Sensitivity Analysis - Science topic

Thank you for your response but I want to know the procedure of sensitivity analysis like what will be the coding or steps in MATLAB to do sensitivity analysis for the mathematical model of inventory. Kindly guide me for this.

Steftcho P. Dokov

Saaty, the creator opf AHP stated in writing that you can't use fuzzy in AHP, because the latter is already fuzzy

Look up univariate sensitivity analysis :)

To move an object from its old Y dimension to a new Y dimension based on your 3D analysis, you can follow these general steps:

Note that the specific steps may vary depending on the software you are using for your 3D analysis. Consult the software documentation or help resources for detailed instructions on how to perform translations or transformations in your particular software.

Hello, your problem is only mass balance when you mix air at different oxygen content with syngas? Or your problem is the effect of the oxygen on the final gas composition after the reaction?

In both case, you don't vary the concentration of the oxygen keeping the constant of the air stream because this variable is not present.

While, if this is not a problem you can vary the mole o mass flow of the oxygen (the air flow will change) and then you can write in the tabulate section the formula mole oxygen in air/ mole air (this is the inlet concentration of the oxygen that you set) and in the same way you can write mole oxygen in the gas after mixer / mole gas after mixer (that is the final concentration oxygen i.e. your result). It is obvious that you define all variable that you will write in tabulate.

If you have to keep constant the air flow, so you can try to find the variable concentration in the property set and you will se in vary section.

BR,

Domenico Flagiello

See my attached paper where I performed a univariate sensitivity analysis. It tells you what to do there :)

There are lot of researches in google scholar, you can find many types of research done in the same. Sandesh Karki may be interested to work in the same.

Thank you very much for sharing your thoughts, Dr. Sébastien Buczinski Joseph Whittaker.

Precisely! @Abdul Wahab

Please feel free to contact me if you have any questions.

Thank you very much for your valuable information.

A DNK is where a researcher makes a comment or asked a question with so many abbreviations that one simply Doesn't Know what s/he is talking about. Best wishes David Booth

Without going into too much detail, I wonder if a slightly different approach would solve your problem.

The Spearman rank correlation coefficient is the Pearson correlation coefficient estimated for ranks. Therefore, I suggest that you give up the formula you used. Instead, find ranks and estimate Pearson correlation coefficient for ranks.

Amir Mustakim Ab Rashid may use a statistical method to find the error in between the final answers.

Use the below code in MATLAB software.

i=[0.9332 -1.2736 -0.9796 1.2489

1.6467 0.0158 0.6810 -0.9129

-0.7345 -0.8109 2.1678 -1.3348

-0.0144 1.9623 1.5066 1.1229

-1.8064 1.2488 -0.4296 -0.3624

-1.0439 0.3471 -1.6714 -1.1997]; % Weights between input and hidden layer

O=[-0.7313 0.0880 0.5374 0.2884 -0.2156 -0.3838]; % Weights between hidden layer and output layer

d=size(i);

i=abs(i);

O=abs(O);

ii=sum(i')';

for k=1:d(1) % define for loop for each input as below

R1(k)=i(k,1)*O(1,k)/ii(k,1);

end

sum(R1);

for k=1:d(1)

R2(k)=i(k,2)*O(1,k)/ii(k,1);

end

sum(R2);

for k=1:d(1)

R3(k)=i(k,3)*O(1,k)/ii(k,1);

end

sum(R3);

for k=1:d(1)

R4(k)=i(k,4)*O(1,k)/ii(k,1);

end

sum(R4);

% calculate the percentage for each input as below

RR1=sum(R1)/(sum(R1)+sum(R2)+sum(R3)+sum(R4))*100;

RR2=sum(R2)/(sum(R1)+sum(R2)+sum(R3)+sum(R4))*100;

RR3=sum(R3)/(sum(R1)+sum(R2)+sum(R3)+sum(R4))*100;

RR4=sum(R4)/(sum(R1)+sum(R2)+sum(R3)+sum(R4))*100;

% percentage of variables.

R=[RR1,RR2,RR3,RR4]'

Well, mesh independence is usually done for most critical conditions, like highest velocity involved.

Hi,

I suggest you see the links on the topic.

Best regards

Hello Frost,

To your specific question, does the computed value (using the "Sensitivity" option, which solves for ES) using G*Power for a manova problem yield the f^2 associated with Pillai's trace (V): Yes.

Cohen's f^2 is a ratio of explained variation divided by unexplained variation (where the two values: explained, unexplained, sum to 1). It has been likened to a "signal" to "noise" ratio, from communications research.

Good luck with your work.

