How do people look at art? Are there any differences between how experienced and inexperienced art viewers look at a painting? We approach these questions by analyzing and modeling eye movement data from a cognitive art research experiment, where the eye movements of twenty test subjects, ten experienced and ten inexperienced art viewers, were recorded while they were looking at paintings.

Eye movements consist of stops of the gaze as well as jumps between the stops. Hence, the observed gaze stop locations can be thought of as a spatial point pattern, which can be modeled by a spatio-temporal point process. We introduce some statistical tools to analyze the spatio-temporal eye movement data, and compare the eye movements of experienced and inexperienced art viewers. In addition, we develop a stochastic model, which is rather simple but fits quite well to the eye movement data, to further investigate the differences between the two groups through functional summary statistics.

Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based on environmental predictors. To do this, we estimate the contribution of environmental variables, such as water depth and water temperature, to cholera outbreaks in the context of a disease transmission model. We implement a method which simultaneously accounts for disease dynamics and environmental variables in a Susceptible-Infected-Recovered-Susceptible (SIRS) model. The entire system is treated as a continuous-time hidden Markov model, where the hidden Markov states are the numbers of people who are susceptible, infected or recovered at each time point, and the observed states are the numbers of cholera cases reported. We use a Bayesian framework to fit this hidden SIRS model, implementing particle Markov chain Monte Carlo methods to sample from the posterior distribution of the environmental and transmission parameters given the observed data. We test this method using both simulation and data from Mathbaria, Bangladesh. Parameter estimates are used to make short-term predictions that capture the formation and decline of epidemic peaks. We demonstrate that our model can successfully predict an increase in the number of infected individuals in the population weeks before the observed number of cholera cases increases, which could allow for early notification of an epidemic and timely allocation of resources.

Motivated by an empirical analysis of the Childhood Asthma Management Project, CAMP, we introduce a new screening procedure for varying coefficient models with ultrahigh-dimensional longitudinal predictor variables. The performance of the proposed procedure is investigated via Monte Carlo simulation. Numerical comparisons indicate that it outperforms existing ones substantially, resulting in significant improvements in explained variability and prediction error. Applying these methods to CAMP, we are able to find a number of potentially important genetic mutations related to lung function, several of which exhibit interesting nonlinear patterns around puberty.

Quantile residual lifetime analysis is conducted to compare remaining lifetimes among groups for survival data. Evaluating residual lifetimes among groups after adjustment for covariates is often of interest. The current literature is limited to comparing two groups for independent data. We propose a pseudo-value approach to compare quantile residual lifetimes given covariates between multiple groups for independent and clustered survival data. The proposed method considers clustered event times and clustered censoring times in addition to independent event times and censoring times. We show that the method can also be used to compare multiple groups on the cause-specific residual life distribution in the competing risk setting, for which there are no current methods which account for clustering. The empirical Type I errors and statistical power of the proposed study are examined in a simulation study, which shows that the proposed method controls Type I errors very well and has higher power than an existing method. The proposed method is illustrated by a bone marrow transplant data set.

In this paper we propose a unified, probabilistically coherent framework for the analysis of task-related brain activity in multi-subject fMRI experiments. This is distinct from two-stage “group analysis” approaches traditionally considered in the fMRI literature, which separate the inference on the individual fMRI time courses from the inference at the population level. In our modeling approach we consider a spatiotemporal linear regression model and specifically account for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject nonparametric variable selection prior. For posterior inference, in addition to Markov chain Monte Carlo sampling algorithms, we develop suitable variational Bayes algorithms. We show on simulated data that variational Bayes inference achieves satisfactory results at more reduced computational costs than using MCMC, allowing scalability of our methods. In an application to data collected to assess brain responses to emotional stimuli our method correctly detects activation in visual areas when visual stimuli are presented.

Understanding neuronal activity in the human brain is an extremely difficult problem both in terms of measurement and statistical modeling. We address a particular research question in this area: the analysis of human intracranial electroencephalogram (iEEG) recordings of epileptic seizures from a collection of patients. In these data, each seizure of each patient is defined by the activities of many individual recording channels. The modeling of epileptic seizures is challenging due the large amount of heterogeneity in iEEG signal between channels within a particular seizure, between seizures within an individual, and across individuals. We develop a new nonparametric hierarchical Bayesian model that simultaneously addresses these multiple levels of heterogeneity in our epilepsy data. Our approach, which we call a multi-level clustering hierarchical Dirichlet process (MLC-HDP), clusters over channel activities within a seizure, over seizures of a patient and over patients. We demonstrate the advantages of our methodology over alternative approaches in human EEG seizure data and show that its seizure clustering is close to manual clustering by a physician expert. We also address important clinical questions like “to which seizures of other patients is this seizure similar?”

