Carlos M. Marin

Monte Carlo analysis and Bayesian decision theory for assessing the effects of waste sites on groundwater. I: Theory

Abstract A sequential Bayesian risk methodology is outlined for addressing the problem of permitting waste sites under conditions of imperfect information. Topics covered include use of preposterior analysis to evaluate candidate sampling plans and prior/posterior analysis of risk. The algorithm is sufficiently general that it can be adapted to accommodate any specific groundwater contaminant transport model or site configuration. In the following paper an example is provided to show the details of application to a numerical groundwater transport model. The methodology described here is being incorporated into an advisory computer system for North Carolina groundwater quality modeling and management needs.

Monte Carlo analysis and Bayesian decision theory for assessing the effects of waste sites on groundwater, II: Applications

Abstract In the preceding paper a sequential Bayesian risk methodology is presented for the assessment of the effects of waste sites on groundwater. Specific details of the Monte Carlo implementation depend on the contaminant transport model employed. In the present paper the modifications used to adapt a deterministic numerical transport model for Monte Carlo analysis in the sequential algorithm are presented, followed by a sensitivity analysis of the resulting stochastic transport model. The sensitivity analysis assesses the impacts of the various sources of uncertainty incorporated, and emphasizes the need to explicitly consider such uncertainty in the process of risk assessment for regulatory decision. Similar modifications to a wide range of contaminant transport models have been incorporated into an advisory computer system for groundwater quality modeling and management.

ANALYSIS OF SHORT-RUN DOMESTIC WATER SUPPLY TRANSFERS UNDER UNCERTAINTY

From the perspective of water supply managers, supply reliability can be more important than economic benefit. This study uses four alternative models of water supply allocation to examine issues of reliability and welfare maximization arising from short-run inter-city water transfers. The results of this work show that the economic gain from water transfers may be relatively small. However, water transfers can significantly improve system reliability, thus providing strong incentives for transfer arrangements among water authorities. We apply the models in a case study on the island of Cyprus.

Long run price inflexibility and efficiency loss for municipal water supply

Abstract A marginal cost pricing (MCP) policy for a publicly produced good leads to politically unacceptable price fluctuations when economies of scale exist in plant construction. A partial equilibrium analysis of water supply defines a general, optimal, constant price for water which is a weighted average of the annual marginal short run and capacity expansion costs. For special cases of arithmetic or geometric growth in demand, the demand growth rate and the discount rate determine the fraction of capital costs which a constant price will recover. Under conditions which favor the MCP policy, the constant pricing policy produces ⩾ 98.5% of the net benefits produced by the MCP policy.

Empirical Bayes regionalization methods for spatial stochastic processes

Many geophysical properties can be described as spatial stochastic processes, including spatially correlated hydraulic conductivity fields. Use of regional data can potentially improve estimation of such processes. We consider the case in which observations at each of several sites are described by a general linear model, while the parameters of these models arise from a common regional distribution. Parametric empirical Bayes methods enable the determination of the parameters of the regional distribution via maximum likelihood. However, such methods have not been utilized for spatial stochastic processes. We develop the application of a simple iterative technique for maximum likelihood estimation of the regional parameters, and demonstrate its use with a common parameterization of the spatial covariance structure. Synthetic data tests show the potential for substantial reduction in estimation risk through use of such techniques.

EMPIRICAL BAYES ESTIMATION AND INFERENCE FOR THE PHOSPHORUS–CHLOROPHYLL RELATIONSHIP IN LAKES

ABSTRACT State and regional agencies frequently must use a model or models to assess limnological relationships, like that between phosphorus and chlorophyll, in a large number of lakes. If lake behavior in all lakes is essentially identical, then it is reasonable to pool information across lakes concerning the relationships and to make inferences on the basis of a universal model. Alternatively, if all lakes are unique, then inferences must be drawn from lake-specific models. The truth probably lies somewhere in between these two extremes. On that basis, empirical Bayes estimation is used to fit a simple model relating phosphorus to chlorophyll in lakes. The model is then applied to each lake in such a way that the chlorophyll prediction is based on both lake-specific and regional lake information. For lakes as a whole, the empirical Bayes estimator should result in improved predictions over standard approaches.