An introduction to Bayesian methods for analyzing chemistry data

Armstrong, N.; Hibbert, David Brynn

doi:10.1016/j.chemolab.2009.04.001

Cited by 54 publications

(25 citation statements)

References 15 publications

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“…Uncertainty in reported lead compliance results from variability among samples associated with true differences in lead concentrations among locations, and sampling and analysis uncertainty in the statistical summary of these variations caused by using a finite sample size. 26 In this work, the estimate of the 90 th percentile of the distribution in the sampled data set is the parameter of interest, and the criteria of interest is whether this estimated value exceeds 15 ppb (the AL). Quantifying the uncertainty in this value requires the determination of a predictive distribution for the parameter of interest.…”

Section: Methodsmentioning

confidence: 99%

Using Compliance Data to Understand Uncertainty in Drinking Water Lead Levels in Southwestern Pennsylvania

Schwetschenau

Small

VanBriesen

2020

Environ. Sci. Technol.

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The historical use of lead in potable water plumbing systems has caused significant public health challenges. The Lead and Copper Rule requires utilities to take action if the 90 th percentile lead concentration exceeds the action level (AL) of 15 ppb. Assessment of the AL is based on a sample of homes representing a relatively small fraction of connections. Due to the intentional nonrepresentative sampling approach, the full set of conditions influencing lead concentrations in a large distribution system may be poorly characterized. Further, there is uncertainty in assessing statistical parameters such as the 90 th percentile concentration. This work demonstrates methods to compute the uncertainty in the 90 th percentile statistic and assesses the associated effect on compliance outcomes. The method is demonstrated on four utilities in southwest Pennsylvania (referred to as A, B, C, and D). For Utility A, evaluation of the 90 th percentile showed an increase over time in observed and estimated values and the value's uncertainty. This type of change in the uncertainty might have served as an early warning of the exceedance that followed. This could have triggered more timely review of operational changes in order to avoid the effects of noncompliance on utility costs and consumer confidence.

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Section: Methodsmentioning

confidence: 99%

Using Compliance Data to Understand Uncertainty in Drinking Water Lead Levels in Southwestern Pennsylvania

Schwetschenau

Small

VanBriesen

2020

Environ. Sci. Technol.

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“…Any data pretreatment has been described elsewhere. 10,12 Solving the Integral of Equation 13. Solving eq 13 for a different number of configurations constitutes the core computation of this approach.…”

Section: ■ Experimental Sectionmentioning

confidence: 99%

“…The likelihood can be calculated by applying the marginalization rule 13 over all parameters that are influencing D:…”

mentioning

confidence: 99%

Bayesian Approach for Peak Detection in Two-Dimensional Chromatography

Vivó-Truyols

2012

Anal. Chem.

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A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual one-dimensional peaks have been originated from the same compound and should then be arranged in a two-dimensional peak. The merging algorithm is based on Bayesian inference. The user sets prior information about certain parameters (e.g., second-dimension retention time variability, first-dimension band broadening, chromatographic noise). On the basis of these priors, the algorithm calculates the probability of myriads of peak arrangements (i.e., ways of merging one-dimensional peaks), finding which of them holds the highest value. Uncertainty in each parameter can be accounted by adapting conveniently its probability distribution function, which in turn may change the final decision of the most probable peak arrangement. It has been demonstrated that the Bayesian approach presented in this paper follows the chromatographers' intuition. The algorithm has been applied and tested with LC × LC and GC × GC data and takes around 1 min to process chromatograms with several thousands of peaks.

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“…[40][41][42] A literature review [43][44][45][46][47][48][49] teaches that the Bayesian inversion framework has been used in chemistry, specifically in combustion chemistry and associated mechanisms as well as in chemometrics, forensic sciences, medical testing, microbiology/DNA analysis, chromatography and mass spectrometry, environmental chemistry, and occupational health and safety, among other areas as detailed by Hibbert and Armstrong in their highly recommended reviews. 50,51 However, the Bayesian inversion approach is still not widely employed in mechanistic chemistry in general and there is little to no use in nanoparticle chemistry and mechanisms to the best of our knowledge. *…”

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confidence: 99%

Estimating reaction parameters in mechanism‐enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

et al. 2021

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In order to quantitatively predict nano-as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth.The Bayesian approach addresses the question of "how well do we know our parameters, along with their uncertainties?." The results reveal that Bayesian inversion statistical analysis on an example, prototype Ir 0 ð Þ n nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a "Gold Standard" Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

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An introduction to Bayesian methods for analyzing chemistry data

Cited by 54 publications

References 15 publications

Using Compliance Data to Understand Uncertainty in Drinking Water Lead Levels in Southwestern Pennsylvania

Using Compliance Data to Understand Uncertainty in Drinking Water Lead Levels in Southwestern Pennsylvania

Bayesian Approach for Peak Detection in Two-Dimensional Chromatography

Estimating reaction parameters in mechanism‐enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

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