I don't think there really is such a thing. But if you analyse using a Chi square test, it's kind of like a sensitive analysis because it uses expected values :)

Kindly check this video:

See the attached screenshot for your answer best wishes David Booth

The standard of living dimension is measured by gross national income per capita. The HDI uses the logarithm of income, to reflect the diminishing importance of income with increasing GNI. The scores for the three HDI dimension indices are then aggregated into a composite index using geometric mean.

The problem in the CIs is caused by the practically impossible outlier. As dear Gordon mentioned, an SMD of 15 does not happen. By including such an outlier, the forest function tried to generate a plot with an X-axis from -15 to +15 in a very limited space. So, on the plot, the CI lines will be very narrow.

Of note, the problematic outlier has caused other issues:

Your overall SMD is practically an unweighted average. Why? In the random-effects model, the weight is usually calculated as 1 / (t^2 + vi), and as your t^2 is that large (about 20), the influence of the variance of each effect size (which is usually less than 1) is almost nothing.

Also, such a t^2 is practically impossible. Its square root is about 4.5. We cannot expect such a standard deviation for the effect sizes.

I hope this clarifies the importance of the problematic SMD. I would follow Gordon's recommendation. If I could not find any error in data extraction, and I could not get an answer from the authors, I would exclude this study, and I would write in the manuscript something like "...this study was excluded, as the effect size was practically impossible (SMD = 15), indicating some errors in the report."

Finally, correcting or excluding this SMD will resolve the problem with the CI lines.

Good luck with your work.

Dear Vidya

Unfortunately, what you observed is very common, and again, false.

I am sure that nobody can justify this procedure.

Instead, you can use objective weights fron entropy, or statistics, or still bether, use the marginal values for each criterion. Both are exact, and based on values extracted from the data.

And most important, both can be used to evaluate alternatives. They are not trade-offs.

If more information is needed, please don't hesitate and contact me. I will be happy to help

Try to depend on the fourth order PDE.

I am ready to help.

The sensitivity analysis is better. You can study the sensitivity of the output with respect to the chosen weights using any of the sensitivity analysis methods. In my opinion, one of the most powerful methods is the Non-Intrusive Polynomial Chaos Expansion method (PCE). It is a stochastic method which will show the direct sensitivity of the output to each input parameter and the nonlinear interaction of the input parameters and there effect on the output. You can check the following papers if you want more details:

1) Spatial Variation in Sensitivity of Hurricane Surge Characteristics to Hurricane Parameters

2) Multi-physics modelling andsensitivity analysis of olympic rowing boat dynamics

Let me know if you don't have access to the papers.

Why don't you run Real-Time PCR (LightCycler)? It can be used for quantitative analysis of a gene copy number so it can be used for viruses as well.

You vary the parameters of the MR and see how the output values vary, whether wildly or gradually, and then make comparisons :)

Sensitivity analyses reveal how the model outputs change when more factors enter incrementally into a model, or when a single parameter is fixed while others vary, or when all parameters are fixed while one varies (i.e. univariate). A sensitive parameter is one that elicits a large change in model output for a small change in a given input parameter. The univariate sensitivity of model response (S) with respect to parameter x, is equal to the ratio of the relative change observed in the state variable y for a given relative change in the value x, with y being sensitive to x when S > c. 1, otherwise it is robust.

See: Hamby, D. M. (1994) A review of techniques for parameter sensitivity analysis of environmental models. Environmental Monitoring and Assessment 32: 135-154.

Hi,

Maybe some of these references are of help to you:

Economic Evaluation in Clinical Trials By Henry A. Glick, Jalpa A. Doshi, Seema S. Sonnad, Daniel Polsky 2014 | 272 Pages | ISBN: 0199685029

Economic Evaluation of Cancer Drugs: Using Clinical Trial and Real-World Data by Iftekhar Khan, Ralph Crott, et al. English | 2019 | ISBN: 1498761305 | 442 pages

Design & analysis of clinical trials for economic evaluation & reimbursement: an applied approach using SAS & STATA

Iftekhar Khan

Series: Chapman & Hall/CRC biostatistics series

Publisher: CRC Press, Year: 2015

ISBN: 978-1-4665-0548-3,1466505486

Michael F. Drummond, Mark J. Sculpher, Karl Claxton, Greg L. Stoddart, George W. Torrance,ISBN: 0199665877 | 2015 | 461 pages |

Yes I am

Try to only have 18 then? My huge model on seed dispersal had fewer than 18 :)

Any non-Matlab based solutions ? :-) My university does not provide a license.

Kindly viait..

Dear Mr Ramezanzadeh,

I think this article can helps you to find your answer.

Good luck.

At first you should start with a coarse mesh (may be the software default), then check the targeted parameters.

