1. Introduction to Statistics
ฝัง
- เผยแพร่เมื่อ 14 มิ.ย. 2024
- *NOTE: This video was recorded in Fall 2017. The rest of the lectures were recorded in Fall 2016, but video of Lecture 1 was not available.
MIT 18.650 Statistics for Applications, Fall 2016
View the complete course: ocw.mit.edu/18-650F16
Instructor: Philippe Rigollet
In this lecture, Prof. Rigollet talked about the importance of the mathematical theory behind statistical methods and built a mathematical model to understand the accuracy of the statistical procedure.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
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A statistics class focused on understanding statistics, not just scribbling equations. Very refreshing.
He probably agrees with Mark Twain. I know I do.
"k, epstein." Haha. If I didn't notice this I would have posted a serious reply.
@@ModeratelyAmused Twain gets quoted later on in this series. Data sins.
@@ModeratelyAmused c
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Ve2e2ws
he he. 5 more lectures and you will realize how wrong you are :P
A good professor gets down to the level of a student and stops assuming things. A great professor gets down to the level of the weakest (new to the field) student in the class and makes them feel that they are not alone. And he is an excellent professor. Thank you MIT.
List of lectures (for some reason, lecture 10 doesn't exist so I re-ordered the numbering, which is why there's actually only 23 videos)
Lecture 1: Part 1 - Intro to Statistics
Lecture 2: Part 2 - Intro to Statistics
Lecture 3: Parametric Inference
Lecture 4: Parametric Inference and Likelihood of Estimation
Lecture 5: Maximum of Likelihood Estimation
Lecture 6: Maximum Likelihood of Estimation and Methods of Moments
Lecture 7: Part 1 - Parametric Hypothesis Testing
Lecture 8: Part 2 - Parametric Hypothesis Testing
Lecture 9: Part 3 - Parametric Hypothesis Testing
Lecture 10: Parametric Hypothesis Testing and Testing Goodness of Fit
Lecture 11: Testing Goodness of Fit
Lecture 12: Part 1 - Regression
Lecture 14: Part 2 - Regression
Lecture 15: Part 3 - Regression
Lesson 16: Part 1 - Bayesian Statistics
Lesson 17: Part 2 - Bayesian Statistics
Lesson 18: Part 1 - Principal Component Analysis
Lesson 19: Part 2 - Principal Component Analysis
Lesson 20: Part 1 - Generalized Linear Models
Lesson 21: Part 2 - Generalized Linear Models
Lesson 22: Part 3 - Generalized Linear Models
Lesson 23: Part 4 - Generalized Linear Models
Good luck with your studies~
you are goated for this, thank you!
chyeju kaba sai yaw
THANKS STRANGER FROM THE INTERNET
Thank you so much.
thanks kayla :)
"Statistics is about replacing expectations with averages. That is what all of statistics is about."
gökçe zora oh you look so very sweeeet
Gud
U said it 👍🏾
@@nikhilmanek1966 ur mum
@@nikhilmanek1966 Creep alert
Actual math lecture starts at 13:20
You are awesome. You saved my 13 minutes
Thank youuuu...
Thank you very much. Saved 3 mins
I'm 52 minutes in and he still hasn't actually started on anything.
thank you !!!
In bachelor class I fail in statistics unexpectedly. Now after 15 yrs I listen this like I am in university again. ❤
i am listening this course again because i am now PhD student. To refresh basics is a vital step. thank u MIT
Me too, my department's stats course was a complete nightmare - Bayesian modeling in R with zero fundamentals
this guy knows his stuff. i enjoyed his class very much. Fair grader too, not tough, but fair.
i like the way he prepares to introduce a topic. very thoughtful and enjoyable.
Awesome video. Using it to get ahead for fall! Thank you for providing this to the public. In the age of the internet, knowledge is as cheap as the wifi!
material is as cheap as the wifi, not knowledge !
Both should be free
@@irwinjones3960 They are quasi-public goods, they won't be provided by the free market and taxpayers won't be willing to pay for them.
I got moved and rocked. Thanks for uploading!! Watching from Tokyo, Japan. (In my shabby apartment room. I am a low income Tokyo city's resident.)
