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Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention's influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

Estimating the timing of the occurrence of events that characterize growth cycles in vegetation from time series of remote sensing data is desirable for a wide area of applications. For example, the timings of plant life cycle events are very sensitive to weather conditions and are often used to assess the impacts of changes in weather and climate. Likewise, understanding crop phenology can have a large impact on agricultural strategies. To study phenology using remote sensing data, the timings of annual phenological events must be estimated from noisy time series that may have many missing values. Many current state-of-the-art methods consist of smoothing time series and estimating events as features of smoothed curves. A shortcoming of many of these methods is that they do not easily handle missing values and require imputation as a preprocessing step. In addition, while some currently used methods may be extendable to allow for temporal uncertainty quantification, uncertainty intervals are not usually provided with phenological event estimates. We propose methodology utilizing Bayesian dynamic linear models to estimate the timing of key phenological events from remote sensing data with uncertainty intervals. We illustrate the methodology on weekly vegetation index data from 2003 to 2007 over a region of southern India, focusing on estimating the timing of start of season and peak of greenness. Additionally, we present methods utilizing the Bayesian formulation and MCMC simulation of the model to estimate the probability that more than one growing season occurred in a given year.

Spatially structured discrete data arise in diverse areas of application, such as forestry, epidemiology, or soil sciences. Data from several binary variables are often collected at each location. Variation in distributional properties across the spatial domain is of interest. The specific application that motivates our work involves characterizing historical distributions of two species of Oak in the Driftless Area in the Midwestern United States. Scientists are interested in understanding the patterns of interaction between species, as well as their relationships to spatial covariates. Accounting for spatial dependence is not only of inherent interest but also reduces prediction mean squared error, and is necessary for obtaining appropriate measures of uncertainty (i.e., standard errors and confidence intervals). To address the needs of the application, we introduce a centered bivariate autologistic model, which accounts for the statistical dependence in two response variables simultaneously, for the association between them and for the effect of spatial covariates. The model proposed here offers a relatively stable large-scale model structure, with model parameters which can be interpreted in the usual sense across levels of dependence. Since the model allows for separate dependence parameters for each variable, it offers, in essence, the equivalent of a model with a non-separable covariance function. The flexible model framework permits straightforward generalizations to structures with more than two variables, a temporal component, or an irregular lattice domain. Supplementary materials accompanying this paper appear on-line.

We present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid. The method produces point estimators that require no spatial variance estimates to compute, unlike least squares methods for variogram fitting, but are as efficient as the best least squares estimator in large samples. Our approach also produces confidence regions for the variogram, without requiring knowledge of the full joint distribution of the spatial data. In addition, the empirical likelihood formulation extends to spatial regression problems and allows simultaneous inference on both spatial trend and variogram parameters. We examine the asymptotic behavior of the estimator analytically, and investigate its behavior in finite samples through simulation studies.

The application of Markov random field models to problems involving spatial data on lattice systems requires decisions regarding a number of important aspects of model structure. Existing exploratory techniques appropriate for spatial data do not provide direct guidance to an investigator about these decisions. We introduce an exploratory quantity that is directly tied to the structure of Markov random field models based on one-parameter exponential family conditional distributions. This exploratory diagnostic is shown to be a meaningful statistic that can inform decisions involved in modeling spatial structure with statistical dependence terms. In this article, we develop the diagnostic, illustrate its use in guiding modeling decisions with simulated examples, and reexamine a previously published application.

Remote sensing observations that vary in response to plant growth and senescence can be used to monitor crop development within and across growing seasons. Identifying when crops reach specific growth stages can improve harvest yield prediction and quantify climate change. Using the Level 2 vegetation optical depth (VOD) product from the European Space Agency’s Soil Moisture and Ocean Salinity (SMOS) satellite, we retrospectively estimate the timing of a key crop development stage in the United States Corn Belt. We employ nonlinear curves nested within a hierarchical modeling framework to extract the timing of the third reproductive development stage of corn (R3) as well as other new agronomic signals from SMOS VOD. We compare our estimates of the timing of R3 to United States Department of Agriculture (USDA) survey data for the years 2011, 2012, and 2013. We find that 87%, 70%, and 37%, respectively, of our model estimates of R3 timing agree with USDA district-level observations. We postulate that since the satellite estimates can be directly linked to a physiological state (the maximum amount of plant water, or water contained within plant tissue per ground area) it is more accurate than the USDA data which is based upon visual observations from roadways. Consequently, SMOS VOD could be used to replace, at a finer resolution than the district-level USDA reports, the R3 data that has not been reported by the USDA since 2013. We hypothesize the other model parameters contain new information about soil and crop management and crop productivity that are not routinely collected by any federal or state agency in the Corn Belt.

Ecologists are interested in characterizing succession processes, in particular monitoring the spread of invasive species and their effect on resident species. In situations for which binary response variables representing presence or absence of plants are observed over a spatial lattice, it may be desirable to use a model that accounts for the statistical dependence in the data, as well as the effect of potential covariates. One such model is the autologistic regression model. We show that the typical parameterization of the autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, and propose an alternative (centered) parameterization that overcomes this difficulty. We use the centered autologistic model to study the dynamics over time of two species, Rumex acetosella and Lonicera japonica, in an abandoned agricultural field in New Jersey, and compare the results to those obtained from using the traditional autologistic parameterization.

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

Many applications of spatial statistics involve evaluating a likelihood over samples of several hundred data locations. If the underlying field is Gaussian with some spatial covariance structure, this evaluation involves calculating the inverse and determinant of the covariance matrix. Although this is feasible for up to about 100 observations, it is often troublesome for sample sizes larger than 100. To take advantage of the benefits of maximum likelihood estimates for large arrays of data, it is necessary to establish efficient approximations to the likelihood. We consider several such approximations based on grouping the observations into clusters and building an estimating function by accounting for variability both between and within groups. This way, the estimation becomes practical for considerably larger data sets. In this thesis we present the proposed alternatives to the likelihood function, and an analysis of the asymptotic efficiency of the estimators yielded by them. The theoretical method applies to any kind of spatial process, but an analogous time series model is used for illustration and explicit computation. In this context, since the standard Fisher information techniques of calculating the asymptotic variance of the alternative estimators would not lead to correct conjectures, we employ a method based on the “information sandwich” technique and a Corollary to the Martingale Central Limit Theorem (application to quadratic forms of independent normal random variables). Furthermore, we illustrate the asymptotic behavior of the alternative parameters in the spatial setting with results from a simulation study.