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Brian J. Reich

Publications and source records attributed to Brian J. Reich.

70 records · Page 4Linked to original sources
arXiv2017

A Test for Isotropy on a Sphere using Spherical Harmonic Functions

Analysis of geostatistical data is often based on the assumption that the spatial random field is isotropic. This assumption, if erroneous, can adversely affect model predictions and statistical inference. Nowadays many applications consider data over the entire globe and hence it is necessary to check the assumption of isotropy on a sphere. In this paper, a test for spatial isotropy on a sphere is proposed. The data are first projected onto the set of spherical harmonic functions. Under isotropy, the spherical harmonic coefficients are uncorrelated whereas they are correlated if the underlying fields are not isotropic. This motivates a test based on the sample correlation matrix of the spherical harmonic coefficients. In particular, we use the largest eigenvalue of the sample correlation matrix as the test statistic. Extensive simulations are conducted to assess the Type I errors of the test under different scenarios. We show how temporal correlation affects the test and provide a method for handling temporal correlation. We also gauge the power of the test as we move away from isotropy. The method is applied to the near-surface air temperature data which is part of the HadCM3 model output. Although we do not expect global temperature fields to be isotropic, we propose several anisotropic models with increasing complexity, each of which has an isotropic process as model component and we apply the test to the isotropic component in a sequence of such models as a method of determining how well the models capture the anisotropy in the fields.

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arXiv2017

MIMIX: a Bayesian Mixed-Effects Model for Microbiome Data from Designed Experiments

Recent advances in bioinformatics have made high-throughput microbiome data widely available, and new statistical tools are required to maximize the information gained from these data. For example, analysis of high-dimensional microbiome data from designed experiments remains an open area in microbiome research. Contemporary analyses work on metrics that summarize collective properties of the microbiome, but such reductions preclude inference on the fine-scale effects of environmental stimuli on individual microbial taxa. Other approaches model the proportions or counts of individual taxa as response variables in mixed models, but these methods fail to account for complex correlation patterns among microbial communities. In this paper, we propose a novel Bayesian mixed-effects model that exploits cross-taxa correlations within the microbiome, a model we call MIMIX (MIcrobiome MIXed model). MIMIX offers global tests for treatment effects, local tests and estimation of treatment effects on individual taxa, quantification of the relative contribution from heterogeneous sources to microbiome variability, and identification of latent ecological subcommunities in the microbiome. MIMIX is tailored to large microbiome experiments using a combination of Bayesian factor analysis to efficiently represent dependence between taxa and Bayesian variable selection methods to achieve sparsity. We demonstrate the model using a simulation experiment and on a 2x2 factorial experiment of the effects of nutrient supplement and herbivore exclusion on the foliar fungal microbiome of $\textit{Andropogon gerardii}$, a perennial bunchgrass, as part of the global Nutrient Network research initiative.

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arXiv2016

A Markov-switching model for heat waves

Heat waves merit careful study because they inflict severe economic and societal damage. We use an intuitive, informal working definition of a heat wave-a persistent event in the tail of the temperature distribution-to motivate an interpretable latent state extreme value model. A latent variable with dependence in time indicates membership in the heat wave state. The strength of the temporal dependence of the latent variable controls the frequency and persistence of heat waves. Within each heat wave, temperatures are modeled using extreme value distributions, with extremal dependence across time accomplished through an extreme value Markov model. One important virtue of interpretability is that model parameters directly translate into quantities of interest for risk management, so that questions like whether heat waves are becoming longer, more severe or more frequent are easily answered by querying an appropriate fitted model. We demonstrate the latent state model on two recent, calamitous, examples: the European heat wave of 2003 and the Russian heat wave of 2010.

