Probabilistic programming for nitrate pollution control: Comparing different probabilistic constraint approximations

Kampas, Athanasios; White, Ben

doi:10.1016/s0377-2217(02)00254-0

Cited by 25 publications

(13 citation statements)

References 39 publications

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“…Nor do we assume that the distribution of the pollution load (mass -mg) in the 271 root zone approximates the distribution of N concentration in the river, which is likely to 272 distort instrument cost-effectiveness and policy ranking. Also, since our approach does not 273 involve approximating the deterministic equivalent of a probabilistic constraint in a chance 274 constrained programming framework, therefore we don't have to estimate the correlation 275 coefficient between emissions (Kampas and White, 2003). The parameters for the normal and lognormal distributions were estimated from the data's mean and the mean of the log, respectively, whereas those of the truncated normal over the interval of concentration greater that 2 mg/L (arbitrarily chosen) were obtained by maximum likelihood.…”

Section: 45 Underlying Pollutant Distribution Assumptionmentioning

confidence: 99%

Transferability of Policies to Control Agricultural Nonpoint Pollution in Relatively Similar Catchments

Aftab

Hanley

Baiocchi

2017

Ecological Economics

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Section: 45 Underlying Pollutant Distribution Assumptionmentioning

confidence: 99%

Transferability of Policies to Control Agricultural Nonpoint Pollution in Relatively Similar Catchments

Aftab

Hanley

Baiocchi

2017

Ecological Economics

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“…He presented the main idea related with the stochastic goal programming and chance-constraint linear goal programming. Kampas and White [8] have suggested the programming based on probability for the control of nitrate pollution in their studies and compared this with the approaches of various probabilistic constraints. Yang and Wen [9] presented a chance-constrained programming model for transmission system planning in the competitive electricity market environment.…”

Section: Introductionmentioning

confidence: 99%

Gamma distribution approach in chance-constrained stochastic programming model

Atalay¹,

Apaydin²

2011

J Inequal Appl

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In this article, a method is developed to transform the chance-constrained programming problem into a deterministic problem. We have considered a chance-constrained programming problem under the assumption that the random variables a ij are independent with Gamma distributions. This new method uses estimation of the distance between distribution of sum of these independent random variables having Gamma distribution and normal distribution, probabilistic constraint obtained via Essen inequality has been made deterministic using the approach suggested by Polya. The model studied on in practice stage has been solved under the assumption of both Gamma and normal distributions and the obtained results have been compared.

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“…Therefore, even if the choice is restricted to assuming one of these two distributions, it is not obvious which one to choose, despite the fact that ideally we want to use a distribution that restricts pollution loads to the positive domain. Also of note is that previous research has shown that chance-constrained programming models are sensitive to the distributional assumptions made [13,17,28]. 3 In this paper we explore an alternative way to address the problem, namely to truncate a symmetric distribution.…”

Section: Introductionmentioning

confidence: 99%

Distributional Assumptions in Chance-Constrained Programming Models of Stochastic Water Pollution

Kataria¹,

Elofsson

Hasler

2009

Environ Model Assess

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In the water management literature both the normal and log-normal distribution are commonly used to model stochastic water pollution. The normality assumption is usually motivated by the central limit theorem, while the log-normality assumption is often motivated by the need to avoid the possibility of negative pollution loads. We utilize the truncated normal distribution as an alternative to these distributions. Using probabilistic constraints in a cost-minimization model for the Baltic Sea, we show that the distribution assumption bias is between 1% and 60%. Simulations show that a greater difference is to be expected for data with a higher degree of truncation. Using the normal distribution instead of the truncated normal distribution leads to an underestimation of the true cost. On the contrary, the difference in cost when using the normal versus the lognormal can be positive as well as negative.

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Probabilistic programming for nitrate pollution control: Comparing different probabilistic constraint approximations

Cited by 25 publications

References 39 publications

Transferability of Policies to Control Agricultural Nonpoint Pollution in Relatively Similar Catchments

Transferability of Policies to Control Agricultural Nonpoint Pollution in Relatively Similar Catchments

Gamma distribution approach in chance-constrained stochastic programming model

Distributional Assumptions in Chance-Constrained Programming Models of Stochastic Water Pollution

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