Then increase the accuracy of the mesh ( make it finer) and check the same targeted parameter.

Then further repeat it with finer and finer meshes, and check the same output parameter.

You should repeat it till you got a mesh independent solution.

And you can present this data in your paper.

Best regards

Waqar Khan ,

First of all, you do not Need to carry out a feature sensitivity analysis. It is not a requirement, but just an added bonus.

Secondly, in most applications, Feature Selection (via feature importances) and Feature Sensitivity are similar and complementary. Adding feature sensitivity after feature selection seems to be overkill. (More on this later)

While there are many different algorithms for estimating the sensitivity of a model on a set of features, I believe that you may be relatively new to Machine learning and suggest that you start with a couple of simple approaches:

a) How sensitive is the model to changes in the value of a feature? The classical way to carry this out is to shuffle or perturb the values of feature and see the magnitude of change in the model prediction.

b) How is the model affected if a certain feature's measurement is missing?

These 2 approaches would be a good point to start with sensitivity analysis. In case you are short on time and need to get results quickly, there are good libraries that can carry out sensitivity analysis for you. For instance, the pytolemaic package can do sensitivity analysis for most python ML models and generates pretty good reports, along with figures automatically (https://pypi.org/project/pytolemaic/).

I looked at the paper. I don't really like muticentre trials precisely because of this problem and their attempt to reduce bias, which actually introduces further bias. However, I believe there is no problem comparing the two treatments, even though they differ in duration, since the variable considered is time to treatment failure. The protocols are different, but failure is defined the same for both treatments i.e. platelet count < 30 x 10^9. Next time, they should really plan for equal duration of trials at one facility, examine treatment success, and maybe not publish in open access :)

The 'meta summarize' command should be available in Stata 16. Sounds more like you have a typing error somewhere in your code. This can result in the 'unrecognized' error.

A good reference for technical help on Stata code is the Stata Forum: https://www.statalist.org/forums/

Kind regards

Alex Kørup

This paper may help you:

I agree with Ali Yasen Mohamedahmed To solve high I²-heterogeneity issues this RG link may be useful:

It's change in what YOU DID not some other test method. They want to know how your answer changes if you change important parameters a little bit in what YOU DID ALREADY. This is not some other statistical test. David Booth. Here's a dumb example:

Suppose you have the equation 2x=6. X=3 is the solution. They wish to know how sensitive the solution is if you Change 6 to say 6.05 calculate the new x and compare it to x=3. That's sensitivity. GOOD LUCK DB

Use mutual information or entropy theory

Dear Mahmut

Thank you for considering that I can answer your question.

However I don't have an answer because I don't know in detail the method our friend Thanh posed.

I already mentioned Thanh that it is improbable that after 0.5% the selected alternative holds, because most probable the intervening criteria are decreasing their Lambda as long as the Lambda of one criterion is changed, and then, their margins of variation are decreasing simultaneously, until a moment where the selected criterion ceases to be important for the best selection, and then, a new criterion is now responsible, and most probably producing a change on the initial ranking.

This can be clearly seen when the original straight line of a certain objective, changes to another straight line, but with a lower slope, corresponding to a lower marginal cost, and then originating a convex curve, which represents the utility curve

Trying to answer your specific question, and always according to my reasoning, it appears that it is not natural that the same procedure produces alternatives changes for lambda values below 05, which agrees with what I said above, and suddenly, from 0.5 > lambda< 1, it remains constant. I would check this

I am attaching the resulting curves produced by SIMUS/IOSA, published in one of my books, for solving a problem, where the best alternatives was subject to two criteria C3 and C5, and their simultaneous variation. The curve of the left is from increasing criteria C1 and C5 at the same time. That on the left is for decreasing.

Observe that the curve on the left shows a straight line and for a certain value changes forming a convex curve

HI

This article can help you

Maybe you can consider the recursive least squares algorithm (RLS) with forgetting factor (RLS-FF). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the RLS-FF algorithm, acquired data is weighted according to its age, with increased weight given to the most recent data. The correlation parameters are updated gradually.

Application example ― I have applied the RLS-FF algorithm to estimate the parameters from the K_La correlation, used to predict the O₂ gas-liquid mass-transfer, hence giving increased weight to most recent data:

Hello Nneka,

Sensitivity reflects the proportion of true positives (on some criterion variable) that a given indicator flags as positive. A value of 1 indicates that every true positive case was so identified/flagged by your indicator variable.

This could occur if:

1. The indicator scores are genuinely indicative of and highly corresponding to true status (this is the ideal case; the others which follow are not).

