TY - JOUR

T1 - Bayesian modeling of virus removal efficiency in wastewater treatment processes

AU - Ito, T.

AU - Kato, T.

AU - Takagishi, K.

AU - Okabe, S.

AU - Sano, D.

N1 - Publisher Copyright:
© IWA Publishing 2015 Water Science & Technology.

PY - 2015/11

Y1 - 2015/11

N2 - Left-censored datasets of virus density in wastewater samples make it difficult to evaluate the virus removal efficiency in wastewater treatment processes. In the present study, we modeled the probabilistic distribution of virus removal efficiency in a wastewater treatment process with a Bayesian approach, and investigated how many detect samples in influent and effluent are necessary for accurate estimation. One hundred left-censored data of virus density in wastewater (influent and effluent) were artificially generated based on assumed log-normal distributions and the posterior predictive distribution of virus density, and the log-ratio distribution were estimated. The estimation accuracy of distributions was quantified by Bhattacharyya coefficient. When it is assumed that the accurate estimation of posterior predictive distributions is possible when a 100% positive rate is obtained for 12 pairs of influent and effluent, 11 out of 144, 60 out of 324, and 201 out of 576 combinations of detect samples gave an accurate estimation at the significant level of 0.01 in a Kruskal-Wallis test when the total sample number was 12, 18, and 24, respectively. The combinations with the minimum number of detect samples were (12, 9), (16, 10), and (21, 8) when the total sample number was 12, 18, and 24, respectively.

AB - Left-censored datasets of virus density in wastewater samples make it difficult to evaluate the virus removal efficiency in wastewater treatment processes. In the present study, we modeled the probabilistic distribution of virus removal efficiency in a wastewater treatment process with a Bayesian approach, and investigated how many detect samples in influent and effluent are necessary for accurate estimation. One hundred left-censored data of virus density in wastewater (influent and effluent) were artificially generated based on assumed log-normal distributions and the posterior predictive distribution of virus density, and the log-ratio distribution were estimated. The estimation accuracy of distributions was quantified by Bhattacharyya coefficient. When it is assumed that the accurate estimation of posterior predictive distributions is possible when a 100% positive rate is obtained for 12 pairs of influent and effluent, 11 out of 144, 60 out of 324, and 201 out of 576 combinations of detect samples gave an accurate estimation at the significant level of 0.01 in a Kruskal-Wallis test when the total sample number was 12, 18, and 24, respectively. The combinations with the minimum number of detect samples were (12, 9), (16, 10), and (21, 8) when the total sample number was 12, 18, and 24, respectively.

KW - Bayesian model

KW - Left-censored data

KW - Truncated log-normal distribution

KW - Virus removal efficiency

KW - Wastewater treatment

UR - http://www.scopus.com/inward/record.url?scp=84954504815&partnerID=8YFLogxK

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U2 - 10.2166/wst.2015.402

DO - 10.2166/wst.2015.402

M3 - Article

C2 - 26540540

AN - SCOPUS:84954504815

SN - 0273-1223

VL - 72

SP - 1789

EP - 1795

JO - Water Science and Technology

JF - Water Science and Technology

IS - 10

ER -