
MIT OCW: Statistics for Applications (2016) - tosh
https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/lecture-slides/
======
norcon4
I got the chance to casually work through this course while stuck at home
during COVID-19. I highly recommend it to anybody who has a surface-level
understanding of statistics and wants to dive deep. This is NOT a course for
absolute beginners. It is rigorous and thorough. Overall a great resource,
especially the notes, but the lecturer is entertaining too.

~~~
slooonz
> This is NOT a course for absolute beginners

I disagree with that, as long as you have some mathematics background
(calculus, a bit of linear algebra), and an understanding of probability
theory (which can be taken from the prerequisite course
[https://www.edx.org/course/probability-the-science-of-
uncert...](https://www.edx.org/course/probability-the-science-of-uncertainty-
and-data)), this course is self-sufficient and does not need prior knowledge
of the subject.

I was a complete beginner in the subject and I am able to follow the course
without too much difficulties.

~~~
wenc
I took a look at the material (the slides on Method of Moments, in particular)
and my feeling is that it is a particularly mathematically-heavy treatment of
statistics. As it states in its goals, it aims to introduce the _mathematical
theory_ of statistics. On the course's main page, it is listed as a senior
undergraduate/graduate course. The style tends toward being expository rather
pedagogical -- it's a very French/European approach to teaching mathematics.

It does seem to require mathematical maturity beyond the basics, and in my
opinion this is likely not accessible to most beginners without some advanced
mathematical training.

If you find it accessible as a beginner then I congratulate you on your
mathematical prowess.

~~~
int3
"Basic" is ill-defined, but I think sloonz is right about it only requiring
calc + linalg, which most CS / Eng majors will have taken.

~~~
wenc
So I've taught undergrad courses, and my sense is, the average US college
engineering sophomore with linalg and say Calculus II (but no Real Analysis)
might struggle with this material somewhat. They may know the material for
linalg and calculus (and may have gotten As), but my feeling is that many
would not have reached the mathematical maturity to truly internalize
concepts.

I would place this course maybe at the senior level (with graduate level
cross-registration)...400-500 level elective.

What is your sense?

\--

Side note: it's interesting in that in other countries, e.g. say France, the
math curriculum is so darned advanced. In undergrad Year 1 at École
Polytechnique, real analysis and variational methods are already covered in
common courses.

[https://programmes.polytechnique.edu/en/ingenieur-
polytechni...](https://programmes.polytechnique.edu/en/ingenieur-
polytechnicien-program/program-details/year-1-of-the-ingenieur-polytechnicien-
program)

Functional analysis in Year 2.

[https://programmes.polytechnique.edu/en/ingenieur-
polytechni...](https://programmes.polytechnique.edu/en/ingenieur-
polytechnicien-program/program-details/year-2-of-the-ingenieur-polytechnicien-
program)

Then again the top French schools filter out non-math folks via classes prépas
and exams.

~~~
nightski
I'm in the demographic you describe, yet I've had a hard time finding
resources to develop that "mathematical maturity" short of going back to
graduate school. Which I'd love to do, but am at a point in my career where
that would be devastatingly expensive to my future since these are the prime
earning and wealth building years.

I wish there was more of a self directed way to achieve this.

~~~
ghufran_syed
I just finished an MS in math and statistics a long time after doing a non-
mathematical undergrad degree. I feel a _lot_ of what is called mathematical
maturity is actually getting comfortable doing proofs, which I think is hard
to learn while also learning more advanced math. I would recommend working
through "Mathematical proofs" by Polimeni/Chartrand/Zhang. Unlike math at an
earlier level, you can't just check your answers against the official ones to
see if you made a mistake - writing proofs is more like writing essays, the
grammar is the easy bit, it's the process of putting the arguments together in
the right detail and the right order that's important and hard to do without
feedback. So you also need to get feedback from mathematicians on your proofs
if possible. The best way to do that if you don't have a buddy who happens to
be a mathematician is to learn to use LaTeX and ask questions on
math.stackexchange.com.

