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Discussion > Want to learn about probability?

Often confused at the mathematical and statistical basis of claims about climate?
Wish you understood more about modelling uncertainty?

I can heartily recommend the free edX course MITx: 6.041x Introduction to Probability - The Science of Uncertainty which has just kicked off again this week. It is not a maths primer, it tries to make it approachable for those with limited mathematics, but obviously you will need a little to follow the coursework and pass the exams if you wish to do so.

For someone like me who covered the material quite a number of years ago, I find these free courses to be excellent top-ups (and a way to study things outside my professional interests, such as the arts), and they would be an good way to begin educating yourself for those who do not have the time or inclination to do a residential course.

I'm sure our learned friends from the other side would welcome everyone raising their game.

Let me know if anyone takes it up.

Jan 29, 2016 at 10:57 AM | Unregistered CommenterTheBigYinJames

Hmmm... ~2½ hours a week for 16 weeks. Not a trivial commitment.

Jan 29, 2016 at 12:20 PM | Registered CommenterMartin A

It's probably 10 hours or more, if you include reading, problems, exams etc. I think the 2.5 hours is just the lecture videos. Since it's free, I don't suppose there's any harm in giving it a go, and dropping out if time becomes a problem. From experience, they also leave the course materials on the site for some time after the end of the course, so even though you will have missed the submission deadlines, you will still be able to finish the materials at a slower pace.

You can also spin off tutorial discussion groups, so if there were a suitable number of Hillers on there we could hive off our own study group to talk over the materials.

(I've enrolled on it again in case anyone wants to join me - if I get the nod on here, I'll post something on the course forum page so people from here can get in touch)

Jan 29, 2016 at 12:59 PM | Unregistered CommenterTheBigYinJames

The Syllabus:

Unit 0: Overview (released Fri. Jan 29)

Unit 1: Probability models and axioms (released Fri. Jan 29; Sections 1.1-1.2)
L1: Probability models and axioms
Problem Set 1 due on Feb 10

Unit 2: Conditioning and independence (released Fri. Feb 5; Sections 1.3-1.5)
L2: Conditioning and Bayes' rule
L3: Independence
Problem Set 2 due on Feb 17

Unit 3: Counting (released Fri. Feb 12; Section 1.6)
L4: Counting
Problem Set 3 due on Feb 24

Unit 4: Discrete random variables (released Fri. Feb 19; Sections 2.1-2.7)
L5: Probability mass functions and expectations
L6: Variance; Conditioning on an event; Multiple r.v.'s
L7: Conditioning on a random variable; Independence of r.v.'s
Problem Set 4 due on Mar 2

Exam 1: Covers material from L1 to L7 (released Wed. Mar 2; due on Mar 9)

Unit 5: Continuous random variables (released Fri. Feb 26; Sections 3.1-3.5)
L8: Probability density functions
L9: Conditioning on an event; Multiple r.v.'s
L10: Conditioning on a random variable; Independence; Bayes' rule
Problem Set 5 due on Mar 16

Unit 6: Further topics on random variables (released Fri. Mar 11; Sections 4.1-4.3, 4.5)
L11: Derived distributions
L12: Sums of r.v.'s; Covariance and correlation
L13: Conditional expectation and variance revisited; Sum of a random number of r.v.'s
Problem Set 6 due on Mar 30

Unit 7: Bayesian inference (released Fri. Mar 25 Sections 3.6, 8.1-8.4)
L14: Introduction to Bayesian inference
L15: Linear models with normal noise
L16: Least mean squares (LMS) estimation
L17: Linear least mean squares (LLMS) estimation
Problem Set 7a due on Apr 6
Problem Set 7b due on Apr 13

Exam 2: Covers material from L8 to L17 (released Wed. Apr 13; due on Apr 20)

Unit 8: Limit theorems and classical statistics (released Fri. Apr 8; Sections 5.1-5.4, pp. 466-475)
L18: Inequalities, convergence, and the Weak Law of Large Numbers
L19: The Central Limit Theorem (CLT)
L20: An introduction to classical statistics
Problem Set 8 due on Apr 27

Unit 9: Bernoulli and Poisson processes (released Fri. Apr 22; Sections 6.1-6-2)
L21: The Bernoulli process
L22: The Poisson process
L23: More on the Poisson process
Problem Set 9 due on May 11

Unit 10: Markov chains (released Fri. Apr 29; Sections 7.1-7-4)
L24: Finite-state Markov chains
L25: Steady-state behavior of Markov chains
L26: Absorption probabilities and expected time to absorption
Problem Set 10 due on May 18

Final Exam (released Wed. May 18; due on May 24)

*Note: Problem set and exam due dates are at the end of the specified date, at 23:59 UTC.

