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.
You’re describing a good teacher, a good professor is the one who produces new knowledge constantly, i.e., publishes a lot of (highly cited) papers. In top universities, professors assume their audience are geniuses, so they barely explain trivial concepts and seldom provide their students with technical details. C’est la vie
@@RealGigaMind precisely, that's the point. If you receive just great minds, you don't have to produce them. This explains why admission into top universities, in every country, is quite hard. You're missing the point, Professors don't aim to be good teachers but to be good researchers. The college system is designed in such a way: publish or perish instead of teaching as much as you can. Someone with a high publication record has a better chance of being hired at any University than another candidate with a lower record although the latter is a better teacher. Perhaps, in the foreseeable future, AI will produce great minds instead of natural intelligence hehe. Teaching could be the sort of job, where AI might replace its human counterpart.
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!
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~
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
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!
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.
"Statistics is about replacing expectations with averages ... everytimes you see an expectation you replace it by an average" this resume all this lecture.
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.
🎯 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
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
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.
@@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.
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
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.
🎯 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
(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
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.
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
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
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,
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
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 🤣
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?
Most of the people don't know that,Statistics is a subject of Science.🇧🇩🇧🇩🇧🇩 But we can't think any sectors that, where Statistics aren’t use.Thanks a lot for your explanation.
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
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.
Hi, relative to undergraduate curriculum, would this be considered Intermediate Statistics / Statistics II, following an intro-level college stats class? Thanks!
I took stats 35 years ago, and worked as a statistician for a decade before switching to medical translation. I am interested now in my retirement to see how much I remember.
@@astudent8475 I switched because the medical info data-processing company I worked at moved way across the city and would have added another hour's commute each way. We also had two small kids in daycare and translation is something I can do from a home office. As I am an expat American, there was a niche for a medical/pharmaceutical native-English speaking translator. My wife worked at a pharmaceutical company designing clinical trials, and these require reams of documents to be sent to regulatory agencies in the EU and USA, primarily. It was much harder for her to withdraw to child-care duties than it was for me. I quite enjoyed the dad role, and didn't really miss company culture. Satisfied?🍻😉
I don't understand, when rolling 2 dice, the number 7 is the most likely to happen? The students agreed as well as the prof. agreed to that! I though all numbers have the same probability, of course considering the dice to be balanced, no cheating. I feel stupid! 30:50
I am also learning, but here is my understanding, 2 is the minimum number as total of 2 dices, and 12 is the maximum. (2+12) / 2 =14/2 = 7. In other words, to create 7 , the combination can be (1,6) (6,1) (2,5) (5,2) (3,4) (4,3) and we have 6 pairs to create 7. Other numbers, for example 8 , we cannot use 1 in either of dice, as we cannot create 8 if one of the dice is 1, another dice cannot be more than 6 . To create 8 (2,6)(6,2)(3,5)(5,3)(4,4) so we have 5 pairs. If we continue to count pairs for other numbers, I think we can understand that 7 is the number which we can create more pairs than others.
The government should sponsor Edx format to keep accessible education for everyone because it costs less to raise education level of children than to have large labor force waiting for social security
The average person cannot learn valuable skills from this type of lecture. MIT grads have great careers because they're smart to begin with. They aren't made smart by these lectures.
Where can I find the equation used in the last example, so I can understand exactly what each letter and placement means etc? Without that info, I got lost rather quickly in fully grasping it.. thanks 🙏🏼 I want to do a few similar problems so I can understand.. 😅
You can find the lecture notes on MIT OpenCourseWare at: ocw.mit.edu/courses/18-650-statistics-for-applications-fall-2016/. Best wishes on your studies!
There are no problem solutions available for this version of the course. You might want to look at the 2015 version. It has problem sets with solutions: ocw.mit.edu/courses/18-443-statistics-for-applications-spring-2015/. We hope this helps. Best wishes on your studies!
This course is not for pure math students. From the syllabus, "This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods." See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/18-650F16. Best wishes on your studies!
There are X logical statements that explains Y algebra is useful to learn in science and tech; and Y it can be used to do N things in life, for any kinds of operation that 1 can care to image, including the use of imaginary numbers for complex tasks themselves. It is all about integration and the sequences that have to be followed to achieve equality and reason in all of knowledge, so that we can have the opportunity to be the greatest at numeration and denomition as well as domination of those lessor; for X > Y when X have more knowledge then Y. Y? Because of Z!
No it's 2/3. Condition is to include possibility of having number less than or equal to two. There are only two conditions 1 and 2. So probability will be 2/6*2 (last 2 is for dollar).