An alternative is to do the proof and abstract algebra courses via
(asymmetric) distance learning at
[https://westcottcourses.com/courses.html](https://westcottcourses.com/courses.html)

I know someone who took these courses and felt like they got good feedback on
their homeworks from the profs running the course.

Feel free to get in touch if you want to chat, I spent a long time trying to
self-learn this stuff before starting my math MS, so happy to help in any way
I can!

~~~
marai2
Since it's seems like you were already motivated and interested in learning
Math on your own, how would you describe what your learnings were before you
enrolled in formal studies? In other words if you could travel back in time to
talk to yourself before you made the decision to enroll in a Master's program,
what would the younger you have asked the older you and what would be the
response? For example I'm thinking a reply might be like "well you're going to
miss out on opportunities xyz by commiting to a Master's program, but because
I know you and know you wouldn't be happy without satisfying your desire to
learn Math in a more formal study the trade of is worth it. And you don't know
this yet but when you start learning about P,Q,R you'll really get a kick out
of it" :-)

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slooonz
There is an EdX version of it (with problem sets) :
[https://www.edx.org/course/fundamentals-of-
statistics](https://www.edx.org/course/fundamentals-of-statistics)

~~~
luhego
I am taking the course right now. It is very good but it is also very hard.
You need to spend between 10-20 hours each week for the lectures and
homeworks.

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clircle
Looks like a very nice list of topics. Glad to see GLMs in there -- I think if
more folks had exposure to GLMs, then we could dispel the myth that statistics
is a bag of tricks. GLMs are a very awesome expansion of regression that
connect many themes in statistics.

~~~
dnquark
Not only are GLMs there, this is far and beyond the clearest explanation of
GLMs I've ever seen. If you've ever wanted to learn the theory behind logistic
regression, the last 3 lectures are a must-watch.

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skwb
I sorta disagree with the order in which things are taught. I don't
particularly like that likelihood is taught before regression, when there's a
really easy (and intuitive!) reason to learn it.

I like the way that I was taught when I took biostats in graduate school. We
fist covered t-test and ANOVA as a way to intuitively compare differences
among groups. From that, we then generalized our approach, and learned that
linear regression is a generalized form, which happens to have a closed form
solution. From linear regression, we then learned about logistic regression
and odds ratios, and about the log-link formulation. But drats! We don't have
a closed form solution to calculating our Betas. But we can estimate a good
set of them using likelihood!

Statistics is often fraught with nuance, and I think the more we can convince
to do more thinking about what we're trying to accomplish with a statistical
analysis and how to prove it should have more emphasis over just "lets just
make an alphabet soup out of our slide decks!". That's not to say you
shouldn't have mathematical rigor, but mathematical rigor without an intuitive
understanding is potentially giving the impression that more complex analysis
== better analysis.

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fizixer
How does this (or its EdX version) compare with ESL?
([https://amzn.com/0387848576](https://amzn.com/0387848576))

~~~
whymauri
I took this class in-person before reading ESL. I'd say there's more overlap
between this class (18.650) and the class textbook All of Statistics
(Wasserman) than ESL.

That said, ESL is a better companion than Wasserman if you want to apply the
statistics to ML and don't plan on studying the graduate-level statistics
courses. ESL + 18.650 + 9.520 (Statistical Learning Theory, Poggio and Sasha
Raklin) covers 95% of the math and statistics I've seen in ML research.

~~~
scared2
Link to 9.520 [https://cbmm.mit.edu/lh-9-520](https://cbmm.mit.edu/lh-9-520)

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bicepjai
I had a negative experience with this course. I have taken lot of statistics
courses in Coursera and edX. I tried this course in edx and found it not well
organized and reasoned out; I don’t remember instances to give examples for,
just my opinion. FYI: I have very high respect for mit, it’s professors and
ocw courses

~~~
cuchoi
Which courses do you recommend?

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snigacookie
What's a good online course that will help provide me a refresher on my maths?

