We propose median polish for functional multivariate analysis of variance (FMANOVA) with the implementation of depth for multivariate functional data. As an alternative to classical mean estimation, functional median polish estimates the functional grand effect and factor effects based on functional medians in one‐way and two‐way additive FMANOVA models. Median polish estimates in FMANOVA are visually

In this paper, we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatiotemporal dependence. Specifically, we propose to consider stochastic processes obtained through a monotone transformation of scaled version of χ 2 random processes. The latter is well known in the specialized literature and originates by summing independent copies of a squared Gaussian

Protection and safety authorities recommend the use of model averaging to determine the benchmark dose approach as a scientifically more advanced method compared to the NOAEL approach for obtaining a reference point and deriving health‐based guidance values. Model averaging however highly depends on the set of candidate dose‐response models and such a set should be rich enough to ensure that a well

Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the location for a function's value. Gaussian processes are a generalization of the multivariate normal distribution to function space and, in this paper, they

We propose a Kalman filter algorithm to provide a formal statistical analysis of space‐time data with an autoregressive structure in time. The Kalman filter technique allows to capture the temporal dependence as well as the spatial correlation structure through state‐space equations, and it is aimed to perform statistical inference in terms of parameter estimation and prediction at unobserved locations

As per the records of the World Health Organization, the first formally reported incidence of Zika virus occurred in Brazil in May 2015. The disease then rapidly spread to other countries in Americas and East Asia, affecting more than 1,000,000 people. Zika virus is primarily transmitted through bites of infected mosquitoes of the species Aedes (Aedes aegypti and Aedes albopictus). The abundance of

Saudi Arabia has recently established its renewable energy targets as part of its “Vision 2030” proposal, which represents a roadmap for reducing the country's dependence on oil over the next decade. This study provides a foundational assessment of the wind resource in Saudi Arabia that serves as a guide for the development of the outlined wind energy component. The assessment is based on a new high‐resolution

Incorporating covariates in the second‐ structure of spatial processes is an effective way of building flexible nonstationary covariance models. Fitting these covariances requires covariates to already exist at locations where there is response data. However, studies in environmental statistics often involve covariate and response data that are misaligned in space. A common strategy to remedy this

To study trends in extreme precipitation across the United States over the years 1951–2017, we analyze 10 climate indexes that represent extreme precipitation, such as annual maximum of daily precipitation and annual maximum of consecutive five‐day average precipitation. We consider the gridded data produced by the CLIMDEX project (http://www.climdex.org/gewocs.html), constructed using daily precipitation

We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N. We

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes

The assessment of long‐term trends in environmental extremes is a challenging and important subject in the current discussion on global climate change. We propose a new approach for evaluating temporal trends and spatial homogeneity in extremes accounting also for spatial dependence. Based on exceedances over a space–time threshold, we provide estimators for a so‐called scedasis function and the extreme

We develop a Bayesian model–based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates. Specifically, we consider a two‐stage

We address the issue of performing portmanteau testing inference using time series data that assume values in the standard unit interval. The motivation involves modeling the time series dynamics of the proportion of stocked hydroelectric energy in the South of Brazil. Our focus lies in the class of beta autoregressive moving average (βARMA) models. In particular, we wish to test the goodness‐of‐fit

Characterization of heatwave duration is becoming increasingly important in environmental research as they pose a significant threat to many human lives worldwide. Although several quantification of the extremities of a heatwave have been proposed in literature, they are mostly improvised and there does not exist a universally accepted definition of heatwave. In this article, we devise a probabilistic

A new sampling strategy for design‐based environmental monitoring is proposed. It has the potential to produce superior estimators for totals of environmental variables and their changes over time. In the strategy, we combine two concepts known as spatially balanced sampling and coordination of samples. Spatially balanced sampling can provide superior estimators of totals, while coordination of samples

