7. Confidence Intervals

MIT 6.0002 Introduction to Computational Thinking and Data Science, Fall 2016
Instructor: John Guttag

Prof. Guttag continues discussing Monte Carlo simulations.

License: Creative Commons BY-NC-SA

[leixun]

*My takeaways:*
1. Generating normally distributed data in code 0:45
2. Probability density function for distribution 8:10
3. Not everything is normal distributed 20:29
4. The central limit theorem 22:50
5. Pi is calculated using Monte Carlo Simulation 32:21
- Standard deviation gets better with more samples 42:00

[Syncromatic]

Hmm, of the 43k people who watched "6. Monte Carlo Simulation", only 6k bothered to watch confidence intervals.
Estimate the amount of the 43k who are gamblers trying to beat the system.

[andreafavero]

"This is really amazing that this is true, and dramatically useful."
This statement, at 25:19, it not only true CLT ... but also for this couse: Thank you!

[annakh]

statistics are basics indeed but this course really helps me learn doing these stuff in python, thank you Mit <3

[idragonb]

Just thought you might be interested - the example that you gave from the book of Kings that seems to estimate pi as 3 has an interesting tradition associated with it. There is a concept of 'written' and 'read' in the reading of the scriptures and in this case 'line' is read and 'the line' is written. Hebrew has values associated with each letter and if we use the value of 'the line' you get 111 and 'line' is 106. If you use this as a factor to multiply the apparent 3 - you get a pretty good estimate of pi...
הקו = 111
קו = 106
111/106*3= 3.1415

[RupertBruce]

The weights in that Python code will be 1.0 always. From the description, it ought to be the count of each 'x' in a bin, divided by the number of values in the bin (which could be zero...). Discard the weights!

[stephenadams]

Didn't you get a better estimate going from 1000 needles to 2000? Isn't 3.139 closer to Pi than 3.148 so it's an improvement isn't it? But it looks still be true from your samples that the simulations are not monotonically getting better.

[sharonchan]

Thank you! This course teaches soooo much better than the lecture provided in my university!

[standman]

I would like to know when doing a monte carlo simulation why do we use Normal Inverse function in Excel?

[sibinh]

Great lecture! Like professor's humor, particularly this 34:35 :)

[bibop]

46:31 The slide says "both are factually correct". But i don't understand how the 2nd statement is true. Is it correct to say that the value of pi is between X and Y with probability 0.95, when in fact we know that the value of pi is between those X and Y with a probability of 1 ? The 2nd statement implies that the value of pi is not between X and Y with a probability of 0.05, which is false.

[rastislavsvoboda]

8:55
PDF formula in red rectangle is missing /
in code, factor2 is correct

[newbie]

Would be great if sir you could also show the plots for more number of trials, so that we could observe the trends becoming gaussian :)

[madinasaidova]

37:07 I am confused with the equation needle in circle/needle in square = area of circle/area of square

[ElVerdaderoAbejorro]

I did not get the weight parameter in the formula shown at the beginning. It says [1/numSamples]*len(dist). However, numSamples is and dist has always a length of as well, so the weight will end up as 1. Am I missing something?

[rgi]

Could somebody please explain why the precision is chosen to be .005 for the estimation of Pi? And what did he mean by saying "should probably use 1.96 instead of 2"? There are two "2" in the code, which one he meant? The whole lecture is titled "Confidence Intervals", but the actual topic is just skimmed in a couple of sentences 😳

[lee_badda]

Can someone tell me the code v[0][30:70] means? 6:14

[logosfabula]

11:44 could you expand on "the probability of any particular point is 0"?

[adiflorense]

24:23 in conclusion the subset is in the set

[seanpitcher]

I'm going to have my tutoring students watch these videos. You, sir, are an amazing teacher. And you are wrong about Mike Pence thinking pi is 3. He would never defile his mind with thinking of the value of pi. He knows this kind of unnatural fiddling with numbers is the devils work and would never participate in knowing of any part of it.