Sufficient Statistics and the Factorization Theorem

This video teaches you all about sufficient statistics - what they are, why they're important and useful, and how to find them using the factorization theorem, with examples for the Binomial and Poisson distribution.

[@charlesSTATS]

I love how you put the context of sufficiency in real life chance events. Thank you for this gold video!

[@ops428]

I'm glad I found your channel. I have never seen a better explanation of mathematical statistics, nobody else is even close! You are doing an amazing job there

[@briangreco2718]

Thanks for the kind words :)

[@phillipmunkhuwa5435]

Great explanation

[@qkdnrnskfirnsvabk]

Thanks for the straightforward explanation!! Now I can understand why "sufficient" is sufficient!

[@user-ps6vx8xr6l]

Thank you very much!!!
Very clear, usefull and understandable

[@RoyalYoutube_PRO]

3:04 I love how he describe the indepence of these samples by talking about the coins coming from '3 sets of 10 flips' ... this ensures that the second sample isn't reliant on the first and the third sample isn't reliant on the second and first and so on... in other words, the samples are independent
If the samples were taken from a single set of binomial, the probabilty of success of second flip as well as first flip is dependent on success or fail of first sample

[@briangreco2718]

To be clear, we are still assuming all the 30 flips are independent and have the same probability of heads - we are just changing how summarize the data. Whether we talking about each flip individually, 3 sets of 10, or 1 set of 30, all 30 coin flips are independent.

[@jwbpark]

you are a genius

[@dolynk]

This is a great, intuitive explanation. Thanks!

[@briangreco2718]

Thanks, glad you found it helpful!

[@DonFranciscoUSF]

This is a fantastic explanation, clear, simple, and short :)

[@briangreco2718]

Thank you!

[@yasamanboroon-zn2lu]

It was awesome please continue 🔥

[@awongiwengxanga7196]

Thank you!

[@briangreco2718]

Thanks for watching!

[@maryziperman4410]

thank you soooooo much. this was so helpful for my college final in mathematical statistics at Texas a&m!!!! you are incredibly gifted!

[@briangreco2718]

Thanks, Mary, I'm glad it helped!

[@raltonkistnasamy6599]

thank u so much man u explained it so so well

[@briangreco2718]

Thanks, glad you enjoyed it!

[@TaoLeaf]

Keep up the good work!

[@briangreco2718]

Thank you, lots more to come!

[@ashsingh2175]

great!

[@aldenc.9461]

Really impressed with your videos, keep on making more!

[@briangreco2718]

Thank you, many more to come!

[@raltonkistnasamy6599]

thank u thank u thank u

[@matteomorellini5974]

Thanks for the video, I'm not grasping only one concept: why is the summation of X_i sufficient in the binomial case (I assume this means we won't need the number of trials)? Shouldn't we know the number of successes with respect to the total trials? For example of course the summation of X_i = 3 where n=5 and where n=100 should give different probabilities

[@briangreco2718]

Yes, you're totally correct. We do need to know the number of trials, but that's usually known to us already, so in that case the # of successes is equivalent to the proportion of successes because we can just divide by the (already known) number of trials. (If the number of trials were *also* an unknown parameter that we were trying to learn about, then the number of successes alone would not be sufficient for learning about the probability of success). Let me know if that makes sense or if I can try to clarify further.

[@matteomorellini5974]

@@briangreco2718 yep that's more than 🥁🥁🥁sufficient! Thanks again

[@nimeshamohottige9872]

Great work.Thank you

[@ninuuh]

I have questions about statistical inference. Can you help me solve them?

[@briangreco2718]

If you have a question related to the video, I may be able to help. If it’s not related to the video, I probably can’t help.

[@ninuuh]

@@briangreco2718 It is about statistical inference, unbiased estimator and sufficient statistic

[@ninuuh]

It is related to statistical inference, adequate statistics and an unbiased estimator@@briangreco2718

[@ninuuh]

It is about statistical inference, unbiased estimator and sufficient statistic​@@briangreco2718

[@ninuuh]

@@briangreco2718 Yes, related to the video