. This paper developed a 200KW EEFS machine in the light of drive motors of the high power air conditioning compressor, and introduced the operate principle and basic parameters of the motor. The EEFS machine was optimized through FEM analysis and simulated with Maxwell 2D in a comprehensive consideration of performance indexes such as rated voltage and power. By changing basic sizes of the motor, electromagnetic performances, loss and efficiency of different structures of EEFS machine were compared to get the most suitable structure, and a proposal of radial distribution was given. The performance included the phase flux-linkage, back electromotive force (EMF) waveforms, no load characteristics and load characteristics, etc. The results provided theoretical basis of the development of high reliability of the doubly salient motor.

Properly segmenting multiband images of the Sun by their thermal properties will help determine the thermal structure of the solar corona. However, off-the-shelf segmentation algorithms are typically inappropriate because temperature information is captured by the relative intensities in different passbands, while the absolute levels are not relevant. Input features are therefore pixel-wise proportions of photons observed in each band. To segment solar images based on these proportions, we use a modification of k-means clustering that we call the H-means algorithm because it uses the Hellinger distance to compare probability vectors. H-means has a closed-form expression for cluster centroids, so computation is as fast as k-means. Tempering the input probability vectors reveals a broader class of H-means algorithms which include spherical k-means clustering. More generally, H-means can be used anytime the input feature is a probabilistic distribution, and hence is useful beyond image segmentation applications.

This paper presents a new approach to demosaicing of spatially sampled image data observed through a color filter array, in which properties of Smith-Barnwell filterbanks are employed to exploit the correlation of color components in order to reconstruct a subsampled image. The method is shown to be amenable to wavelet-domain denoising prior to demosaicing, and a general framework for applying existing image denoising algorithms to color filter array data is also described. Results indicate that the proposed method performs on a par with the state of the art for far lower computational cost, and provides a versatile, effective, and low-complexity solution to the problem of interpolating color filter array data observed in noise.

We present a unified framework for coupling the EM algorithm with the Bayesian hierarchical modeling of neighboring wavelet coefficients of image signals. Within this framework, problems with missing pixels or pixel components, and hence unobservable wavelet coefficients, are handled simultaneously with denoising. The hyper-parameters of the model are estimated via the marginal likelihood by the EM algorithm, and a part of the output of its E-step automatically provide optimal estimates, given the specified Bayesian model, of the noise-free image. This unified empirical-Bayes based framework, therefore, offers a statistically principled and extremely flexible approach to a wide range of pixel estimation problems including image denoising, image interpolation, demosaicing, or any combinations of them.

In this work, we consider the problem of wavelet image denoising when some of the pixel values are unobserved. Our approach is to treat those unobserved pixels as missing data and adopt the self-consistency principle to define a "best" wavelet estimate for the true image. We propose fast and effective algorithms for computing such a self-consistent wavelet estimate. The practical performance of our proposal is evaluated via a simulation study. A possible application of this work is image inpainting.