1. Introduction to Statistics 

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.

A statistics class focused on understanding statistics, not just scribbling equations. Very refreshing.

i am listening this course again because i am now PhD student. To refresh basics is a vital step. thank u 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~

In bachelor class I fail in statistics unexpectedly. Now after 15 yrs I listen this like I am in university again. ❤

Actual math lecture starts at 13:20

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

this guy knows his stuff. i enjoyed his class very much. Fair grader too, not tough, but fair.

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!

i like the way he prepares to introduce a topic. very thoughtful and enjoyable.

"Statistics is about replacing expectations with averages. That is what all of statistics is about."

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.

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

"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 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.

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

This class sounds amazing, best of two mid terms damn

This course is excellent, so much needed in the modern world.

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

Came for the Bayesian statistics lecture, stayed for the whole class. Great lectures! thank you

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.

Instruction begins at 13:22

Statistics is replacing expectations with average. Thank you

"Statistics is about replacing expectations with averages ... everytimes you see an expectation you replace it by an average" this resume all this lecture.

Course starts on 13:23...

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.

👏👏👏congratulations from Brazil for the class !

🎯 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

Thank you for posting !

Excellent proclamation! : 36:00 There is no randomness. Randomness is a big rug, underwhich we sweep everything we don't understand.

This is the statistics class we actually wanted to take but didn't get.

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!!! 👍👍👍👍👍

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.

Where is the video he was planning to post on Stellar for the statistical table?

Wow , feels nice to hear a statistics lecture from an MIT professor peeping from ceiling

(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

Statistics is replacing expectation with averages: frame it, get a tattoo, I don't care... I'm sold.

25:10 it is NOT a toin coss

Hi, relative to undergraduate curriculum, would this be considered Intermediate Statistics / Statistics II, following an intro-level college stats class? Thanks!

"randomness is a big rug under which we sweep everything we don't understand" I fucks with this

Not a single dislike. This video bring my faith to humanity back.

awesome video. thank you!

I am taking MBA, the statistics lessons is very useful. Thank you for sharing

Starts at 13:20

13:20 course start

Please record your introductry number theory lectures

Thanks for sharing this

Could you add Lecture 10 and 16 from this year (2017)?

Where can the problem set of 30 questions that he mentioned be found?

Thank you Liam Neeson

Could you provide the solutions to the assignments and recitation materials?

Going through a tough time, I hope things get better

"Biased" is the word that u were looking for :)

The lecturer is awesome.

really like the lecturer, god bless!

I love his sense of humor - the flashmob lol

"Statistics is about replacing expectations with averages."

1:10:29 X_i follows gaussian(or normal) distribution

It's a "toin coss"!

What Software does Prof. Rigollet use to make these slides? I guess it's RMarkdown but can someone confirm?

Please record mathematical statistics 18.655, thanks!

Statistics are about knowing the distribution of the entire poppulation given the distribution of one dataset

Is there a change to get access to the mandatory lessons? Thanks for sharing the course!

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

@59:25, what do we mean by confidence and how can one compute it?

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?

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!

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,

please post the course for introduction to probability! :D thank you for the videos btw!

MIT is King. Period.

as long as your expectations are average about life, you will do fine with statistics.

Thank you

So, "estimate" is the same thing with "expectation"?

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

53:24 I guess that's what everyone feels after talking so quick for a long time :D

thank you

Maybe it is posible put subtitles spanish, gracias.

1:14:30 Omg I must say this class is a delight specially the sigma part. I was so surprised. Maybe it is something simple but it wasnt for me because I always Just use the equation.

Anybody else see that salmon-fluke pun opportunity at 17:25? Coulda been legendary...

Thank you so much

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.

Are the samples really independent? The 2 59s, they probably impacted.

Lecturer :"i am actually tend to speak faster , so I hope y'all understand" Me : play in 2x speed

Charting and statement are possibilities in realizing models.

What courses would be beneficial for applied economics and econometrics students? Thanks in advance!

Gotta read that article on kissing so I can better understand statistics...

I am not in the class but I still watched the first 13:20 minutes

13:25

Is this course a prerequisite for machine learning?