The prerequisites listed in the syllabus: Probability theory at the level of 18.440 Probability and Random Variables. Some linear algebra (matrices, vectors, eigenvalues). See the course materials for more info at: ocw.mit.edu/18-650F16. Best wishes on your studies!
I am terrible at Math, but need to take statistics. I am a hard worker though. Any advice? Is it impossible to master for someone who isn't good at Math? :(
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.
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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.
You’re describing a good teacher, a good professor is the one who produces new knowledge constantly, i.e., publishes a lot of (highly cited) papers. In top universities, professors assume their audience are geniuses, so they barely explain trivial concepts and seldom provide their students with technical details. C’est la vie
@@isaacbernardocaicedocastro4835 That's basically a printer. Printers don't produce great minds. Printers only produce files.
@@RealGigaMind precisely, that's the point. If you receive just great minds, you don't have to produce them. This explains why admission into top universities, in every country, is quite hard. You're missing the point, Professors don't aim to be good teachers but to be good researchers. The college system is designed in such a way: publish or perish instead of teaching as much as you can. Someone with a high publication record has a better chance of being hired at any University than another candidate with a lower record although the latter is a better teacher. Perhaps, in the foreseeable future, AI will produce great minds instead of natural intelligence hehe. Teaching could be the sort of job, where AI might replace its human counterpart.
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 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
Same here
In bachelor class I fail in statistics unexpectedly. Now after 15 yrs I listen this like I am in university again. ❤
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 :)
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.
this guy knows his stuff. i enjoyed his class very much. Fair grader too, not tough, but fair.
"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.
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
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 !!!
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.
Came for the Bayesian statistics lecture, stayed for the whole class. Great lectures! thank you
You are like me.. Also into pyMC3?
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😂
"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?
the prof gave us the greatest book suggestion ever 'ALL of STATISTICS by Larry Wasserman'. Merci bcp
Is this course suitable for adding in Data Science syllabus ?
@@TheClinchMagazine i think it's more mathematical than data science inclined
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
🎯 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.*
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It looks as if the smart person of the class just sent me his notes lol
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?
i like the way he prepares to introduce a topic. very thoughtful and enjoyable.
Statistics is replacing expectations with average. Thank you
Not a single dislike. This video bring my faith to humanity back.
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
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.
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
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.
Instruction begins at 13:22
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?
🎯 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.*
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Course starts on 13:23...
Veeraiah Palanivel s
(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
25:13 toin coss. well i guess his brain needs a playback speed of 0.75. love these lectures
This class sounds amazing, best of two mid terms damn
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
This is the statistics class we actually wanted to take but didn't get.
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.
"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 🤷🏾♂️
Starts at 13:20
13:23 why should you study statistics???
Wow , feels nice to hear a statistics lecture from an MIT professor peeping from ceiling
I am taking MBA, the statistics lessons is very useful. Thank you for sharing
Lies again? Sex Tape Paris
@@NazriB what 😳
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
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,
Thank you Liam Neeson
Is this the same as introduction to statistics for economists???
"Statistics is about replacing expectations with averages."
as long as your expectations are average about life, you will do fine with statistics.
42:34 can someone explain the probability question again pls?
thank you so much
Frrom FPT university in VIet Nam with love
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
Charting and statement are possibilities in realizing models.
13:25
Thank You.
Thanks!
Thanks! :)
You answered before I asked. Thx.
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 🤣
👏👏👏congratulations from Brazil for the class !
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?
Most of the people don't know that,Statistics is a subject of Science.🇧🇩🇧🇩🇧🇩 But we can't think any sectors that, where Statistics aren’t use.Thanks a lot for your explanation.
Lecturer :"i am actually tend to speak faster , so I hope y'all understand"
Me : play in 2x speed
The lecturer is awesome.
At 23:00 why would reusing data for different questions lead to wrongful conclusion ?
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.
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!
MIT is King. Period.
Could you provide the solutions to the assignments and recitation materials?
arent they in their website?
This class kicked my ass.. ok bye before commercials end 🏃♀️
"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
I took stats 35 years ago, and worked as a statistician for a decade before switching to medical translation. I am interested now in my retirement to see how much I remember.
@@astudent8475
I switched because the medical info data-processing company I worked at moved way across the city and would have added another hour's commute each way. We also had two small kids in daycare and translation is something I can do from a home office. As I am an expat American, there was a niche for a medical/pharmaceutical native-English speaking translator. My wife worked at a pharmaceutical company designing clinical trials, and these require reams of documents to be sent to regulatory agencies in the EU and USA, primarily. It was much harder for her to withdraw to child-care duties than it was for me. I quite enjoyed the dad role, and didn't really miss company culture.
