Monte-Carlo Propagation of Uncertainty

How do the uncertainties in measurements affect the uncertainty in the result? There are many ways to deal with this problem, but this Monte-Carlo technique is easy and very effective.

[@ItisAbuTDMM]

Nice Tutorial. Thanks!

[@tylerjones6918]

Simple and clean explanation, thank you!

[@sspickle]

Glad it was helpful!

[@ricardodealmeida5485]

Great video. Thank you!

[@shiyunqiu8228]

Thank you so much. This video is very clear and informative!

[@ajphysicsdomain5429]

Good job...👌

[@benyaminhr]

Thanks

[@stephenpuryear]

Steve this is a great start! Could you illustrate Monte Carlo components that are also correlated?

[@sspickle]

I guess you could try something like this: math.stackexchange.com/questions/163470/generating-correlated-random-numbers-why-does-cholesky-decomposition-work

[@a.n.m.taufiqelahi5895]

Great video! Thank you very much! How to calculate the percent contribution from each variable while using Monte Carlo propagation?

[@sspickle]

I suppose you could dial back the variance of the other variables to see the effect of only one. Is that what you mean?

[@pmale90]

but, what if data is not normally distributed (non Gaussian) ?

[@sspickle]

Then it depends. A gaussian is just a reasonable guess that's easy to generate (and suggested by the central limit theorem). If you know what the distribution is, just use that instead. If you don't, and you have reason to believe it's not gaussian, then you're in tough spot.

[@firassami7399]

Thanks for providing the excellent expains
I just wanna ask you about the distribution. It is not normal distribution. If you repeat the run 100 times and every time you can calculate the mean . Finaly you will have 100 mean values and then you could plot the histogram. This way you will get normal distribution and could give you more accurate results...do you agree with me ?

[@ricardodealmeida5485]

I think that you're referring to the central limit theorem right? I don't think it applies here because if you repeat the run 100 with the same values, it will produce the same distribution, no? If so, then the summary statistics won't be meaningful.

[@KoiKen8]

Thank you! Great explanation! I’m doing my bachelor’s thesis on this topic. Do you know any good bibliography on the theory behind these Montecarlo methods for error propagation? It would be of great help

[@sspickle]

Sorry, I really don't! Sorry. If you find something good, let me know! I can add a link to the description.

[@mohamedibrahim1836]

First, the statstical sampling way is more generative than the quadratic rule that is over simplification. But I also wonder have you thought of sampling from a multivariable covariance distribution instead of single independent?

[@sspickle]

Yes, I think I replied to a question about that in the comments earlier. You can certainly do it! However, this activity is for sophomore students, just learning about random numbers and estimating uncertainty, so that's really out of scope for this particular video.

[@mohamedibrahim1836]

@@sspickle Thanks for reply, also thanks for the clear tutorial :)

[@abdulrahmansalem9660]

hello, thank you so much for your video, so are there different codes between Python and Matlab??

[@sspickle]

I'm not a Matlab user, but I'm sure there are corresponding features of Matlab that would accomplish the same result.

[@abdulrahmansalem9660]

@@sspickle Thank you and I appreciate it.

[@sergiomiguellopezramirez5670]

Could you please share your Jupiter notebook, you really nailed it...!

[@sspickle]

Check this repo: github.com/sspickle/instrumentation-projects and see the file: proj7/MCPropagationOfUncertainty.ipynb

[@toivosamuelmabote9395]

@@sspickle Thanks

[@sspickle]

@@toivosamuelmabote9395 github.com/sspickle/instrumentation-projects/blob/master/proj7/MCPropagationOfUncertainty.ipynb

[@Sky-lw5pr]

Why do you put 2*rhoMC.std() instead of just rhoMC.std() at the end? where did the 2 came from?

[@sspickle]

Well, assuming a normal distribution a 95% confidence interval is +/- 2*sigma. Note that it's clearly *not* a normal distribution but this will give a rough estimate of the interval. You could do better by computing the cumulative distribution and searching for the 2.5% and 97.5% limits, but I didn't go into such things in this video. Maybe that would be a good follow up sometime?

[@cengizhancengiz1919]

interesting, I think i missing something in my code... each time I run my code, i get a different plot. Is not supposed to be consistent with the plot but have variable ranges?

[@sspickle]

How many points are you using? If it's a small number you would expect some variation.

[@cengizhancengiz1919]

​@@sspickle ​ makes sense! my familiarity with Python is not high, so I forgot to specify the bins=np.linespace(5,20,21) part after asking for pl.hist(rhoMC). Thank you kindly. Also, I'm assigned to develop an MC analysis for development schedule predictions and figured Python would be a good tool to use. Do you have any recommendations on what to prioritize when exploring Python to develop this analysis tool? Your advice is much appreciated

[@sspickle]

I would start with pandas, numpy, and scipy but there are many others!
@@cengizhancengiz1919

[@vishalsaini5021]

Sir..I want to calculate the uncertainty of solar radiation data of 8760 hours with the help of Monte Carlo Simulation in MATLAB.... Please guide me on how to achieve the same

[@sspickle]

Sorry, I have no idea what you mean by this. Also, I'm not a MATLAB user, so I can't really help with that.

[@vishalsaini5021]

Dear Steve is it possible to calculate uncertainty associated with solar radiation data using Monte Carlo Simulation in MS Excel