Jan 29, 2016 at 1:05 PM | Unregistered CommenterTheBigYinJames

Length: 16 weeks
Effort: 12 hours/week

I mistyped. I meant to say ~2½ hours a day for 16 weeks. Not a trivial commitment.

I'd like to see past exam papers.

Jan 29, 2016 at 3:04 PM | Registered CommenterMartin A

Breaks the honor code for me to show you it, I'm afraid.

I'm halfway through the first module, and enjoying it thoroughly.

Jan 29, 2016 at 3:32 PM | Unregistered CommenterTheBigYinJames

It says "The contents of this course are essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability)". (Nearest I ever got to MIT was driving through Cambridge, MA.)

MIT gives examples of test papers

for example:

Jan 29, 2016 at 7:18 PM | Unregistered CommenterMartin A

Given that PLoS ONE has just published a paper which claims to derive a formula for a cumulative probability density function which is not monotonic upwards, I think that problems with understanding elementary probability theory are far more widespread than anyone has imagined.

Jan 31, 2016 at 10:27 AM | Registered CommenterJonathan Jones

I've signed up, but I have no idea whether in the time I'll have available I'll be able to keep up. I'll give it a couple of weeks to see how it goes and then either bail out or continue.

Jan 31, 2016 at 11:56 AM | Registered CommenterMartin A


Jan 31, 2016 at 5:15 PM | Unregistered CommenterMartin A

Thanks for the heads up TBYJ, not heard of edX before, generally looks good, could be a new hobby.

As a full time pro gambler I like to think I have a good handle on practical probabilities but it's many years since my maths degree so very rusty on theory. So I signed up today out of curiosity and started on Unit 1.

Really like the style of clear bite size videos with follow up questions. Easy to skip through the trivial stuff too to keep it interesting, so a bit like doing puzzles. The tests fit neatly in between races so it suits my lifestyle. Bit of a trip down memory lane as well, it's even had me integrating to find areas under a curve, can't remember the last time I did that! So, so far so good. Whether it will be any practical use, time will tell.

Also followed your link JJ but wish I hadn't, it so makes my blood boil. We're supposed to be in a time of austerity yet we can fund an army of "academics" to study this absolute BS. Seriously, who would care if this stuff never existed? No-one that's who. That it's being produced by a bunch of total nincompoops who can't do basic stats and survived the much vaunted peer review process (plus got some positive mentions in the comments) only makes it much worse. Somewhere there's a burger bar missing a flipper. Nurse!

Feb 1, 2016 at 6:26 PM | Registered CommenterSimonW

Bit of a trip down memory lane as well, it's even had me integrating to find areas under a curve, can't remember the last time I did that!

Yes, integrating x^2, at least they chose an easy one! That and the binomial expansions brought it all back.

Feb 2, 2016 at 9:12 AM | Unregistered CommenterTheBigYinJames

I like it. Just what I was hoping for interesting intellectual change from Sudoku!

So I skimmed through the whole Unit 1 course stuff in about 2 hours (I like the ability to change video speed).

Had some time later so thought I may as well have a go at the Unit 1 "Exam". Hmm, well it certainly wasn't all easy (at least to me) and had to sleep on one of them (the car parking formula one). Not allowed to discuss until after the deadline I think so won't post it here.

Just done it now and well chuffed to find I've got 'em all right. Life in the old dog yet. This is just the intro so I presume it will get harder and make my brain hurt.

Looks like I have to wait 9 days for the next installment though.

I've been thinking of doing an OU course for a while but mislaid my round tuit. This is free and easily accessible so a great alternative (not bothered about certificates).