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arXiv2016

Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process

The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms. Theoretically, soft-thresholded Gaussian processes provide large prior support for the spatially varying coefficients that enjoy piecewise smoothness, sparsity and continuity, characterizing the important features of imaging data. Also, under some mild regularity conditions, the soft-thresholded Gaussian process leads to the posterior consistency for both parameter estimation and variable selection for scalar-on-image regression, even when the number of true predictors is larger than the sample size. The proposed method is illustrated via simulations, compared numerically with existing alternatives and applied to Electroencephalography (EEG) study of alcoholism.

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arXiv2016

Data Mining to Investigate the Meteorological Drivers for Extreme Ground Level Ozone Events

This project aims to explore which combinations of meteorological conditions are associated with extreme ground level ozone conditions. Our approach focuses only on the tail by optimizing the tail dependence between the ozone response and functions of meteorological covariates. Since there is a long list of possible meteorological covariates, the space of possible models cannot be explored completely. Consequently, we perform data mining within the model selection context, employing an automated model search procedure. Our study is unique among extremes applications as optimizing tail dependence has not previously been attempted, and it presents new challenges, such as requiring a smooth threshold. We present a simulation study which shows that the method can detect complicated conditions leading to extreme responses and resists overfitting. We apply the method to ozone data for Atlanta and Charlotte and find similar meteorological drivers for these two Southeastern US cities. We identify several covariates which help to differentiate the meteorological conditions which lead to extreme ozone levels from those which lead to merely high levels.

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arXiv2016

Modeling Multivariate Mixed-Response Functional Data

We propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence among the functional responses through the dependence of the latent process. Our framework easily accommodates additional covariates. We offer a way to estimate the multivariate latent covariance, allowing for implementation of multivariate functional principal components analysis (FPCA) to specify basis expansions and simplify computation. We demonstrate our method through both simulation studies and an application to real data from a periodontal study.

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arXiv2015

Quantile regression for mixed models with an application to examine blood pressure trends in China

Cardiometabolic diseases have substantially increased in China in the past 20 years and blood pressure is a primary modifiable risk factor. Using data from the China Health and Nutrition Survey, we examine blood pressure trends in China from 1991 to 2009, with a concentration on age cohorts and urbanicity. Very large values of blood pressure are of interest, so we model the conditional quantile functions of systolic and diastolic blood pressure. This allows the covariate effects in the middle of the distribution to vary from those in the upper tail, the focal point of our analysis. We join the distributions of systolic and diastolic blood pressure using a copula, which permits the relationships between the covariates and the two responses to share information and enables probabilistic statements about systolic and diastolic blood pressure jointly. Our copula maintains the marginal distributions of the group quantile effects while accounting for within-subject dependence, enabling inference at the population and subject levels. Our population-level regression effects change across quantile level, year and blood pressure type, providing a rich environment for inference. To our knowledge, this is the first quantile function model to explicitly model within-subject autocorrelation and is the first quantile function approach that simultaneously models multivariate conditional response. We find that the association between high blood pressure and living in an urban area has evolved from positive to negative, with the strongest changes occurring in the upper tail. The increase in urbanization over the last twenty years coupled with the transition from the positive association between urbanization and blood pressure in earlier years to a more uniform association with urbanization suggests increasing blood pressure over time throughout China, even in less urbanized areas. Our methods are available in the R package BSquare.

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arXiv2014

Modeling the effect of temperature on ozone-related mortality

Climate change is expected to alter the distribution of ambient ozone levels and temperatures which, in turn, may impact public health. Much research has focused on the effect of short-term ozone exposures on mortality and morbidity while controlling for temperature as a confounder, but less is known about the joint effects of ozone and temperature. The extent of the health effects of changing ozone levels and temperatures will depend on whether these effects are additive or synergistic. In this paper we propose a spatial, semi-parametric model to estimate the joint ozone-temperature risk surfaces in 95 US urban areas. Our methodology restricts the ozone-temperature risk surfaces to be monotone in ozone and allows for both nonadditive and nonlinear effects of ozone and temperature. We use data from the National Mortality and Morbidity Air Pollution Study (NMMAPS) and show that the proposed model fits the data better than additive linear and nonlinear models. We then examine the synergistic effect of ozone and temperature both nationally and locally and find evidence of a nonlinear ozone effect and an ozone-temperature interaction at higher temperatures and ozone concentrations.