The prevalence of sequencing experiments in genomics has led to an increased use of methods for count data in analyzing high-throughput genomic data to perform analyses. The importance of shrinkage methods in improving the performance of statistical methods remains. A common example is gene expression data, where the counts per gene are often modeled as some form of an overdispersed Poisson. Shrinkage estimates of the per-gene dispersion parameter have led to improved estimation of dispersion, particularly in the case of a small number of samples.

We address a different count setting introduced by the use of sequencing data: comparing differential proportional usage via an overdispersed binomial model. We are motivated by our interest in testing for differential exon skipping in mRNA-Seq experiments. We introduce a novel shrinkage method that models the overdispersion with the double binomial distribution proposed by Efron [J. Amer. Statist. Assoc. 81 (1986) 709–721].

Our method (WEB-Seq) is an empirical Bayes strategy for producing a shrunken estimate of dispersion and effectively detects differential proportional usage, and has close ties to the weighted-likelihood strategy of edgeR developed for gene expression data [Bioinformatics 23 (2007) 2881–2887, Bioinformatics (Oxford, England) 26 (2010) 139–140]. We analyze its behavior on simulated data sets as well as real data and show that our method is fast, powerful and gives accurate control of the FDR compared to alternative approaches. We provide implementation of our methods in the R package DoubleExpSeq available on CRAN.

The detection of local genomic signals using high-throughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihood-based framework for such scans, and derive formulas for false positive rate control and power calculations. The framework can also accommodate modified processes that involve overdispersion. As a specific, detailed example, we consider the detection of insertions and deletions by paired-end DNA-sequencing. We propose several statistics for this problem, compare their power under current experimental designs, and illustrate their application on an Illumina Platinum Genomes data set.

For many complex environmental processes such as air pollution, the underlying physical mechanism usually provides valuable insights into the statistical modeling. In this paper, we propose a statistical air quality model motivated by a commonly used physical dispersion model, called the scalar transport equation. The emission of a pollutant is modeled by covariates such as land use, traffic pattern and meteorological conditions, while the transport and decay of a pollutant are modeled through a convolution approach which takes into account the dynamic wind field. This approach naturally establishes a nonstationary random field with a space–time nonseparable and anisotropic covariance structure. Note that, due to the extremely complex interactions between the pollutant and environmental conditions, the space–time covariance structure of pollutant concentration data is often dynamic and can hardly be specified or envisioned directly. The relationship between the proposed spatial-temporal model and the physics model is also shown, and the approach is applied to model the hourly ozone concentration data in Singapore.

The analysis of GWAS data has long been restricted to simple models that cannot fully capture the genetic architecture of complex human diseases. As a shift from standard approaches, we propose here a general statistical framework for multi-SNP analysis of GWAS data based on a Bayesian graphical model. Our goal is to develop a general approach applicable to a wide range of genetic association problems, including GWAS and fine-mapping studies, and, more specifically, be able to: (1) Assess the joint effect of multiple SNPs that can be linked or unlinked and interact or not; (2) Explore the multi-SNP model space efficiently using the Mode Oriented Stochastic Search (MOSS) algorithm and determine the best models. We illustrate our new methodology with an application to the CGEM breast cancer GWAS data. Our algorithm selected several SNPs embedded in multi-locus models with high posterior probabilities. Most of the SNPs selected have a biological relevance. Interestingly, several of them have never been detected in standard single-SNP analyses. Finally, our approach has been implemented in the open source $R$ package genMOSS.

We consider an urban planning application where Telecom Italia collected mobile-phone traffic data in the metropolitan area of Milan, Italy, aiming to retrieve meaningful information regarding working, residential, and mobility activities around the city. The independent component analysis (ICA) framework is used to model underlying spatial activities as spatial processes on a lattice independent of each other. To incorporate spatial dependence within the spatial sources, we develop a spatial colored ICA (scICA) method. The method models spatial dependence within each source in the frequency domain, exploiting the power of Whittle likelihood and local linear log-spectral density estimation. An iterative algorithm is derived to estimate the model parameters through maximum Whittle likelihood. We then apply scICA to the Italian mobile traffic application.

In property-casualty insurance, claims management is featured with the modeling of a semi-continuous insurance cost associated with individual risk transfer. This practice is further complicated by the multilevel structure of the insurance claims data, where a contract often contains a group of policyholders, each policyholder is insured under multiple types of coverage, and the contract is repeatedly observed over time. The data hierarchy introduces a complex dependence structure among claims and leads to diversification in the insurer’s liability portfolio.

