Functional mixture regression.

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.

When might we break the rules? A statistical analysis of aesthetics in photographs.

High-quality photographs often follow certain high-level rules well known to photographers, but some photographs intentionally break these rules. Doing so is usually a matter of artistry and intuition, and the conditions and patterns that allow for rule-breaks are often not well articulated by photographers. This article first applies statistical techniques to help find and evaluate rule-breaking photographs, and then from these photographs discover those patterns that justify their rule-breaking. With this approach, this article discovered some significant patterns that explain why some high-quality photographs successfully break the common photographic rules by positioning the subject in the center or the horizon in the vertical center. These patterns included reflections, leading lines, crossing objects, ambiguous lines, implied lines, thirds line subjects, and busy foregrounds for center horizon photographs, and symmetry, circular-shaped objects, thirds line elements, gestalt, framing, leading lines, and perspective lines for center subject photographs.

Covariance estimation via fiducial inference.

As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein-von Mises Theorem (Sonderegger and Hannig 2014), we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.

Multiresolution Modeling of High-Latitude Ionospheric Electric Field Variability and Impact on Joule Heating Using SuperDARN Data.

The most dynamic electromagnetic coupling between the magnetosphere and ionosphere occurs in the polar upper atmosphere. It is critical to quantify the electromagnetic energy and momentum input associated with this coupling as its impacts on the ionosphere and thermosphere system are global and major, often leading to considerable disturbances in near-Earth space environments. The current general circulation models of the upper atmosphere exhibit systematic biases that can be attributed to an inadequate representation of the Joule heating rate resulting from unaccounted stochastic fluctuations of electric fields associated with the magnetosphere-ionosphere coupling. These biases exist regardless of geomagnetic activity levels. To overcome this limitation, a new multiresolution random field modeling approach is developed, and the efficacy of the approach is demonstrated using Super Dual Auroral Radar Network (SuperDARN) data carefully curated for the study during a largely quiet 4-hour period on February 29, 2012. Regional small-scale electrostatic fields sampled at different resolutions from a probabilistic distribution of electric field variability conditioned on actual SuperDARN LOS observations exhibit considerably more localized fine-scale features in comparison to global large-scale fields modeled using the SuperDARN Assimilative Mapping procedure. The overall hemispherically integrated Joule heating rate is increased by a factor of about 1.5 due to the effect of random regional small-scale electric fields, which is close to the lower end of arbitrarily adjusted Joule heating multiplicative factor of 1.5 and 2.5 typically used in upper atmosphere general circulation models. The study represents an important step toward a data-driven ensemble modeling of magnetosphere-ionosphere-atmosphere coupling processes.

A MULTI-RESOLUTION MODEL FOR NON-GAUSSIAN RANDOM FIELDS ON A SPHERE WITH APPLICATION TO IONOSPHERIC ELECTROSTATIC POTENTIALS.

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial models for non-Gaussian random fields on a sphere based on a multi-resolution analysis. Using a special wavelet frame, named spherical needlets, as building blocks, the proposed model is constructed in the form of a sparse random effects model. The spatial localization of needlets, together with carefully chosen random coefficients, ensure the model to be non-Gaussian and isotropic. The model can also be expanded to include a spatially varying variance profile. The special formulation of the model enables us to develop efficient estimation and prediction procedures, in which an adaptive MCMC algorithm is used. We investigate the accuracy of parameter estimation of the proposed model, and compare its predictive performance with that of two Gaussian models by extensive numerical experiments. Practical utility of the proposed model is demonstrated through an application of the methodology to a data set of high-latitude ionospheric electrostatic potentials, generated from the LFM-MIX model of the magnetosphere-ionosphere system.

Pattern generation using likelihood inference for cellular automata.

Cellular automata are discrete dynamical systems which evolve on a discrete grid. Recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns. We develop likelihood-based methods for estimating rules of cellular automata aimed at the re-generation of observed regular patterns. Under noisy data, our approach is equivalent to estimating the local map of a stochastic cellular automaton. Direct computations of the maximum likelihood estimates are possible for regular binary patterns. The likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool. We illustrate our method with a series of examples using binary images.

FIBER DIRECTION ESTIMATION, SMOOTHING AND TRACKING IN DIFFUSION MRI.

Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and noninvasive manner through measuring water diffusion. The contribution of this paper is threefold. First, it proposes a new method to identify and estimate multiple diffusion directions within a voxel through a new and identifiable parametrization of the widely used multi-tensor model. Unlike many existing methods, this method focuses on the estimation of diffusion directions rather than the diffusion tensors. Second, this paper proposes a novel direction smoothing method which greatly improves direction estimation in regions with crossing fibers. This smoothing method is shown to have excellent theoretical and empirical properties. Last, this paper develops a fiber tracking algorithm that can handle multiple directions within a voxel. The overall methodology is illustrated with simulated data and a data set collected for the study of Alzheimer's disease by the Alzheimer's Disease Neuroimaging Initiative (ADNI).

A full bayesian approach for boolean genetic network inference.

Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.