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arXiv2014

A spatial capture-recapture model for territorial species

Advances in field techniques have lead to an increase in spatially-referenced capture-recapture data to estimate a species' population size as well as other demographic parameters and patterns of space usage. Statistical models for these data have assumed that the number of individuals in the population and their spatial locations follow a homogeneous Poisson point process model, which implies that the individuals are uniformly and independently distributed over the spatial domain of interest. In many applications there is reason to question independence, for example when species display territorial behavior. In this paper, we propose a new statistical model which allows for dependence between locations to account for avoidance or territorial behavior. We show via a simulation study that accounting for this can improve population size estimates. The method is illustrated using a case study of small mammal trapping data to estimate avoidance and population density of adult female field voles (Microtus agrestis) in northern England.

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arXiv2013

A hierarchical max-stable spatial model for extreme precipitation

Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a max-stable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model.

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arXiv2012

A class of covariate-dependent spatiotemporal covariance functions for the analysis of daily ozone concentration

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model nonstationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely, the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and methods to assess its dependence on local covariate information. The proposed method is used to analyze daily ozone in the southeast United States.

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arXiv2012

Mixture Likelihood Ratio Scan Statistic for Disease Outbreak Detection

Early detection of disease outbreaks is of paramount importance to implementing intervention strategies to mitigate the severity and duration of the outbreak. We build methodology that utilizes the characteristic profile of disease outbreaks to reduce the time to detection and false positive rate. We model daily counts through a Poisson distribution with additive background plus outbreak components. The outbreak component has a parametric form with unknown underlying parameters. A mixture likelihood ratio scan statistic is developed to maximize parameters over a window in time. This provides an alert statistic with early time to detection and low false positive rate. The methodology is demonstrated on three simulated data sets meant to represent E. coli, Cryptosporidium, and Influenza outbreaks.

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arXiv2010

A latent factor model for spatial data with informative missingness

A large amount of data is typically collected during a periodontal exam. Analyzing these data poses several challenges. Several types of measurements are taken at many locations throughout the mouth. These spatially-referenced data are a mix of binary and continuous responses, making joint modeling difficult. Also, most patients have missing teeth. Periodontal disease is a leading cause of tooth loss, so it is likely that the number and location of missing teeth informs about the patient's periodontal health. In this paper we develop a multivariate spatial framework for these data which jointly models the binary and continuous responses as a function of a single latent spatial process representing general periodontal health. We also use the latent spatial process to model the location of missing teeth. We show using simulated and real data that exploiting spatial associations and jointly modeling the responses and locations of missing teeth mitigates the problems presented by these data.

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arXiv2007

A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields

Storm surge, the onshore rush of sea water caused by the high winds and low pressure associated with a hurricane, can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for creating storm surge forecasts for coastal areas. These models are driven primarily by the surface wind forcings. Currently, the gridded wind fields used by ocean models are specified by deterministic formulas that are based on the central pressure and location of the storm center. While these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. A new Bayesian multivariate spatial statistical modeling framework is introduced combining data with physical knowledge about the wind fields to improve the estimation of the wind vectors. Many spatial models assume the data follow a Gaussian distribution. However, this may be overly-restrictive for wind fields data which often display erratic behavior, such as sudden changes in time or space. In this paper we develop a semiparametric multivariate spatial model for these data. Our model builds on the stick-breaking prior, which is frequently used in Bayesian modeling to capture uncertainty in the parametric form of an outcome. The stick-breaking prior is extended to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of kernel functions. This semiparametric spatial model is shown to improve prediction compared to usual Bayesian Kriging methods for the wind field of Hurricane Ivan.

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