Bayesian Methods for Assessing Water Quality

Analysis of parameter uncertainty of a flow and quality stormwater model

Water Science & Technology ◽

10.2166/wst.2009.434 ◽

2009 ◽

Vol 60 (3) ◽

pp. 717-725 ◽

Cited By ~ 18

Author(s):

C. B. S. Dotto ◽

A. Deletic ◽

T. D. Fletcher

Keyword(s):

Water Quality ◽

Bayesian Methods ◽

Flow Model ◽

Model Parameters ◽

Rainfall Runoff ◽

Sources Of Uncertainty ◽

Music Model ◽

Rainfall Runoff Model ◽

Water Quality Models ◽

Runoff Model

Uncertainty is intrinsic to all monitoring programs and all models. It cannot realistically be eliminated, but it is necessary to understand the sources of uncertainty, and their consequences on models and decisions. The aim of this paper is to evaluate uncertainty in a flow and water quality stormwater model, due to the model parameters and the availability of data for calibration and validation of the flow model. The MUSIC model, widely used in Australian stormwater practice, has been investigated. Frequentist and Bayesian methods were used for calibration and sensitivity analysis, respectively. It was found that out of 13 calibration parameters of the rainfall/runoff model, only two matter (the model results were not sensitive to the other 11). This suggests that the model can be simplified without losing its accuracy. The evaluation of the water quality models proved to be much more difficult. For the specific catchment and model tested, we argue that for rainfall/runoff, 6 months of data for calibration and 6 months of data for validation are required to produce reliable predictions. Further work is needed to make similar recommendations for modelling water quality.

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Bayesian Applications in Auditory Research

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-h-astm-18-0228 ◽

2019 ◽

Vol 62 (3) ◽

pp. 577-586 ◽

Cited By ~ 9

Author(s):

Garnett P. McMillan ◽

John B. Cannon

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Bayesian Methods ◽

Prior Distribution ◽

Interim Analysis ◽

Iterative Process ◽

Bayes Theorem ◽

Sound Therapy ◽

The Many ◽

Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

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