Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment
Estimating the risk, P(X > Y), in probabilistic environmental risk assessment of nanoparticles is a problem when confronted by potentially small risks and small sample sizes of the exposure concentration X and/or the effect concentration Y. This is illustrated in the motivating case study of aqua...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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PeerJ Inc.
2015-08-01
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| Series: | PeerJ |
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| Online Access: | https://peerj.com/articles/1164.pdf |
| _version_ | 1797424329536831488 |
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| author | Rianne Jacobs Andriëtte A. Bekker Hilko van der Voet Cajo J.F. ter Braak |
| author_facet | Rianne Jacobs Andriëtte A. Bekker Hilko van der Voet Cajo J.F. ter Braak |
| author_sort | Rianne Jacobs |
| collection | DOAJ |
| description | Estimating the risk, P(X > Y), in probabilistic environmental risk assessment of nanoparticles is a problem when confronted by potentially small risks and small sample sizes of the exposure concentration X and/or the effect concentration Y. This is illustrated in the motivating case study of aquatic risk assessment of nano-Ag. A non-parametric estimator based on data alone is not sufficient as it is limited by sample size. In this paper, we investigate the maximum gain possible when making strong parametric assumptions as opposed to making no parametric assumptions at all. We compare maximum likelihood and Bayesian estimators with the non-parametric estimator and study the influence of sample size and risk on the (interval) estimators via simulation. We found that the parametric estimators enable us to estimate and bound the risk for smaller sample sizes and small risks. Also, the Bayesian estimator outperforms the maximum likelihood estimators in terms of coverage and interval lengths and is, therefore, preferred in our motivating case study. |
| first_indexed | 2024-03-09T08:00:39Z |
| format | Article |
| id | doaj.art-7c88f57fe3004edeb131c982e3d2b4ad |
| institution | Directory Open Access Journal |
| issn | 2167-8359 |
| language | English |
| last_indexed | 2024-03-09T08:00:39Z |
| publishDate | 2015-08-01 |
| publisher | PeerJ Inc. |
| record_format | Article |
| series | PeerJ |
| spelling | doaj.art-7c88f57fe3004edeb131c982e3d2b4ad2023-12-03T00:47:05ZengPeerJ Inc.PeerJ2167-83592015-08-013e116410.7717/peerj.1164Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessmentRianne Jacobs0Andriëtte A. Bekker1Hilko van der Voet2Cajo J.F. ter Braak3Biometris, Wageningen University and Research Centre, Wageningen, The NetherlandsDepartment of Statistics, University of Pretoria, Pretoria, South AfricaBiometris, Wageningen University and Research Centre, Wageningen, The NetherlandsBiometris, Wageningen University and Research Centre, Wageningen, The NetherlandsEstimating the risk, P(X > Y), in probabilistic environmental risk assessment of nanoparticles is a problem when confronted by potentially small risks and small sample sizes of the exposure concentration X and/or the effect concentration Y. This is illustrated in the motivating case study of aquatic risk assessment of nano-Ag. A non-parametric estimator based on data alone is not sufficient as it is limited by sample size. In this paper, we investigate the maximum gain possible when making strong parametric assumptions as opposed to making no parametric assumptions at all. We compare maximum likelihood and Bayesian estimators with the non-parametric estimator and study the influence of sample size and risk on the (interval) estimators via simulation. We found that the parametric estimators enable us to estimate and bound the risk for smaller sample sizes and small risks. Also, the Bayesian estimator outperforms the maximum likelihood estimators in terms of coverage and interval lengths and is, therefore, preferred in our motivating case study.https://peerj.com/articles/1164.pdfBayesian estimatorMaximum likelihood estimatorRisk assessmentSimulationNanoparticle |
| spellingShingle | Rianne Jacobs Andriëtte A. Bekker Hilko van der Voet Cajo J.F. ter Braak Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment PeerJ Bayesian estimator Maximum likelihood estimator Risk assessment Simulation Nanoparticle |
| title | Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment |
| title_full | Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment |
| title_fullStr | Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment |
| title_full_unstemmed | Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment |
| title_short | Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment |
| title_sort | parametric estimation of p x y for normal distributions in the context of probabilistic environmental risk assessment |
| topic | Bayesian estimator Maximum likelihood estimator Risk assessment Simulation Nanoparticle |
| url | https://peerj.com/articles/1164.pdf |
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