L20.5 Confidence Intervals

MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: John Tsitsiklis

License: Creative Commons BY-NC-SA

[matpulvinci]

Very well explained. It’s refreshing to hear someone actually explaining what it actually is, instead of just how we should perceive it.

[spyral]

This has to be the most succinct explanation I've heard by far.

[hagverdiibrahimli]

This man is the best professor I have come across in the stat world.

[ultimate_brando]

Summary for misinterpretation of confidence interval: the statement P(Event) >= 0.95 says that if you do Event then 0.95 of the time it will be true - with the random variables in play for the Event. Thus, if Event is confidence interval estimation, then 0.95 of the time that you construct confidence intervals the true mean will be captured. Since the P(Event) has nothing to do with specific constant (which can be false for any specific computation of the Event), it means that saying the population parameter being in that interval is 0.95 makes no sense since you are not computing the probability of that for your specific values of your parameters, you are instead you are doing a procedure Event that does happen (capture the value you want theta in this case) 0.95 of the time. The event wrt to doing the action "construct confidence interval" and that is the only statement that is true. Anything else is unrelated.

[rockymandayam]

Saying it is syntactically wrong since 0.3, theta, and 0.52 are not random, doesn't make sense to me. For example, let's say a friend tosses a coin 10 times, and we know it is either a fair coint or a biased coin with P(H)=0.8. After observing the 10 coin tosses, we want to know the probability that the friend chose the biased coin to toss. Is this quesiton ill-defined since the friend either chose the biased one or didn't (it already happened, in the past), but it's not a random event, so you can't assign a probability? This seems to go against all the problems we're asked to solve in probability courses. Can anyone clarify?

[jaydenou]

why is the confidence interval ">= 1-alpha" instead of "≈ 1-alpha" or "<= 1-alpha"? If alpha is 0.05, that would be meaning : I am more than 95 % sure that the true mean is within the interval. Shouldn't than be the opposite? It suppose to be : I am less than 95 % sure that the true mean is within the interval. (it sounds more right)