Satisfied?🍻😉
Going through a tough time, I hope things get better
It will man it will
I couldn't find assignment 1 in the website the 30 problem I founded assignment 4 in the place of 1 help please thanks in advance
ocw.mit.edu/courses/18-650-statistics-for-applications-fall-2016/resources/mit18_650f16_pset1/
@@mitocw thanks for the help I wish you the best ocw but I found that the 30 problem the teacher has talked about has changed I think since then
I don't understand, when rolling 2 dice, the number 7 is the most likely to happen? The students agreed as well as the prof. agreed to that! I though all numbers have the same probability, of course considering the dice to be balanced, no cheating. I feel stupid! 30:50
I am also learning, but here is my understanding, 2 is the minimum number as total of 2 dices, and 12 is the maximum. (2+12) / 2 =14/2 = 7.
In other words, to create 7 , the combination can be (1,6) (6,1) (2,5) (5,2) (3,4) (4,3) and we have 6 pairs to create 7.
Other numbers, for example 8 , we cannot use 1 in either of dice, as we cannot create 8 if one of the dice is 1, another dice cannot be more than 6 .
To create 8 (2,6)(6,2)(3,5)(5,3)(4,4) so we have 5 pairs. If we continue to count pairs for other numbers, I think we can understand that 7 is the number which we can create more pairs than others.
Statistics are about knowing the distribution of the entire poppulation given the distribution of one dataset
It's a "toin coss"!
@59:25, what do we mean by confidence and how can one compute it?
The government should sponsor Edx format to keep accessible education for everyone because it costs less to raise education level of children than to have large labor force waiting for social security
The average person cannot learn valuable skills from this type of lecture. MIT grads have great careers because they're smart to begin with. They aren't made smart by these lectures.
Where can I find the equation used in the last example, so I can understand exactly what each letter and placement means etc? Without that info, I got lost rather quickly in fully grasping it.. thanks 🙏🏼 I want to do a few similar problems so I can understand.. 😅
You can find the lecture notes on MIT OpenCourseWare at: ocw.mit.edu/courses/18-650-statistics-for-applications-fall-2016/.
Best wishes on your studies!
@@mitocw thank you!🙏 ☺️
1:10:29
X_i follows gaussian(or normal) distribution
13:20 course start
Great lectures and problem sets. But is it possible to get related solutions? Or is any one working with problem sets? Plz contact me!
There are no problem solutions available for this version of the course. You might want to look at the 2015 version. It has problem sets with solutions: ocw.mit.edu/courses/18-443-statistics-for-applications-spring-2015/. We hope this helps. Best wishes on your studies!
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
really like the lecturer, god bless!
Can someone tell me if it for pure maths students
coz I want a statistics course for Econometrics
This course is not for pure math students. From the syllabus, "This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods." See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/18-650F16. Best wishes on your studies!
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.
I am not in the class but I still watched the first 13:20 minutes
Where can the problem set of 30 questions that he mentioned be found?
There are X logical statements that explains Y algebra is useful to learn in science and tech; and Y it can be used to do N things in life, for any kinds of operation that 1 can care to image, including the use of imaginary numbers for complex tasks themselves. It is all about integration and the sequences that have to be followed to achieve equality and reason in all of knowledge, so that we can have the opportunity to be the greatest at numeration and denomition as well as domination of those lessor; for X > Y when X have more knowledge then Y. Y? Because of Z!
I dont understant why choose 7 on that question.?
Are the samples really independent? The 2 59s, they probably impacted.
30:15..... I thought the answer would be 1/3 however you wrote down 2/3. I don't understand that?
No it's 2/3.
Condition is to include possibility of having number less than or equal to two. There are only two conditions 1 and 2. So probability will be 2/6*2 (last 2 is for dollar).
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.
Why do we have to use statistics in genetics
Milla Rita coz gene follow statistics
30.21 y is it not 1/3
53:24 I guess that's what everyone feels after talking so quick for a long time :D
any suggested youtube prerequisites for this course? kinda hard bc im not smart. thx
The prerequisites listed in the syllabus: Probability theory at the level of 18.440 Probability and Random Variables. Some linear algebra (matrices, vectors, eigenvalues). See the course materials for more info at: ocw.mit.edu/18-650F16. Best wishes on your studies!
This course would have been much better if the course site actually has solution for us to compare our answer with.
That exercise at the end did not come out to have average of 67.5 and Std dev of 18....is it me or did t happen with anyone else
Yes sure, it's average should be 73.86
I am terrible at Math, but need to take statistics. I am a hard worker though. Any advice? Is it impossible to master for someone who isn't good at Math? :(
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.
Can this course be considered a standard Statistical Inference Class?
I like the LaTeX slides