Bayesian Model for Fate and Transport of Polychlorinated Biphenyl in Upper Hudson River

Steinberg, Laura J.; Reckhow, Kenneth H.; Wolpert, Robert L.

doi:10.1061/(asce)0733-9372(1996)122:5(341)

Cited by 14 publications

(7 citation statements)

References 24 publications

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“…The usefulness of Bayesian methods in the environmental sciences has been pointed out by various authors (Freeze, Massmann, Smith, Sperling, and James 1990;Brand and Small 1995;Ellison 1996;Reichert and Omlin 1997;Steinberg, Reckhow, and Wolpert 1996;Omlin and Reichert 1999). Other authors have questioned the Bayesian approach, mainly because of the problem of uniquely specifying prior distributions (e.g., Dennis 1996).…”

Section: Introductionmentioning

confidence: 99%

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

2002

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In the environmental sciences, a large knowledge base is typically available on an investigated system or at least on similar systems. This makes the application of Bayesian inference techniques in environmental modeling very promising. However, environmental systems are often described by complex, computationally demanding simulation models. This strongly limits the application of Bayesian inference techniques, because numerical implementation of these techniques requires a very large number of simulation runs. The development of ef cient sampling techniques that attempt to approximate the posterior distribution with a relatively small parameter sample can extend the range of applicability of Bayesian inference techniques to such models. In this article a sampling technique is presented that tries to achieve this goal. The proposed technique combines numerical techniques typically applied in Bayesian inference, including posterior maximization, local normal approximation, and importance sampling, with copula techniques for the construction of a multivariate distribution with given marginals and correlation structure and with low-discrepancy sampling. This combination improves the approximation of the posterior distribution by the sampling distribution and improves the accuracy of results for small sample sizes. The usefulness of the proposed technique is demonstrated for a simple model that contains the major elements of models used in the environmental sciences. The results indicate that the proposed technique outperforms conventional techniques (random sampling from simpler distributions or Markov chain Monte Carlo techniques) in cases in which the analysis can be limited to a relatively small number of parameters.

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Section: Introductionmentioning

confidence: 99%

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

2002

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“…Ranges for p c þ p f and p v for total PCB were derived from these results by using the relative loadings of the individual congeners found in the NBH samples (Vorhees et al, 1997) and by considering both air temperatures. Steinberg et al (1995) also considered relative loadings in deriving priors. Whitby (1978) reports that approximately 15 per cent of the volume of background average air is in fine particles, and this was used to separate the ranges for p c and p f .…”

Section: Priors and Likelihoodsmentioning

confidence: 99%

Bayesian uncertainty assessment in multicompartment deterministic simulation models for environmental risk assessment

2003

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SUMMARYWe use a special case of Bayesian melding to make inference from deterministic models while accounting for uncertainty in the inputs to the model. The method uses all available information, based on both data and expert knowledge, and extends current methods of 'uncertainty analysis' by updating models using available data. We extend the methodology for use with sequential multicompartment models. We present an application of these methods to deterministic models for concentration of polychlorinated biphenyl (PCB) in soil and vegetables. The results are posterior distributions of concentration in soil and vegetables which account for all available evidence and uncertainty. Model uncertainty is not considered.

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“…The complexity of similar environmental systems often renders them difficult to account deterministically for all the contributing factors in the contaminant process. In that sense, stochastic space/time solutions are reasonably preferred to deterministic model predictions [ Steinberg et al , 1996]. More specifically, we consider the temporal evolution of a nondispersive mass transport process along a river, in which case the physical PDE equation describing the space/time distribution of the component mass concentration X ( p ) is as follows where p = ( s , t ) denotes a space/time point ( s is the one‐dimensional space coordinate along the river direction and t is time), q is the downstream velocity (in [ L ]/[ T ]), and κ is the reaction rate (in 1/[ T ]; κ > 0).…”

Section: Assimilation Of General Knowledge By the Bme Approach: The Smentioning

confidence: 99%

Computational Bayesian maximum entropy solution of a stochastic advection‐reaction equation in the light of site‐specific information

Kolovos

Christakos

Serre

et al. 2002

Water Resources Research

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[1] This work presents a computational formulation of the Bayesian maximum entropy (BME) approach to solve a stochastic partial differential equation (PDE) representing the advection-reaction process across space and time. The solution approach provided by BME has some important features that distinguish it from most standard stochastic PDE techniques. In addition to the physical law, the BME solution can assimilate other sources of general and site-specific knowledge, including multiple-point nonlinear space/time statistics, hard measurements, and various forms of uncertain (soft) information. There is no need to explicitly solve the moment equations of the advection-reaction law since BME allows the information contained in them to consolidate within the general knowledge base at the structural (prior) stage of the analysis. No restrictions are posed on the shape of the underlying probability distributions or the space/time pattern of the contaminant process. Solutions of nonlinear systems of equations are obtained in four space/time dimensions and efficient computational schemes are introduced to cope with complexity. The BME solution at the prior stage is in excellent agreement with the exact analytical solution obtained in a controlled environment for comparison purposes. The prior solution is further improved at the integration (posterior) BME stage by assimilating uncertain information at the data points as well as at the solution grid nodes themselves, thus leading to the final solution of the advection-reaction law in the form of the probability distribution of possible concentration values at each space/time grid node. This is the most complete way of describing a stochastic solution and provides considerable flexibility concerning the choice of the concentration realization that is more representative of the physical situation. Numerical experiments demonstrated a high solution accuracy of the computational BME approach. The BME approach can benefit from the use of parallel processing (the relevant systems of equations can be processed simultaneously at each grid node and multiple integrals calculations can be accelerated significantly, etc.).

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Bayesian Model for Fate and Transport of Polychlorinated Biphenyl in Upper Hudson River

Cited by 14 publications

References 24 publications

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

Bayesian uncertainty assessment in multicompartment deterministic simulation models for environmental risk assessment

Computational Bayesian maximum entropy solution of a stochastic advection‐reaction equation in the light of site‐specific information

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