2. All cases were true positives, in which case the indicator scores don't necessarily have to relate to true status.

3. You have a very small sample size.

4. The indicator variable is actually redundant with the true status measurement (for example: if the indicator variable was BMI score and the true status was whether or not a case was classified as morbidly obese).

Good luck with your work.

Hi there, I am not familiar with dynamic Bayesian networks. However, any results from a newly applied approach need to be validated with evidence from experiments, measurements or other proven algorithms. e.g. a frequentist approach shall have a similar finding. Hopefully is helpful. ~DM

Yes

See sections 3.3-3.5 in this paper: https://acp.copernicus.org/articles/16/11837/2016/acp-16-11837-2016.pdf

One thing to keep in mind is that several meteorological parameters covary. So, just perturbing one of them alone may disturb the geostrophic and hydrostatic balance in the model, creating unrealistic waves in the model solution.

Thank you, Andrea

following

The below paper might be helpful:

By ensuring that the variable isn't declared as a constant. For instance; https://www.tutorialspoint.com/fortran/fortran_constants.htm

Sensitivity analysis is useful to determine the robustness of the optimal solution. If the optimal solution changes significantly, when one of the problem parameters is changed only slightly, then the optimal solution is said to be sensitive to changes in that parameter, otherwise, it is robust.

Sensitivity analysis also gives insights into the problem under study. You can use it to validate your hypotheses about the problem or you can derive conclusions about the relationship of the optimal objective function value to the various parameters of the problem. This helps ground a problem from practice on a more reliable and intuitive basis, and demonstrates its applicability in practice.

One option would be to use the ChiProfiler tool that integrates with TopoToolbox that Sean Gallen (Colorado State University) created. It is available from his Zenodo site for download at https://zenodo.org/record/321868#.YCV91WhKg2w or on Github at https://github.com/sfgallen/ChiProfiler.

Article to reference for use of ChiProfiler is:

Gallen, S.F., Wegmann, K.W.: River profile response to normal fault growth and linkage: An example from the Hellenic forearc of south-central Crete, Greece, Earth Surf. Dynam., 2017, http://www.earth-surf-dynam.net/5/161/2017/.

Dear Prof Adam N. Letchford

Your ideas for dividing the region and using local optimizer are so nice!

Thanks a lot!

Mathematical optimisation kills all heuristics - if you pick them right.

Hi,

Use a finer grids near the wall with hexahedral mesh and try to use another turbulence model like SST model.

Dear Shahroz,

Please, see:

Please check the following:

Usually + or - 25%

A standard trick in these cases is to use the Sherman Morrison formula

However, the inverse of a sparse matrix does not have to be sparse and in particular one does not want to store inverses for sparse large matrices, so that the formula would rather have to be applied to the action A^-1b of the inverse on the right hand side of the linear system, so as to correct the solution to the original linear system A^-1b with a hopefully limited amount of operations.

Please notice that this is a very generic comment, I am sure somebody in the sparse solver community will have studied the problem in much greater depth.

Thanks Chinaza Godswill Awuchi and Andrew Paul McKenzie Pegman fro the help

Hi? You might want to have a look at one of my publications - 10.1016/j.envsoft.2020.104800

I recently conducted a similar study where I applied three different sensitivity analysis methods to fire simulations and compared their results!

Cheers!

Hi? You might want to have a look at one of my publications - 10.1016/j.envsoft.2020.104800

I recently conducted a similar study trying to analyze the impact/influence of a parameter in the model output using a SALib python library! SALib is quite easy to use.

Cheers!

Hi? You might want to have a look at one of my publications - 10.1016/j.envsoft.2020.104800

Dear Vysakh Venugopal

Since such validation is unreliable in most of the cases, mathematicians have presented various benchmarks (case study) and have given a proof for their global optimum. These are why benchmarks are developed in optimization and control (to validate a methodology with a high reliability and confidence). However, we have some benchmarks in optimal control, while the global solution is only the best known optimum, not definitely the absolute one.

If you look deeper into the literature, you have some sensitivity analysis methods that are independent of the sampling techniques!

It means is proportional to :)

Have a look at

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.71.2138&rep=rep1&type=pdf

https://personales.unican.es/gutierjm/papers/ieee97.pdf

The percentage of variation across studies that is due to heterogeneity rather than chance decreased

Have you checked the package sensitivity?

Cochrane's Handbook suggests that it's more important to find out whether a meta-analysis is valid rather than worrying about how to do it. I'd suggest doing heterogeneity analysis and looking at variables like (rstudent, weight of studies, and others).

I suggest that you learn R to get use of packages like "meta" and "metafor".

metafor package has tests that show you which studies influence your final estimate the most. There could be one study that's causing all the heterogeneity.