Environmental extremes often show systematic variation with covariates. Three different nonparametric descriptions (penalized B‐splines, Bayesian adaptive regression splines, and Voronoi partition) for the dependence of extreme value model parameters on covariates are considered. These descriptions take the generic form of a linear combination of basis functions on the covariate domain, but differ

In this study, we begin a comprehensive characterization of temperature extremes in Ireland for the period 1981–2010. We produce return levels of anomalies of daily maximum temperature extremes for an area over Ireland, for the 30‐year period 1981–2010. We employ extreme value theory (EVT) to model the data using the generalized Pareto distribution (GPD) as part of a three‐level Bayesian hierarchical

Understanding the complex relationship between the duration and size of forest fires is important in order to better predict these key characteristics of fires for fire management purposes in a changing climate. Describing this relationship is also important for our fundamental understanding of fire science. Here, we develop and utilize novel techniques for characterizing the distribution of multiple

Animal movement studies have become ubiquitous in animal ecology for the estimation of space use and the analysis of movement behavior. In these studies, animal movement data are primarily collected at regular time intervals. We propose an irregular sampling design that could lead to greater efficiency and information gain in animal movement studies. Our novel sampling design, called lattice and random

The multivariate smooth transition autoregressive model with order k (M‐STAR)(k) is a nonlinear multivariate time series model able to capture regime changes in the conditional mean. The main aim of this paper is to develop a Bayesian estimation scheme for the M‐STAR(k) model that includes the coefficient parameter matrix, transition function parameters, covariance parameter matrix, and the model order

A hierarchical Bayesian model is proposed to quantify the magnitude of extreme surges on the Atlantic coast of Canada with limited data. Generalized extreme value distributions are fitted to surges derived from water levels measured at 21 buoys along the coast. The parameters of these distributions are linked together through a Gaussian field whose mean and variance are driven by atmospheric sea‐level

Color is one of the most important features in any textile material. Due to its competitive price, most of the colorants currently used for textile dyeing are synthetic, originated from nonrenewable sources, and highly pollutant. There is an increasing interest for natural processes to dye fabrics. When new textile dyeing technologies are developed, evaluating the quality of these techniques involves

Atmospheric inverse modeling is a method for reconstructing historical fluxes of green‐house gas between land and atmosphere, using observed atmospheric concentrations and an atmospheric tracer transport model. The small number of observed atmospheric concentrations in relation to the number of unknown flux components makes the inverse problem ill‐conditioned, and assumptions on the fluxes are needed

This paper proposes a novel nonparametric approach to model and reveal differences in the geochemical properties of the soil, when these are described by space–time measurements collected in a spatial region naturally divided into two parts. The investigation is motivated by a real study on a space–time geochemical data set, consisting of measurements of potassium chloride pH, water pH, and percentage

Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM2.5), in which data are usually not measured at all study locations. PM2.5 is also a mixture of many different chemical components. Principal component analysis (PCA) can be incorporated to obtain lowerdimensional representative scores of such multipollutant

One of the major concerns engendered by a warming climate are changing sea levels and their lasting effects on coastal populations, infrastructures, and natural habitats. Sea levels are now monitored by satellites, but long‐term records are only available at discrete locations along the coasts. Sea levels and sea‐level processes must be better understood at the local level to best inform real‐world

In this paper, we use a Bayesian spatial model to spatially interpolate forest inventory data from the Timiskaming and Abitibi River forests in Ontario, Canada. We consider a Bayesian generalized linear geostatistical model and implement a Markov chain Monte Carlo algorithm to sample from its posterior distribution. How spatial predictions for new sites in the forests change as the amount of training

We describe a model for the conditional dependence of a spatial process measured at one or more remote locations given extreme values of the process at a conditioning location, motivated by the conditional extremes methodology of Heffernan and Tawn. Compared to alternative descriptions in terms of max-stable spatial processes, the model is advantageous because it is conceptually straightforward and