As Dr.Regollet mentioned, Statistics is,
z=a+b
For me,
Let,
Live=Audiences+Performers
also, z^=a^+b^ is an equation of a circle.
Life^=Your heartbeat^ + My heartbeat^
Each square means that A heartbeat consists of movement of two ventricles.
The kiss brings me to enter my body, mind and soul. This lecture has given me a new life.
How wonderful! Thank you for inspiring me. I've so refreshed!
I am extremely grateful for this entire series. Thank you. I keep revisiting every time I forget a concept or need to brush up. Having taught in a classroom myself, and having gotten many thanks and compliments from my students over the years, I can tell that he has that same attitude that I learned to embrace - making sure that students understand the concepts and do not just blindly memorize equations. I used to teach computer science (data structures, algorithms and oop languages) at Steven’s inst. in Hoboken.
Loved that you captured your audience with the "kissing Statue" in relation to stats..... very engaging :) since statistics in a Phd program is so painful lol
10:20 prerequisites
14:50 explanation of the scientific process a bit before this. On the collection of data --> hypothesis, which will then be proven or disproven by more data
This class sounds amazing, best of two mid terms damn
"Randomness is a big rug in which we sweep everything, we don't understand." Leap of faith.
51:12 - because Real-time observation feels better.
This course is excellent, so much needed in the modern world.
I took stats last year, it was tough! Luckily my school used Lumen which helped a lot! It had practice problems so you can know what you do wrong, so u can go back and work on it before going on to your official home work. I was able to get an A but it was tough and had to put a lot of extra time aside dedicated just to my homework etc because i am very very bad at math. The lumen program really helped a lot
Can you please tell me what exactly is a lumen program?
Statistics is replacing expectations with average. Thank you
I had to take a stats class as a requirement for my Admin Justice major..after I took this class and achieved in it just by sheer trying hard and studying..I was able to get an A and decided to try science and engineering courses and I did pretty good because I got Fs in HS when I took them. So I thought I'd settle for a career with less education requirement after HS--20 years later I'm a software engineer for a major telahealth company. I'd never would expect this--I thought I'd be a cop
The expectation that I was "bad at math" led me away from pursuing a STEM degree when I graduated high-school. Ten years later I discovered that I was not bad at math, I was just a lazy student and that I might need to put in effort. I hate to think how many people are in the same boat.
I'm sure you'd become a good cop, too.
@@carsonfleetwood572 yeaaa same. I dont know why i hate math back then
What was it like deciding to pursue your software job? Did you ever have doubts or fears of being stuck in a “sit all day at a computer” job?
@@bigchonkerraccoon5046 I decided to pursue a software engineering career bc to me it was like solving a math/physics problem (you have to enjoy solving problems). I do have doubts like "am I an impostor sitting here designing a piece of software for thousands of ppl to use ?"
Sitting all day at a computer not that bad if you are so focused on solving a puzzle. The time goes really fast--obviously I took breaks when needed and lift weights a lot helps. Sounds crazy but many software engineers I know are into working out and body building to balance the hours of sitting.
Came for the Bayesian statistics lecture, stayed for the whole class. Great lectures! thank you
You are like me.. Also into pyMC3?
"Statistics is about replacing expectations with averages ... everytimes you see an expectation you replace it by an average" this resume all this lecture.
this resume all this lecture . . . what?
I wish this was available when I was an undergrad. I would have came to OCW for every single friggin course. But glad its available now, certainly helps with grad school.
I hated taken statistics as an undergrad
This course should be the standard for every statistics across all levels in education. My current statistics course in community colleg is structured ineffectively and goes straight into the math. While this applies a lot more real word situations & lore that makes the class exciting.
"Lore"
@@jasonmaguire7552😂
Instruction begins at 13:22
Course starts on 13:23...
Veeraiah Palanivel s
If Philippe speaks too quickly for you don't forget you can slow down the speed in the settings. I found 0.75 worked for me.
1.5x worked for me
When Philippe said that he has a tendency to speak too fast, he wasn't kidding was he?
This is the statistics class we actually wanted to take but didn't get.
