Error Propagation Made Easy—Or at Least Easier

Gardenier, George H.; Ge, Feng; Demas, J. N.

doi:10.1021/ed1004307

Cited by 17 publications

(31 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The standard error of the mean (SEM) was used to represent the uncertainty of each prime variable measurement, given by Errors were propagated from directly measured prime variables, such as cell density or metabolite concentration, to each calculated variable q = f ( m 1 , m 2 , …) using the equation (Taylor, 1997) where the sum is over all prime variables that influence the calculated value of q . Numerical finite differencing was applied to estimate the partial derivatives with respect to prime variables (Gardenier et al, 2011). Least‐squares linear regression was performed based on Equations (2) and (5) using the propagated uncertainties δx i and δy i associated with x ‐ and y ‐axis variables, respectively, to determine the weight w i of each data point in the sum‐of‐squared residuals (SSR) objective function where MATLAB's lscov command was used to obtain the weighted least‐squares estimate of the best‐fit line.…”

Section: Methodsmentioning

confidence: 99%

ETA: Robust software for determination of cell specific rates from extracellular time courses

Murphy

Young

2013

Biotech & Bioengineering

View full text Add to dashboard Cite

Accurate quantification of cell specific rates and their uncertainties is of critical importance for assessing metabolic phenotypes of cultured cells. We applied two different methods of regression and error analysis to estimate specific metabolic rates from time-course measurements obtained in exponentially growing cell cultures. Using simulated data sets to compute specific rates of growth, glucose uptake, and lactate excretion, we found that Gaussian error propagation from prime variables to the final calculated rates was the most accurate method for estimating parameter uncertainty. We incorporated this method into a MATLAB-based software package called Extracellular Time-Course Analysis (ETA), which automates the analysis workflow required to (i) compute cell specific metabolic rates and their uncertainties, (ii) test the goodness-of-fit of the experimental data to the regression model, and (iii) rapidly compare the results across multiple experiments. ETA was used to estimate the uptake or excretion rate of glucose, lactate, and 18 different amino acids in a B-cell model of c-Myc-driven cancer. We found that P493-6 cells with High Myc expression increased their specific uptake of glutamine, arginine, serine, lysine, and branched-chain amino acids by 2- to 3-fold in comparison to Low Myc cells, but exhibited only modest increases in glucose uptake and lactate excretion. By making the ETA software package freely available to the scientific community, we expect that it will become an important tool for rigorous estimation of specific rates required for metabolic flux analysis and other quantitative metabolic studies.

show abstract

Section: Methodsmentioning

confidence: 99%

ETA: Robust software for determination of cell specific rates from extracellular time courses

Murphy

Young

2013

Biotech & Bioengineering

View full text Add to dashboard Cite

show abstract

“…Finally, the MatLab code also includes a "sensitivity analysis" (adapted from [2]), where students examine how sensitive the final calculated error is to the errors of the different experimental variables. The sensitivity analysis provides students with explicit information about sources of error so they can make a better assessment of possible improvements to the experimental design.…”

Section: Two Additional Tutorial Labs For In-class Instruction and Prmentioning

confidence: 99%

Blended Learning in First Year Engineering Labs

Topper

Clapham

2019

PCEEA

View full text Add to dashboard Cite

In 2000, Queen’s Engineering adopted a new model for laboratory instruction to its common first year program. This involved moving from the traditional weekly physics and chemistry labs to a 12 week course on "Experimentation" - in which students learned how to design their own simple physics and chemistry experiments. Offered in a 12 week term, this course, called APSC100 Module 2, began with two shorter "tutorial labs" to introduce the key elements of experimental design then moved through a 6-week lab rotation where students practiced doing well-designed experiments, and finally culminated in a two week "Experimental Design Project". The authors dedicated the summer of 2017 to restructuring this course. Much of the core content was retained, however significant changes were made to pace, method of content delivery, and deliverables. Changes include:  An improvement in student preparation for the lab, through the introduction of on-line pre-lab content and quizzes, to be completed by students the night before their lab.  The elimination of post-lab homework.  A slower pace of introduction of early content – the original "2 tutorial lab" format was expanded to 4 tutorial labs  The introduction of "electronic lab templates". Templates include the lab instructions as well as blank boxes in which to include diagrams, Excel tables and figures, regression analysis, explanatory text and answers to questions.  A new Arduino-based altimeter lab introduces students to large variable data sets. This paper will review the changes to the course, and report on the outcome of these changes following two years of offering the course in the new format.

show abstract

“…6,7 A Monte Carlo simulation routine for uncertainty propagation has been previously described in the Journal of Chemical Education by Demas et al using a Mathcad routine that can handle up to four input quantities. 5 Monte Carlo methods can be advantageous as compared to the calculus-based approach for error propagation by providing a relatively easy to interpret understanding of the calculation for students and by allowing for the propagation of a wide variety of uncertainty distributions. 4,5 In the teaching laboratory, students are often required to estimate underlying uncertainty distributions of various measurements in the interest of time.…”

Section: ■ Introductionmentioning

confidence: 99%

“…5 Monte Carlo methods can be advantageous as compared to the calculus-based approach for error propagation by providing a relatively easy to interpret understanding of the calculation for students and by allowing for the propagation of a wide variety of uncertainty distributions. 4,5 In the teaching laboratory, students are often required to estimate underlying uncertainty distributions of various measurements in the interest of time. Many measurements in the chemistry laboratory (interpolation of an analog scale, reading of a nonfluctuating digital signal, and others) are best estimated with uncertainty distributions that are non-Guassian (e.g., triangular uncertainty distributions, uniform uncertainty distributions, etc.).…”

Section: ■ Introductionmentioning

confidence: 99%

“…Despite these convenient features, Monte Carlo methods have traditionally been difficult to integrate into the chemistry curriculum due to a lack of availability of easy to implement solutions for carrying out these simulations. 5 A tool developed by the National Institutes of Standards and Technology (NIST) known as the "NIST Uncertainty Machine" makes the propagation of error via the Monte Carlo method readily available via a web interface (http://uncertainty.nist. gov).…”

Section: ■ Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Monte Carlo Uncertainty Propagation with the NIST Uncertainty Machine

Albert

2020

J. Chem. Educ.

View full text Add to dashboard Cite

Monte Carlo simulations for uncertainty propagation take as inputs the uncertainty distribution for each variable and an equation for the calculation of a desired quantity. The desired quantity is then calculated by randomly drawing from the specified uncertainty distributions of the input variables. This calculation is then repeated many times (often 10 6 or greater) with new random drawings each time. The resulting uncertainty distribution of the calculated value is directly obtained from the many random trials. Monte Carlo uncertainty propagation has the advantage of both being easy to interpret and allowing for a wide variety of uncertainty distributions. Monte Carlo uncertainty propagation methods have not been widely used in the undergraduate curriculum due to the lack of availability of easy to implement solutions for carrying out these simulations. Fortunately, the National Institute of Standards and Technology (NIST) developed a Monte Carlo uncertainty propagation calculator, "NIST Uncertainty Machine", that is freely available and accessible via a web interface. The NIST Uncertainty Machine makes the propagation of uncertainty with Monte Carlo simulations easy to implement in the undergraduate curriculum.

show abstract

Error Propagation Made Easy—Or at Least Easier

Cited by 17 publications

References 10 publications

ETA: Robust software for determination of cell specific rates from extracellular time courses

ETA: Robust software for determination of cell specific rates from extracellular time courses

Blended Learning in First Year Engineering Labs

Monte Carlo Uncertainty Propagation with the NIST Uncertainty Machine

Contact Info

Product

Resources

About