Environmental toxicology studies often involve sample values that fall below a laboratory procedure's limit of quantification. Such left-censored data give rise to several problems for regression analyses. First, both covariates and outcome may be left censored. Second, the transformed toxicant levels may not be normal but mixtures of normals because of differences in personal characteristics, e.g

There is substantial interest in assessing how exposure to environmental mixtures, such as chemical mixtures, affect child health. Researchers are also interested in identifying critical time windows of susceptibility to these complex mixtures. A recently developed method, called lagged kernel machine regression (LKMR), simultaneously accounts for these research questions by estimating effects of time-varying

Environmental health and disease mapping studies are often concerned with the evaluation of the combined effect of various socio-demographic and behavioral factors, and environmental exposures on time-to-events of interest, such as death of individuals, organisms or plants. In such studies, estimation of the hazard function is often of interest. In addition to known explanatory variables, the hazard

Environmental health exposures to airborne chemicals often originate from chemical mixtures. Environmental health professionals may be interested in assessing exposure to one or more of the chemicals in these mixtures, but often exposure measurement data are not available, either because measurements were not collected/assessed for all exposure scenarios of interest or because some of the measurements

Modern environmental and climatological studies produce multiple outcomes at high spatial resolutions. Multivariate spatial modeling is an established means to quantify cross-correlation among outcomes. However, existing models typically suffer from poor computational efficiency and lack the flexibility to simultaneously estimate auto- and cross-covariance structures. In this article, we undertake

It is our primary focus to study the spatial distribution of disease incidence at different geographical levels. Often, spatial data are available in the form of aggregation at multiple scale levels such as census tract, county, state, and so on. When data are aggregated from a fine (e.g. county) to a coarse (e.g. state) geographical level, there will be loss of information. The problem is more challenging

It is often the case that researchers wish to simultaneously explore the behavior of and estimate overall risk for multiple, related diseases with varying rarity while accounting for potential spatial and/or temporal correlation. In this paper, we propose a flexible class of multivariate spatio-temporal mixture models to fill this role. Further, these models offer flexibility with the potential for

Fine particulate matter (PM2.5) poses a significant risk to human health, with long-term exposure being linked to conditions such as asthma, chronic bronchitis, lung cancer, atherosclerosis, etc. In order to improve current pollution control strategies and to better shape public policy, the development of a more comprehensive understanding of this air pollutant is necessary. To this end, this work

Measurements recorded over monitoring networks often possess spatial and temporal correlation inducing redundancies in the information provided. For river water quality monitoring in particular, flow-connected sites may likely provide similar information. This paper proposes a novel approach to principal components analysis to investigate reducing dimensionality for spatiotemporal flow-connected network

Spatio-temporal analysis of small area health data often involves choosing a fixed set of predictors prior to the final model fit. In this paper, we propose a spatio-temporal approach of Bayesian model selection to implement model selection for certain areas of the study region as well as certain years in the study time line. Here, we examine the usefulness of this approach by way of a large-scale

Expensive computer codes, particularly those used for simulating environmental or geological processes, such as climate models, require calibration (sometimes called tuning). When calibrating expensive simulators using uncertainty quantification methods, it is usually necessary to use a statistical model called an emulator in place of the computer code when running the calibration algorithm. Though

Ensemble model output statistics (EMOS) is a statistical tool for post-processing forecast ensembles of weather variables obtained from multiple runs of numerical weather prediction models in order to produce calibrated predictive probability density functions. The EMOS predictive probability density function is given by a parametric distribution with parameters depending on the ensemble forecasts

Scientists need appropriate spatial-statistical models to account for the unique features of stream network data. Recent advances provide a growing methodological toolbox for modelling these data, but general-purpose statistical software has only recently emerged, with little information about when to use different approaches. We implemented a simulation study to evaluate and validate geostatistical

The health impact of long-term exposure to air pollution is now routinely estimated using spatial ecological studies, owing to the recent widespread availability of spatial referenced pollution and disease data. However, this areal unit study design presents a number of statistical challenges, which if ignored have the potential to bias the estimated pollution-health relationship. One such challenge

