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