To capture the unique features of policy-level insurance costs, we propose a copula regression for the multivariate longitudinal claims. In the model, the Tweedie double generalized linear model is employed to examine the semi-continuous claim cost of each coverage type, and a Gaussian copula is specified to accommodate the cross-sectional and temporal dependence among the multilevel claims. Estimation and inference is based on the composite likelihood approach and the properties of parameter estimates are investigated through simulation studies. When applied to a portfolio of personal automobile policies from a Canadian insurer, we show that the proposed copula model provides valuable insights to an insurer’s claims management process.

We consider designs for $f$ factors each at $m$ levels, where $f$ is small but $m$ is large. Main effect designs with $mf$ experimental points are presented. For two factors, two types of designs are investigated, termed sawtooth and dumbbell designs, based on a graphical representation. For three factors, cyclic sawtooth designs are considered. The paper seeks optimal and near optimal designs which involve factors with many levels but few observations. It also investigates issues of robustness when as much as one third of the data is structurally missing. An important area of application is in screening for drug discovery and we compare our designs with others using a published data set with two factors each with fifty levels, where the dumbbell design outperforms others and is an example of an inherently unbalanced design dominating more balanced designs.

Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, that is, the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being nonmissing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis–Hastings sampler. We compare and contrast our model performances to the standard nonspatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries.

Bacteria that have developed a reduced susceptibility against antimicrobials pose a major threat to public health. Hence, monitoring their distribution in the general population is of major importance. This monitoring is performed based on minimum inhibitory concentration (MIC) values, which are collected through dilution experiments. We present a semiparametric mixture model to estimate the MIC density on the full continuous scale. The wild-type first component is assumed to be of a parametric form, while the nonwild-type second component is modelled nonparametrically using Bayesian P-splines combined with the composite link model. A Metropolis within Gibbs strategy was used to draw a sample from the joint posterior. The newly developed method was applied to a specific bacterium–antibiotic combination, that is, Escherichia coli tested against ampicillin. After obtaining an estimate for the entire density, model-based classification can be performed to check whether or not an isolate belongs to the wild-type subpopulation. The performance of the new method, compared to two existing competitors, is assessed through a small simulation study.

One of the important questions in the practice of educational testing is how a particular test should be scored. In this paper we consider what an appropriate simple scoring rule should be for the Dutch as a second language test consisting of listening and reading items. As in many other applications, here the Rasch model which allows to score the test with a simple sumscore is too restrictive to adequately represent the data. In this study we propose an exploratory algorithm which clusters the items into subscales each fitting a Rasch model and thus provides a scoring rule based on observed data. The scoring rule produces either a weighted sumscore based on equal weights within each subscale or a set of sumscores (one for each of the subscales). An MCMC algorithm which enables to determine the number of Rasch scales constituting the test and to unmix these scales is introduced and evaluated in simulations. Using the results of unmixing, we conclude that the Dutch language test can be scored with a weighted sumscore with three different weights.

One of the most common analysis tasks in genomic research is to identify genes that are differentially expressed (DE) between experimental conditions. Empirical Bayes (EB) statistical tests using moderated genewise variances have been very effective for this purpose, especially when the number of biological replicate samples is small. The EB procedures can, however, be heavily influenced by a small number of genes with very large or very small variances. This article improves the differential expression tests by robustifying the hyperparameter estimation procedure. The robust procedure has the effect of decreasing the informativeness of the prior distribution for outlier genes while increasing its informativeness for other genes. This effect has the double benefit of reducing the chance that hypervariable genes will be spuriously identified as DE while increasing statistical power for the main body of genes. The robust EB algorithm is fast and numerically stable. The procedure allows exact small-sample null distributions for the test statistics and reduces exactly to the original EB procedure when no outlier genes are present. Simulations show that the robustified tests have similar performance to the original tests in the absence of outlier genes but have greater power and robustness when outliers are present. The article includes case studies for which the robust method correctly identifies and downweights genes associated with hidden covariates and detects more genes likely to be scientifically relevant to the experimental conditions. The new procedure is implemented in the limma software package freely available from the Bioconductor repository.

