Modeling the U.S. national distribution of waterborne pathogen concentrations with application to <i>Cryptosporidium parvum</i>

Crainiceanu, Ciprian M.; Stedinger, Jery R.; Ruppert, David; Behr, Christopher T.

doi:10.1029/2002wr001664

Cited by 23 publications

(16 citation statements)

References 44 publications

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“…It is stressed that MCMC sampling from high‐dimensional posteriors is challenging but by no means insurmountable. Successful examples are provided by, e.g., Crainiceanu et al [2003], Vrugt et al [2008], Thyer et al [2009], and Reichert and Mieleitner [2009] in hydrology, not to mention numerous applications in other fields [e.g., Clark [2003] in ecology, Storz and Beaumont [2002] in genetics, etc. ].…”

Section: Estimation and Predictionmentioning

confidence: 99%

A Bayesian hierarchical approach to regional frequency analysis

Renard¹

2011

Water Resources Research

107

101

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[1] Regional frequency analysis (RFA) has a long history in hydrology, and numerous distinct approaches have been proposed over the years to perform the estimation of some hydrologic quantity at a regional level. However, most of these approaches still rely on strong hypotheses that may limit their application and complicate the quantification of predictive uncertainty. The objective of this paper is to propose a general Bayesian hierarchical framework to implement RFA schemes that avoid these difficulties. The proposed framework is based on a two-level hierarchical model. The first level of the hierarchy describes the joint distribution of observations. An arbitrary marginal distribution, whose parameters may vary in space, is assumed for at-site series. The joint distribution is then derived by means of an elliptical copula, therefore providing an explicit description of the spatial dependence between data. The second level of the hierarchy describes the spatial variability of parameters using a regression model that links the parameter values with covariates describing site characteristics. Regression errors are modeled with a Gaussian spatial field, which may exhibit spatial dependence. This framework enables performing prediction at both gaged and ungaged sites and, importantly, rigorously quantifying the associated predictive uncertainty. A case study based on the annual maxima of daily rainfall demonstrates the applicability of this hierarchical approach. Although numerous avenues for improvement can already be identified (among which is the inclusion of temporal covariates to model time variability), the proposed model constitutes a general framework for implementing flexible RFA schemes and quantifying the associated predictive uncertainty.

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Section: Estimation and Predictionmentioning

confidence: 99%

A Bayesian hierarchical approach to regional frequency analysis

Renard¹

2011

Water Resources Research

107

101

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“…The partition of ET between woody and herbaceous species is allowed through the deployment of overstory and understory eddy flux towers. A Bayesian framework with Markov chain Monte Carlo (MCMC) method that has been applied successfully in many fields [Clark, 2005;Clark and Gelfand, 2006;Crainiceanu et al, 2003;Reis and Stedinger, 2005] is adopted to parameterize the model that describes controlling effect of soil moisture on ET, taking into account the uncertainties in model parameters and in field measurements. The interannual variability in the dependence of ET on soil moisture for heterogeneous environment as well as its components is analyzed using multiyear data.…”

Section: Introductionmentioning

confidence: 99%

Observations and stochastic modeling of soil moisture control on evapotranspiration in a Californian oak savanna

Rubin

Baldocchi

2008

Water Resources Research

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[1] The study of water exchange between soil, plants, and the atmosphere in response to seasonal or periodic droughts is critical to modeling the hydrologic cycle and biogeochemical processes in water-controlled ecosystems. An essential step in such studies is to characterize changes in evaporation and transpiration under water stress. The objectives of this study are to investigate how soil moisture controls the evapotranspiration in a Californian oak savanna that experiences seasonal droughts, using multiyear field observations at the daily and stand scale, and to model these controls stochastically. The influence of soil moisture on evapotranspiration at the stand scale is studied using correlations between tower-based evapotranspiration measurements and representative soil moisture obtained by aggregating point measurements. The observed pattern of this effect is found in agreement with an existing model that features a linear reduction of the evapotranspiration when soil moisture falls below a critical value. The model parameters are inferred using a Bayesian framework, and they are found to vary from year to year because of climate variability. The comparison between various aggregations of soil moisture at the stand scale from point measurements demonstrates that the spatial variability of the soil moisture and the water uptake capacity limited by the root biomass need be taken into account to produce a model that is most resistant to interannual variability. Finally, the parameterized model is used to predict the actual evapotranspiration with uncertainty estimates determined using the joint distribution of the parameters derived from the Bayesian framework. The satisfactory agreement between the predicted and measured evapotranspiration suggests that the calibrated model can be incorporated into water balance studies in the future.

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“…As described previously, the Nahrstedt–Gimbel model comprises known distributions that are commonly applied to quantify random sampling error and nonconstant analytical recovery (USEPA, 2005a; Teunis et al, 1999). The Bayesian technique of Gibbs sampling was used; this is a form of Markov Chain Monte Carlo, which has been widely used to solve models such as the Nahrstedt–Gimbel model (USEPA, 2005a; Crainiceanu et al, 2003; Emelko, 2001). Such techniques allow statistically rigorous inference based on prior knowledge of variability (e.g., from controlled recovery studies) and are preferable to conventional statistical methods (such as t ‐tests) because they can be used to assess zero counts, uncertainty in a single datum, and data that are not normally distributed.…”

Section: Methodsmentioning

confidence: 99%

Quantification of uncertainty in microbial data—reporting and regulatory implications

Emelko¹,

Schmidt²,

Roberson³

2008

Journal AWWA

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Microbial contaminants are often regulated differently than chemical contaminants. Microorganisms are enumerated by techniques that are frequently susceptible to considerable losses, resulting in highly variable recoveries. Accordingly, several treatment technique‐based regulations have evolved for microbial treatment. However, even these regulations ultimately require some reliance on microbial concentration data. Statistical approaches have been developed for the calculation of confidence intervals for microbial concentrations and removals by treatment processes, and these approaches take into account the various errors associated with microbial enumeration. The approaches were used here to demonstrate the relationship between methodological error and the practicality of concentration‐based regulations that require continuous and/or frequent monitoring, demonstrate the necessity of treatment technique‐based regulations such as the Long Term 2 Enhanced Surface Water Treatment Rule, demonstrate that methodological uncertainty is more substantially reduced by increasing organism count than by improving methodological recovery, and propose sampling targets of approximately 10 or more organisms to appreciably reduce the uncertainty associated with microbial quantification

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Modeling the U.S. national distribution of waterborne pathogen concentrations with application to Cryptosporidium parvum

Cited by 23 publications

References 44 publications

A Bayesian hierarchical approach to regional frequency analysis

A Bayesian hierarchical approach to regional frequency analysis

Observations and stochastic modeling of soil moisture control on evapotranspiration in a Californian oak savanna

Quantification of uncertainty in microbial data—reporting and regulatory implications

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