Hi, relative to undergraduate curriculum, would this be considered Intermediate Statistics / Statistics II, following an intro-level college stats class? Thanks!
Yes, it would be. See the Math Major Roadmaps for details: math.mit.edu/academics/undergrad/roadmaps.php. Best wishes on your studies!
👏👏👏congratulations from Brazil for the class !
Not a single dislike. This video bring my faith to humanity back.
25:13 toin coss. well i guess his brain needs a playback speed of 0.75. love these lectures
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
25:10 it is NOT a toin coss
Excellent proclamation! : 36:00 There is no randomness. Randomness is a big rug, underwhich we sweep everything we don't understand.
That's mind blowing.
Not really. The classification of dropping your iphone as a non-random occurrence is dangerously naïve considering is just proves the person making the claim has no true understanding of what randomness is. Literally at the quantum level the uncertainly rule prevails. Therefore Everything we do a random mathematical computation of XOR.
Could you add Lecture 10 and 16 from this year (2017)?
If I am reading the tea leaves correctly, those lectures are the in class exams, so no real material is missing.
Could you provide the solutions to the assignments and recitation materials?
arent they in their website?
Wow , feels nice to hear a statistics lecture from an MIT professor peeping from ceiling
Where is the video he was planning to post on Stellar for the statistical table?
Thank you Liam Neeson
Thank you for posting !
I am taking MBA, the statistics lessons is very useful. Thank you for sharing
Lies again? Sex Tape Paris
@@NazriB what 😳
What Software does Prof. Rigollet use to make these slides?
I guess it's RMarkdown but can someone confirm?
Looks like Latex with Beamer package.
"Statistics is about replacing expectations with averages."
"Biased" is the word that u were looking for :)
I also guess the same but it May be sample bias
yep. i guessed the same
13:20 course start
"randomness is a big rug under which we sweep everything we don't understand"
I fucks with this
I've always believed that with the right amount of data and analysis, nothing is really random 🤷🏾♂️
it depends on the side we sleep on, take average of a persons sleeping side, there will be a natural tilt already because of that. also right hand gives more control and balance.
I'm just wondering whether 67.5 is correct. I may be missing something, but as far as I run my R code, it says 73.866. Did I miss something ?
Below is my code and results.
--
(base) demo@ubuntu:~/SelfStudy/MIT-OCSW/18.650-Fundamental-of-Statistics$ ./1_1hour12mins.R
[1] 73.86667
[1] 73.86667
(base) demo@ubuntu:~/SelfStudy/MIT-OCSW/18.650-Fundamental-of-Statistics$ cat 1_1hour12mins.R
#! /usr/bin/env Rscript
x
got the same result, i tried 34 instead of 134 just in case that was the typo, much closer not the one tough
🎯 Key Takeaways for quick navigation:
00:29 *📚 The course "Fundamentals of Statistics" (formerly "Statistics for Applications") aims to provide an introductory understanding of statistics, focusing on theoretical guarantees and mathematical principles.*
01:54 *📊 The course emphasizes building error bars and understanding how to choose between statistical estimators, providing a foundation for making predictions and interpreting data.*
04:21 *🎓 The course prepares students for more advanced topics like machine learning, emphasizing the statistical fundamentals necessary for understanding algorithms and data-driven decision-making.*
05:19 *📝 Homework assignments are due weekly, with the best 10 out of 11 counted toward the final grade, comprising 30% of the total.*
08:11 *📚 Two midterms will be held in class, with only the better score of the two counted, contributing to 30% of the final grade.*
09:35 *🕒 The final exam will be three hours long, accounting for 40% of the total grade, allowing notes but not textbooks.*
12:00 *📄 Lecture slides and other materials will be posted on Stellar, providing resources for students to study and review outside of class.*
13:27 *📊 Statistics plays a crucial role in interpreting scientific studies and making informed decisions based on data, highlighting the importance of understanding statistical concepts in various fields.*
17:43 *🧮 Statistical tools are essential for distinguishing meaningful results from random fluctuations, addressing issues like p-hacking and ensuring the reliability of scientific findings.*
