The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used to determine the properties of dark energy and the nature of gravity, because light from those galaxies is bent by gravity from the intervening dark matter. The observed galaxy images appear distorted, although only slightly, and their shapes must be precisely disentangled from the effects of pixelisation, convolution and noise. The worldwide gravitational lensing community has made significant progress in techniques to measure these distortions via the Shear TEsting Program (STEP). Via STEP, we have run challenges within our own community, and come to recognise that this particular image analysis problem is ideally matched to experts in statistical inference, inverse problems and computational learning. Thus, in order to continue the progress seen in recent years, we are seeking an infusion of new ideas from these communities. This document details the GREAT08 Challenge for potential participants. Please visit www.great08challenge.info for the latest information.

Some astronomy projects require a blind search through a vast number of hypotheses to detect objects of interest. The number of hypotheses to test can be in the billions. A naive blind search over every single hypothesis would be far too costly computationally. We propose a hierarchical scheme for blind search, using various “resolution” levels. At lower resolution levels, “regions” of interest in the search space are singled out with a low computational cost. These regions are refined at intermediate resolution levels and only the most promising candidates are finally tested at the original fine resolution. The optimal search strategy is found by dynamic programming. We demonstrate the procedure for pulsar search from satellite gamma-ray observations and show that the power of the naive blind search can almost be matched with the hierarchical scheme while reducing the computational burden by more than three orders of magnitude.

An enormous amount of observations on Cosmic Microwave Background radiation has been collected in the last decade, and much more data are expected in the near future from planned or operating satellite missions. These datasets are a goldmine of information for Cosmology and Theoretical Physics; their efficient exploitation posits several intriguing challenges from the statistical point of view. In this paper we review a number of open problems in CMB data analysis and we present applications to observations from the WMAP mission.

Whether a dwarf spheroidal galaxy is in equilibrium or being tidally disrupted by the Milky Way is an important question for the study of its dark matter content and distribution. This question is investigated using 328 recent observations from the dwarf spheroidal Leo I. For Leo I, tidal disruption is detected, at least for stars sufficiently far from the center, but the effect appears to be quite modest. Statistical tools include isotonic and split point estimators, asymptotic theory, and resampling methods.

Color-Magnitude Diagrams (CMDs) are plots that compare the magnitudes (luminosities) of stars in different wavelengths of light (colors). High nonlinear correlations among the mass, color, and surface temperature of newly formed stars induce a long narrow curved point cloud in a CMD known as the main sequence. Aging stars form new CMD groups of red giants and white dwarfs. The physical processes that govern this evolution can be described with mathematical models and explored using complex computer models. These calculations are designed to predict the plotted magnitudes as a function of parameters of scientific interest, such as stellar age, mass, and metallicity. Here, we describe how we use the computer models as a component of a complex likelihood function in a Bayesian analysis that requires sophisticated computing, corrects for contamination of the data by field stars, accounts for complications caused by unresolved binary-star systems, and aims to compare competing physics-based computer models of stellar evolution.

The surprising discovery of an accelerating universe led cosmologists to posit the existence of “dark energy”—a mysterious energy field that permeates the universe. Understanding dark energy has become the central problem of modern cosmology. After describing the scientific background in depth, we formulate the task as a nonlinear inverse problem that expresses the comoving distance function in terms of the dark-energy equation of state. We present two classes of methods for making sharp statistical inferences about the equation of state from observations of Type Ia Supernovae (SNe). First, we derive a technique for testing hypotheses about the equation of state that requires no assumptions about its form and can distinguish among competing theories. Second, we present a framework for computing parametric and nonparametric estimators of the equation of state, with an associated assessment of uncertainty. Using our approach, we evaluate the strength of statistical evidence for various competing models of dark energy. Consistent with current studies, we find that with the available Type Ia SNe data, it is not possible to distinguish statistically among popular dark-energy models, and that, in particular, there is no support in the data for rejecting a cosmological constant. With much more supernova data likely to be available in coming years (e.g., from the DOE/NASA Joint Dark Energy Mission), we address the more interesting question of whether future data sets will have sufficient resolution to distinguish among competing theories.

We propose the use of a new false discovery rate (FDR) controlling procedure as a model selection penalized method, and compare its performance to that of other penalized methods over a wide range of realistic settings: nonorthogonal design matrices, moderate and large pool of explanatory variables, and both sparse and nonsparse models, in the sense that they may include a small and large fraction of the potential variables (and even all). The comparison is done by a comprehensive simulation study, using a quantitative framework for performance comparisons in the form of empirical minimaxity relative to a “random oracle”: the oracle model selection performance on data dependent forward selected family of potential models. We show that FDR based procedures have good performance, and in particular the newly proposed method, emerges as having empirical minimax performance. Interestingly, using FDR level of 0.05 is a global best.

This paper considers small-area estimation with lung cancer mortality data, and discusses the choice of upper-level model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We give a general methodology for both evaluating the data evidence for different models and averaging over plausible models to give robust area effect distributions. We reanalyze the data of Tsutakawa [Biometrics 41 (1985) 69–79] on lung cancer mortality rates in Missouri cities, and show the differences in conclusions about the city rates from this methodology.