Any recommendations for another worthwhile edX course to keep me going?

Feb 2, 2016 at 10:02 AM | Registered CommenterSimonW

If you go to your dashboard and click the Find New Courses button on the top right, then it gives a list on the right hand side of upcoming and due-to-begin courses, categorised by subject.

Feb 2, 2016 at 10:44 AM | Unregistered CommenterTheBigYinJames

If you are good at holding in vomit, you could try

Feb 2, 2016 at 10:48 AM | Unregistered CommenterTheBigYinJames


There is also (archived) Modeling Climate Change with David Archer as presenter. Archer has papers concluding that human released CO₂ remains in the atmosphere for tens of thousands of years.

I'm struggling with getting the parking lot solution into a closed form expression for general n...

Feb 2, 2016 at 12:17 PM | Registered CommenterMartin A

My vomit holding capabilities aren't what they used to be, particularly related to climate change activities, so I'll pass on those two thanks. Also I don't want to encourage them. When my appointment as benevolent dictator arrives (in the post apparently) I'd close down the whole flipping industry of wasters.

Some great courses available on edX, I can see this keeping me entertained for years. From the toughness of the Probability one I guess you can't just dive in and pick up Astrophysics in an evening though. I want something more "recreational" to complement the current one so I've gone for this one:

Body Matters

So Body and Mind sorted!

Looking forward to the next Probability module.

Feb 2, 2016 at 10:56 PM | Registered CommenterSimonW

Another edX course to note.!

Making Sense of Climate Science Denial

Climate change is real, so why the controversy and debate? Learn to make sense of the science and to respond to climate change denial.

Feb 17, 2016 at 9:33 PM | Registered CommenterMartin A

Notice the dependence on ignorance and confusion that the climate obsessed rely on:
"climate change is real".
As the kids say, "way to go Capt. Obvious".
No one denies the climate changes, except for the climate obsessed who apparently believe the climate only started changing since Industrialization.

Feb 17, 2016 at 11:15 PM | Unregistered Commenterhunter

Ye Gods, is that for real. Just as I was getting to like edX they let that lot of deluded fools in. That's very disappointing. Probably go the same way as the TED talks now then.

And what a packed Rogues Gallery, presumably all on the public purse to spout their drivel. We really need someone with the gumption to stand up and cut off their funding.

Well after my initial enthusiasm I've been distracted and only got around to Unit 2 last night. A lot to get through and ended up missing the deadline for the test so good job I'm doing it for amusement only. Got a different answer for one part too and not sure why so I've raised a query. (Qn 3d: Oscar in the forest, if anyone else is still doing it).

Really liking the course and questions still though.

Feb 18, 2016 at 2:52 PM | Registered CommenterSimonW

SimonW - Somebody evidently had a problem with that question at their first attempt by overlooking that the probability of his finding his dog in B on day 1 is zero if he only looked in A.

Feb 18, 2016 at 6:00 PM | Unregistered CommenterMartin A

BYIJ - Thank you for your original posting pointing out the availability of the course.

On Wednesday (deadline for the 1st exam), I decided to stop keeping up with MITx 6.041x.

It had been taking more time than I could afford to spend and, even though I was getting problem marks in the 90% - 100% range, it was more often by plugging in the right formula than from having really understood things in depth. I wanted to go back and re-do the first four units, working from a textbook, to get a complete understanding of it all. This would have needed even more time.

Although the material remains available for self study after the deadlines have passed, it's unfortunate (from my perspective) that the automatic marking system becomes unavailable for a unit once a deadline has passed. This makes it more difficult to test oneself on the material if working at one's own pace.

I hope that I'll find the motivation to work through the rest of the course, but continuing at my own pace, while going back over the basic stuff to finish up with a complete grasp of the fundamentals covered in the first four units.

Thanks again from pointing out the availability of the course.

Mar 11, 2016 at 1:26 PM | Registered CommenterMartin A

Alas, I have lapsed as well, due to other commitments. I have completed a few other self-paced courses (you can filter the list on the right) which were easier to fit in.

Mar 11, 2016 at 2:08 PM | Unregistered CommenterTheBigYinJames