20:36 *🌊 Building dikes in the Netherlands in the 10th century showcased an early application of statistics, using data on previous floods to inform dike construction.*
21:04 *💼 Statistics plays a crucial role in determining insurance premiums, with calculations based on the expected cost of insurance claims.*
21:59 *💊 Clinical trials exemplify statistical success stories, with rigorous testing protocols required by the FDA to evaluate the effectiveness of new drugs.*
23:25 *🧬 Genetic studies, like those investigating Alzheimer's disease, rely on statistics to analyze large datasets and identify associations between genes and diseases.*
25:20 *🎲 Understanding and taming randomness is essential in statistics, enabling decision-making based on data analysis.*
26:13 *📊 Statistical concepts like average, fair premium, quantifying chance, and significance are fundamental for interpreting data and making informed decisions.*
28:10 *🔢 Statistics involves finding basic numbers from data, unlike probability where basic numbers are given, allowing for the estimation of parameters from data.*
32:50 *📉 Statisticians simplify complex models to estimate parameters accurately, understanding that model errors may occur but are necessary for data analysis.*
37:40 *🤝 Good modeling in statistics requires choosing plausible simple models based on domain knowledge, emphasizing the importance of understanding the problem domain.*
39:27 *🎲 Statistics involves describing outcomes based on known truths or distributions, enabling predictions or data generation.*
40:25 *📊 Statistics involves reversing the process of probability, moving from data to infer the truth or distribution that generated it.*
41:51 *📈 Statistical analysis focuses on predicting average outcomes or macro properties of datasets, not exact individual outcomes.*
43:39 *📉 In statistics, data is used to estimate parameters like effectiveness or proportion, incorporating error margins for uncertainty.*
45:32 *🧰 The course emphasizes understanding statistical methods mathematically, with a focus on modeling assumptions and their implications.*
47:54 *🎓 The course offers an applied statistical perspective, focusing on building estimators within specific modeling frameworks rather than data analysis or software implementation.*
49:49 *🤔 Statistical thinking involves framing questions, hypotheses, and variables in a way that allows for quantifiable analysis and inference.*
53:34 *📋 Statistical experiments involve observing samples from populations, estimating parameters, and making inferences about the population based on sample data.*
01:03:28 *📊 Accuracy in an estimator refers to its stability and proximity to the true value being estimated.*
01:04:25 *🎯 The volatility of an estimator can impact its effectiveness; stable estimators offer consistent results over various samples.*
01:05:20 *📈 Statistical modeling involves making assumptions about observed data, such as assuming randomness and independence.*
01:06:17 *📊 Bernoulli distribution is commonly used to model random variables with two possible outcomes, making it useful for binary data.*
01:14:45 *💡 In statistics, expectations are often replaced by averages to simplify calculations, a key concept for estimation.*
Made with HARPA AI
awesome video. thank you!
as long as your expectations are average about life, you will do fine with statistics.
Going through a tough time, I hope things get better
It will man it will
Where can the problem set of 30 questions that he mentioned be found?
At 30:00 - It doesn't matter wether you go with with Alice or Bob. They should be getting the same amount of money, as the number of dots greater than or equal to 3 has 4/6 sides of the dice covered (3, 4, 5 and 6 -> 4/6 -> 2/3). Am I mistaken?
(1) Introduction to Statistics
1. Intro
2. Prerequisites
3. Why Should you Study Statistics
4. The Salmon Experiment
5. The History of Statistics
6. Why Statisctis
7. Randomness
8. Real Randomness
9. Good Modeling
10. Probability vs Statistics
11. Course Objectives
12. Statistics
Please record your introductry number theory lectures
Statistics is replacing expectation with averages: frame it, get a tattoo, I don't care...
I'm sold.
please post the course for introduction to probability! :D thank you for the videos btw!
th-cam.com/play/PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo.html
This is a good one from Harvard
@@atrijitdas1704 thank you!
Please record mathematical statistics 18.655, thanks!
really like the lecturer, god bless!