🎯 Key Takeaways for quick navigation: 00:29 📚 *The course, 18.650, titled "Fundamentals of Statistics," aims to cover statistical concepts, emphasizing theoretical guarantees, and their application to real-life situations.* 01:54 🧮 *Mathematical equations will be used extensively, focusing on theoretical understanding, estimation, and the construction of error bars in statistical thinking.* 03:23 🌐 *The course aims to equip students with the ability to formulate statistical problems mathematically, choose appropriate methods for specific questions, and understand the limitations of statistical methods.* 04:51 📚 *The course prepares students for more advanced statistical and machine learning classes, emphasizing both algorithmic and statistical components.* 05:19 📅 *The class schedule includes lectures on Tuesdays and Thursdays, with mandatory problem-solving recitations on Wednesdays.* 06:17 📝 *Weekly homework, consisting of 11 problem sets, contributes to 30% of the final grade. PDF files are required for submission, and late homework is accepted within 24 hours, no questions asked.* 08:39 📚 *Two midterms, on October 3 and November 7, account for 30% of the final grade, with only the better score considered. Midterms are closed-book and closed-notes.* 09:35 📘 *The final exam, lasting three hours, counts for 40% of the grade and allows notes but not books.* 12:29 📖 *No required textbook for the course, with lecture slides, video lectures, and problems provided. Recommended reading includes "All of Statistics" by Wasserman.* 13:55 📊 *Studying statistics is essential due to its prevalence in news, scientific studies, and fields like machine learning. Critical evaluation of studies and understanding statistical processes are emphasized.* 17:43 📉 *Awareness of statistical issues, like p-hacking, is crucial to discern the reliability of scientific studies and avoid misinterpretation of statistical findings.* 19:07 📊 *Statistics is essential for making decisions based on data, even when faced with uncertainty or incomplete information.* 20:36 🌊 *Historical example: Statistics played a crucial role in determining the height of dikes in the Netherlands to protect against floods by analyzing past flood data.* 21:31 💰 *Statistics is widely used in insurance to set premiums based on the expected cost of coverage, considering probabilities of events like iPhone damage.* 22:29 🧪 *Clinical trials rely on statistics to determine the effectiveness of new drugs, addressing challenges like sample size, placebo effects, and significance.* 23:25 🧬 *Genetics studies, like those related to Alzheimer's disease, involve statistical modeling to analyze large datasets and answer important questions.* 24:50 📉 *Statistics helps understand and manage randomness in data, providing insights into floods, insurance, clinical trials, and genetics.* 26:13 🎲 *Probability is the study of randomness, and it forms the basis for understanding and describing uncertain events in statistics.* 28:39 🎲 *Probability often deals with well-defined scenarios, while statistics involves estimating parameters and building models based on observed data.* 32:50 📊 *Statistics aims to simplify complex processes into models with a few parameters, allowing for parameter estimation from observed data.* 37:40 🔄 *Good modeling in statistics involves choosing plausible simple models while considering domain knowledge, even though there might be model errors.* 38:37 🌐 *Understanding the problem you're working on is crucial, involving aspects like sociology, biology, and engineering.* 39:27 🎲 *Probability starts with known parameters, describing expected outcomes, while statistics works backward to infer truth from observed data.* 41:51 📊 *Probability deals with known parameters, predicting averages and macro properties, while statistics deals with observed data, making inferences about underlying parameters.* 42:46 🔍 *Statistics involves making predictions based on limited data, incorporating uncertainties and potential errors.* 44:08 🧮 *The course focuses on understanding the mathematical foundations of statistical methods, emphasizing modeling assumptions like independence and identical distribution (IID).* 45:32 📉 *The course does not extensively cover data analysis but rather provides a mathematical toolbox for statistical methods.* 46:00 💻 *Mention of statistical software like R and Python, with an upcoming course on computational statistics using R.* 47:54 📚 *The course challenges students with advanced statistical concepts, promising valuable learning despite potential difficulty.* 50:15 📊 *Reference to a study on kissing couples, highlighting the importance of statistical thinking in framing and analyzing questions.* 54:33 📈 *Estimating an unknown parameter (p) involves collecting data (n couples) and calculating the proportion (p hat), emphasizing the importance of sample size for reliable estimates.* 58:12 🤔 *Statistical conclusions vary based on confidence levels. Choosing a threshold, e.g., 72%, is arbitrary and depends on study design and confidence desired.* 59:36 🎲 *Estimators and estimates differ. Estimators, being random variables, focus on accuracy, balancing volatility (variance) and proximity to the true value (bias).* 01:02:29 📏 *Accuracy of an estimator is measured by variance (volatility), aiming for stability over different samples. Bias assesses how close the estimator's average is to the true value.* 01:05:20 🤔 *Modeling assumptions are crucial. In a study on couples kissing, assumptions include couples being independent, each having a Bernoulli-distributed turning preference, and parameters being the same across couples.* 01:08:35 🧠 *Homogeneous population assumption simplifies modeling, stating conclusions about the overall population rather than individual differences.* 01:13:47 📊 *In statistics, replace expectations with averages. The estimate for the standard deviation (sigma) involves replacing expectations with averages to compute a sample estimate.* Made with HARPA AI

38:33 I feel this is the best ad for people thinking of becoming a statistician, you get to play in everybody's backyard! AND grill them for information in their field! It's like exclusive access that you're paid to have 🤣

Super video lecture

this is lullaby to me

Is this the same as introduction to statistics for economists???

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

I really need indepth statistical knowledge for applications from a Proficient Tutor even if it's within a short period of time as I can learn anything fast if I am serious and really interested. Not all these confusion they're giving us in school.

Thanks a lot

Anybody knows what the corresponding textbook is? Thank you very much!