In this paper, we derive forms of estimators and associated variances for regression calibration with instrumental variables in longitudinal models that include interaction terms between two unobservable predictors and interactions between these predictors and covariates not measured with error; the inclusion of the latter interactions generalize results we previously reported. The methods are applied

A new methodology is proposed for the analysis, modeling and forecasting of data collected from a wireless sensor network. Our approach is considered in the framework of a functional data analysis paradigm where observed data is represented in a functional form. To reduce dimensionality, functional principal components analysis is applied to highlight important underlying characteristics and find patterns

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of P-splines, we propose a Bayesian framework for choosing the smoothing parameter, which allows the construction of fully automatic data-driven methods for fitting flexible models to spatiotemporal data. An implementation, which is highly computationally

In this paper we present a novel, flexible, and multi-purpose class of designs for initial exploration of the parameter spaces of computer models, such as those used to study many features of the environment. The idea applies existing technology aimed at expanding a Latin Hypercube (LHC) in order to generate initial LHC designs that are composed of many smaller LHCs. The resulting design and its component

Long series of simulated rainfall are required at point locations for a range of applications, including hydrological studies. Clustered point process-based rainfall models have been used for generating such simulations for many decades. These models suffer from a major limitation, however: their stationarity. Although seasonality can be allowed by fitting separate models for each calendar month or

Preferential sampling has been defined in the context of geostatistical modeling as the dependence between the sampling locations and the process that describes the spatial structure of the data. It can occur when networks are designed to find high values. For example, in networks based on the U.S. Clean Air Act monitors are sited to determine whether air quality standards are exceeded. We study the

Antarctica is the world's largest fresh-water reservoir, with the potential to raise sea levels by about 60 m. An ice sheet contributes to sea-level rise (SLR) when its rate of ice discharge and/or surface melting exceeds accumulation through snowfall. Constraining the contribution of the ice sheets to present-day SLR is vital both for coastal development and planning, and climate projections. Information

Spatial regression models have grown in popularity in response to rapid advances in GIS (Geographic Information Systems) technology that allows epidemiologists to incorporate geographically indexed data into their studies. However, it turns out that there are some subtle pitfalls in the use of these models. We show that presence of covariate measurement error can lead to significant sensitivity of

Determining the Antarctic contribution to sea-level rise from observational data is a complex problem. The number of physical processes involved (such as ice dynamics and surface climate) exceeds the number of observables, some of which have very poor spatial definition. This has led, in general, to solutions that utilise strong prior assumptions or physically based deterministic models to simplify

Time series studies have suggested that air pollution can negatively impact health. These studies have typically focused on the total mass of fine particulate matter air pollution or the individual chemical constituents that contribute to it, and not source-specific contributions to air pollution. Source-specific contribution estimates are useful from a regulatory standpoint by allowing regulators

With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate

We introduce a method for statistically identifying the optimal locations of deep tubewells (dtws) to be installed in Matlab, Bangladesh. Dtw installations serve to mitigate exposure to naturally occurring arsenic found at groundwater depths less than 200 meters, a serious environmental health threat for the population of Bangladesh. We introduce an objective function, which incorporates both arsenic

A fundamental goal in nano-toxicology is that of identifying particle physical and chemical properties, which are likely to explain biological hazard. The first line of screening for potentially adverse outcomes often consists of exposure escalation experiments, involving the exposure of micro-organisms or cell lines to a library of nanomaterials. We discuss a modeling strategy, that relates the outcome

Public health researchers often estimate health effects of exposures (e.g., pollution, diet, lifestyle) that cannot be directly measured for study subjects. A common strategy in environmental epidemiology is to use a first-stage (exposure) model to estimate the exposure based on covariates and/or spatio-temporal proximity and to use predictions from the exposure model as the covariate of interest in