Starts at 13:20
PERSONAL NOTES
1. Say p = 60% from n samples. How many samples would it guarantee that p > 50%? We need a model for this. The goal for our model is that the density must be as narrow as possible (least possible volatility), and the value that we're looking for is as close as it is likely to be. Assumptions: random (good way to model lack of infos, otherwise non-math wouldd suffice), i.i.d,
Thanks for sharing this
Lecture aside, I just wanna say that the course structure of 30% assignments, 2x 15% midterms and a 40% Final is very smart.
Looks like grading is more focused on learning throughout the semester to engage the students.
Courses with 50% Final and 2x 25% midterms or similar does not do anything to help students learn in the long term. Great class structure
I agree!
in my country the final is 100% of your grade and you need to pass two midterms to be allowed to have a go at the final. Such an insane system my country has lol
Is there a change to get access to the mandatory lessons? Thanks for sharing the course!
The lecturer is awesome.
It's a "toin coss"!
Statistics are about knowing the distribution of the entire poppulation given the distribution of one dataset
Why is it such a common spoonerism that he says "toin coss" instead of coin toss @25:16? I have the exact same issue when giving a lesson!
What courses would be beneficial for applied economics and econometrics students? Thanks in advance!
can anyone please provide the links to the extra videos he said he'll be uploading. Like the Gaussian Distribution one up on stellar. I searched stellar MIT but couldn't find it.
The Stellar course management system has been developed to support delivery of classes to students at MIT. Note that access to most Stellar class Web sites is limited to class participants. Any materials we do have available for the course can be found on MIT OpenCourseWare at: ocw.mit.edu/18-650F16. On a quick check, it doesn't look like these extra videos were given to MIT OpenCourseWare.
is this course applicable for lab analysis of data using statistical methods ? im a physics student wondering if this is worth the time to learn
yes
MIT is King. Period.
13:25
Thank You.
Thanks!
Thanks! :)
You answered before I asked. Thx.
Could someone please illustrate how the 7 has the most high probability for the problem at 31:00
Chose a number between 2 and 12
Win 100$ if you chose the sum of the 2 dice.
I didn't quite understand how its 7
Nevermind. I understood.
Most numbers add upto 7
i also confused at fist and then i realize 7 has the most combination than other numbers
There are 36 ways to get a total.
Only one way to get a total of 2, which is double 1.
But there are six ways to get a total of 7, which is the maximum number of ways for any particular total, and so this is the most likely total.
Gotta read that article on kissing so I can better understand statistics...
Thank you
thank you so much
Frrom FPT university in VIet Nam with love
Maybe it is posible put subtitles spanish, gracias.
1:10:29
X_i follows gaussian(or normal) distribution
thank you
53:24 I guess that's what everyone feels after talking so quick for a long time :D
Is there any one one who can help me which book or slides this course is based on? It would be very great, thank you.
This course doesn't have a text listed, but in case this helps, the previous version taught by Peter Kempthorne used J.A. Rice: Mathematical Statistics and Data Analysis. Duxbury Press, 2006. www.amazon.com/exec/obidos/ASIN/0534399428/ref=nosim/mitopencourse-20. Good luck with your studies!
@59:25, what do we mean by confidence and how can one compute it?
So, "estimate" is the same thing with "expectation"?
This class kicked my ass.. ok bye before commercials end 🏃♀️
I am not in the class but I still watched the first 13:20 minutes
Thank you so much
this is lullaby to me
Lecturer :"i am actually tend to speak faster , so I hope y'all understand"
Me : play in 2x speed
😯🤣😝
Is this course a prerequisite for machine learning?
Is this the same as introduction to statistics for economists???
Anybody knows what the corresponding textbook is? Thank you very much!
The course does not seem to have a textbook listed. View the complete course at: ocw.mit.edu/18-650F16. Best wishes on your studies!
Are the samples really independent? The 2 59s, they probably impacted.
I love his sense of humor - the flashmob lol
Anybody else see that salmon-fluke pun opportunity at 17:25? Coulda been legendary...
Thanks a lot
At 23:00 why would reusing data for different questions lead to wrongful conclusion ?
Can we find the solutions for the problem sets?
Sorry, the instructor did not give solutions to the problem sets. Maybe some kind soul has them posted somewhere.