The amplified fragment length polymorphism (AFLP) method produces anonymous genetic markers from throughout a genome. We extend the nucleotide substitution model of AFLP evolution to additionally include insertion and deletion processes. The new Sub-ID model relaxes the common assumption that markers are independent and homologous. We build a Markov chain Monte Carlo methodology tailored for the Sub-ID model to implement a Bayesian approach to infer AFLP marker evolution. The method allows us to infer both the phylogenies and the subset of markers that are possibly homologous. In addition, we can infer the genome-wide relative rate of indels versus substitutions. In a case study with AFLP markers from sedges, a grass-like plant common in North America, we find that accounting for insertion and deletion makes a difference in phylogenetic inference. The inference of topologies is not sensitive to the prior settings and the Jukes–Cantor assumption for nucleotide substitution. The model for insertion and deletion we introduce has potential value in other phylogenetic applications.

Much of the trading activity in Equity markets is directed to brokerage houses. In exchange they provide so-called “soft dollars,” which basically are amounts spent in “research” for identifying profitable trading opportunities. Soft dollars represent about USD 1 out of every USD 10 paid in commissions. Obviously they are costly, and it is interesting for an institutional investor to determine whether soft dollar inputs are worth being used (and indirectly paid for) or not, from a statistical point of view. To address this question, we develop association measures between what broker–dealers predict and what markets realize. Our data are ordinal predictions by two broker–dealers and realized values on several markets, on the same ordinal scale. We develop a structural equation model with latent variables in an ordinal setting which allows us to test broker–dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. The method is then used to analyze our dataset.

Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high density grid, which can then be used to generate meteorological maps at a broad range of spatial and temporal scales. In addition to point predictions, quantifications of uncertainty are also needed. One way to accomplish this is to provide multiple simulations of the relevant meteorological quantities conditional on the observed data taking into account the various uncertainties in predicting a space-time process at locations with no monitoring data. Using a high-quality dataset of minute-by-minute measurements of atmospheric pressure in north-central Oklahoma, this work describes a statistical approach to carrying out these conditional simulations. Based on observations at 11 stations, conditional simulations were produced at two other sites with monitoring stations. The resulting point predictions are very accurate and the multiple simulations produce well-calibrated prediction uncertainties for temporal changes in atmospheric pressure but are substantially overconservative for the uncertainties in the predictions of (undifferenced) pressure.

In many scientific settings data can be naturally partitioned into variable groupings called views. Common examples include environmental (1st view) and genetic information (2nd view) in ecological applications, chemical (1st view) and biological (2nd view) data in drug discovery. Multi-view data also occur in text analysis and proteomics applications where one view consists of a graph with observations as the vertices and a weighted measure of pairwise similarity between observations as the edges. Further, in several of these applications the observations can be partitioned into two sets, one where the response is observed (labeled) and the other where the response is not (unlabeled). The problem for simultaneously addressing viewed data and incorporating unlabeled observations in training is referred to as multi-view transductive learning. In this work we introduce and study a comprehensive generalized fixed point additive modeling framework for multi-view transductive learning, where any view is represented by a linear smoother. The problem of view selection is discussed using a generalized Akaike Information Criterion, which provides an approach for testing the contribution of each view. An efficient implementation is provided for fitting these models with both backfitting and local-scoring type algorithms adjusted to semi-supervised graph-based learning. The proposed technique is assessed on both synthetic and real data sets and is shown to be competitive to state-of-the-art co-training and graph-based techniques.

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae.

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.

The last two decades have seen intense scientific and regulatory interest in the health effects of particulate matter (PM). Influential epidemiological studies that characterize chronic exposure of individuals rely on monitoring data that are sparse in space and time, so they often assign the same exposure to participants in large geographic areas and across time. We estimate monthly PM during 1988–2002 in a large spatial domain for use in studying health effects in the Nurses’ Health Study. We develop a conceptually simple spatio-temporal model that uses a rich set of covariates. The model is used to estimate concentrations of PM₁₀ for the full time period and PM_2.5 for a subset of the period. For the earlier part of the period, 1988–1998, few PM_2.5 monitors were operating, so we develop a simple extension to the model that represents PM_2.5 conditionally on PM₁₀ model predictions. In the epidemiological analysis, model predictions of PM₁₀ are more strongly associated with health effects than when using simpler approaches to estimate exposure.

Our modeling approach supports the application in estimating both fine-scale and large-scale spatial heterogeneity and capturing space–time interaction through the use of monthly-varying spatial surfaces. At the same time, the model is computationally feasible, implementable with standard software, and readily understandable to the scientific audience. Despite simplifying assumptions, the model has good predictive performance and uncertainty characterization.

Identifying promising compounds from a vast collection of feasible compounds is an important and yet challenging problem in the pharmaceutical industry. An efficient solution to this problem will help reduce the expenditure at the early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu and Johnson [Technometrics 48(2006) 273–283] proposed the SELC algorithm. Although powerful, it fails to extract substantial information from the data to guide the search efficiently, as this methodology is not based on any statistical modeling. The proposed approach uses Gaussian Process (GP) modeling to improve upon SELC, and hence named $\mathcal{G}$-SELC. The performance of the proposed methodology is illustrated using four and five dimensional test functions. Finally, we implement the new algorithm on a real pharmaceutical data set for finding a group of chemical compounds with optimal properties.

Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liquidity. We find that more liquid stocks based on financial characteristics have lower noise and noise-to-signal ratio measured from their high frequency returns. We then examine whether there exists a common, market-wide, factor in high frequency stock-level measurements of noise, and whether that factor is priced in asset returns.

The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilevel functional principal component analysis (MFPCA), a novel statistical methodology designed to extract core intra- and inter-subject geometric components of multilevel functional data. Though motivated by the SHHS, the proposed methodology is generally applicable, with potential relevance to many modern scientific studies of hierarchical or longitudinal functional outcomes. Notably, using MFPCA, we identify and quantify associations between EEG activity during sleep and adverse cardiovascular outcomes.