The use of water quality indicators is of crucial importance to identify risks to the environment, society and human health. In particular, the Chlorophyll type A (Chl-a) is a shared indicator of trophic status and for monitoring activities it may be useful to discover local dangerous behaviours (for example, the anoxic events). In this paper we consider a comprehensive data set, covering the whole Adriatic Sea, derived from Ocean Colour satellite data, during the period 2002–2012, with the aim of identifying homogeneous areas. Such zonation is becoming extremely relevant for the implementation of European policies, such the Marine Strategy Framework Directive. As an alternative to clustering based on an “average” value over the whole period, we propose a new clustering procedure for the time series. The procedure shares some similarities with the functional data clustering and combines nonparametric quantile regression with an agglomerative clustering algorithm. This approach permits to take into account some features of the time series as nonstationarity in the marginal distribution and the presence of missing data. A small simulation study is also presented for illustrating the relative merits of the procedure.

Modeling and estimation of correlation coefficients is a fundamental step in risk management, especially with the aftermath of the financial crisis in 2008, which challenged the traditional measuring of dependence in the financial market. Because of the serial dependence and small signal-to-noise ratio, patterns of the dependence in the data cannot be easily detected and modeled. This paper introduces a common factor analysis into the conditional correlation coefficients to extract the features of dependence. While statistical properties are thoroughly derived, extensive empirical analysis provides us with common patterns for the conditional correlation coefficients that give new insight into a number of important questions in financial data, especially the asymmetry of cross-correlations and the factors that drive the cross-correlations.

One important problem in microbiome analysis is to identify the bacterial taxa that are associated with a response, where the microbiome data are summarized as the composition of the bacterial taxa at different taxonomic levels. This paper considers regression analysis with such compositional data as covariates. In order to satisfy the subcompositional coherence of the results, linear models with a set of linear constraints on the regression coefficients are introduced. Such models allow regression analysis for subcompositions and include the log-contrast model for compositional covariates as a special case. A penalized estimation procedure for estimating the regression coefficients and for selecting variables under the linear constraints is developed. A method is also proposed to obtain debiased estimates of the regression coefficients that are asymptotically unbiased and have a joint asymptotic multivariate normal distribution. This provides valid confidence intervals of the regression coefficients and can be used to obtain the $p$-values. Simulation results show the validity of the confidence intervals and smaller variances of the debiased estimates when the linear constraints are imposed. The proposed methods are applied to a gut microbiome data set and identify four bacterial genera that are associated with the body mass index after adjusting for the total fat and caloric intakes.

We propose a spatially-explicit approach for modeling genetic variation across space and illustrate how this approach can be used to optimize spatial prediction and sampling design for landscape genetic data. We propose a multinomial data model for categorical microsatellite allele data commonly used in landscape genetic studies, and introduce a latent spatial random effect to allow for spatial correlation between genetic observations. We illustrate how modern dimension reduction approaches to spatial statistics can allow for efficient computation in landscape genetic statistical models covering large spatial domains. We apply our approach to propose a retrospective spatial sampling design for greater sage-grouse (Centrocercus urophasianus) population genetics in the western United States.

Mixed-mode surveys are becoming more popular recently because of their convenience for users, but different mode effects can complicate the comparability of the survey results. Motivated by the Private Education Expenditure Survey (PEES) of Korea, we propose a novel application of fractional imputation to handle mixed-mode survey data. The proposed method is applied to create imputed values of the unobserved counterfactual outcome variables in the mixed-mode surveys. The proposed method is directly applicable when the choice of survey mode is self-selected. Variance estimation using Taylor linearization is developed. Results from a limited simulation study are also presented.

In a natural experiment, treatment assignments are made through a haphazard process that is thought to be as-if random. In one form of the natural experiment, encouragement to accept treatment rather than treatments themselves are assigned in this haphazard process. This encouragement to accept treatment is often referred to as an instrument. Instruments can be characterized by different levels of strength depending on the amount of encouragement. Weak instruments that provide little encouragement may produce biased inferences, particularly when assignment of the instrument is not strictly randomized. A specialized matching algorithm can be used to strengthen instruments by selecting a subset of matched pairs where encouragement is strongest. We demonstrate how weak instrument tests can guide the matching process to ensure that the instrument has been sufficiently strengthened. Specifically, we combine a matching algorithm for strengthening instruments and weak instrument tests in the context of a study of whether turnout influences party vote share in US elections. It is thought that when turnout is higher, Democratic candidates will receive a higher vote share. Using excess rainfall as an instrument, we hope to observe an instance where unusually wet weather produces lower turnout in an as-if random fashion. Consistent with statistical theory, we find that strengthening the instrument reduces sensitivity to bias from an unobserved confounder.

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, that is, sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge, this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled nonparametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over-parameterized, we employ an $\ell_{1}$ penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com.