
Monte Carlo theory, methods and examples (2013) - pmalynin
http://statweb.stanford.edu/~owen/mc/
======
onikolas
Fun trivia: Stan Ulam was on sick-leave and was playing solitaire. He came up
with the Monte Carlo method while trying to calculate the probability of a
successful solitaire game. The method was named after his uncle's favorite
place to gamble.

When he got back from sick-leave, he immediately began applying it to his
work: calculations leading to the fusion bomb.

I find that little background stories like this help students to get engaged
with subject.

~~~
Ntrails
I've been thinking a bit about hands of solitaire recently as I play it on my
phone on the commute to work. It's cool to know that it's an interesting
problem to other people as well.

At the same time, you know, I didn't even think to _use_ Monte Carlo let alone
design the damned thing...

~~~
zeristor
As I understand it he got bored of the game itself, and was thinking about it
at a higher level.

I've been playing it heavily recently though, and it seems to be so well
weighted. Completing games about 10% of the time.

Trying to work out strategies to finish more games.

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abowenmc
Author here: I was pleased to see this while attending MCM 2017 (Monte Carlo
methods). I'm open to reports about mistakes in the notes, or even thoughts on
which further topics (from within MCMC, QMC, SMC, ETC) are most worthy of
coverage in future chapters.

~~~
olsgaard
Thank you for releasing this book. I've just started working with simulations
to solve some toy problems I've been pondering, and couldn't solve analytical,
so the timing of this post is impeccable!

I've read the first chapter and it is very well written and easy to follow,
and the exercises look really good.

I have 2 questions:

1) Are you open reports on minor spelling/grammar mistakes? (There's a missing
full-stop on page 6, and on page 4 you write "in the road" instead of "on the
road". Really minor things.)

2) Do you consider the current chapters "done"?

~~~
abowenmc
I'm happy to get helpful suggestions. With enough eyeballs, every typo is
shallow. I'm easy to find online.

The current chapters are done enough to post. They could change somewhat later
but only to another 'done' state.

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mturmon
Professor Owen has been a leader in Monte Carlo, sampling, and experimental
design. He recently chaired the relevant conference
([http://mcqmc2016.stanford.edu](http://mcqmc2016.stanford.edu)). People who
do experimental design should have some understanding of what QMC, for
example, can offer -- standard error reduction by 1/n as opposed to just
1/sqrt(n).

He was also one of the few statisticians who was seriously interested in
neural nets _long_ before they became fashionable, serving as a reviewer of
learning theory work for NIPS.

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kummap
We made an algorithm for Monte Carlo related random number generation. It
makes slightly worse random numbers fast, but in a way which is good in some
situations. I am still very excited about it!

Please see our paper: An Efficient Method for Generating Discrete Random
Variables with General Distributions for example from
[http://dl.acm.org/citation.cfm?id=2935745&CFID=782777315&CFT...](http://dl.acm.org/citation.cfm?id=2935745&CFID=782777315&CFTOKEN=49114698)

or just email to some of the authors to get the pdf ...

~~~
SeanDav
I am a layman in this field and not read the paper (behind a paywall), but not
sure I see how using a method that requires random numbers to generate random
numbers makes sense?

~~~
Maken
It's not a method to generate random numbers, but to re-distribute random
numbers according to an arbitrary distribution. In general RNG generate purely
uniform distributions.

~~~
kummap
Too bad it's too late to use your words on the paper

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noir_lord
I remember using Monte Carlo to calculate Pi on an XT back in the late 80's
(the explanation was in a kids math book), iirc (it's been a while) it took
all night to get to 4 sig fig, it was an interesting demonstration.

~~~
keithpeter
I've done that one with a basic maths class using rice grains dropped on a
circle drawn on graph paper and then in a spreadsheet with rand() function
generating the coords. Seems to help understanding.

Someone here suggested extending to finding the volume of the Steinmetz solid
which I must get round to.

~~~
noir_lord
Yeah it was in a book with a title like "Fun with Maths" or something
unusually for that type of book it's title was true.

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wodenokoto
Judging from the copyright notices, this hasn't been updated since 2013.

Did the author finish the book and leave this draft online, or was it never
finished?

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phatoni
I remember simulating the Monty Hall problem with random numbers, because it
was hard to imagine.

~~~
styrophone
I did the same thing to help me get my head around it. For anyone else finding
it difficult to imagine the probabilities in Monty Hall intuitively, consider
replacing the 3 doors with 100 doors. After you choose the first door, the
host opens 98 of the remaining 99 doors. That generalization, at least for me,
helps to show that the problem can be reduced to the choice of 1 door vs all
unchosen doors.

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wfunction
Why is there so much written on Monte Carlo theory and (comparatively) hardly
anything on Las Vegas theory?

~~~
jamesrom
Because what happens in Vegas... doesn't fit stochastic calculus.

~~~
musikele
HERO :D

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yebsido1
Fooled by Randomness by Nassim Nicholas Taleb talks about the Monte Carlo
theory extensively.

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Chris2048
It's interesting that MC can work best with non-random numbers :-)

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Asdfbla
I always wonder where the upvotes for those posts that simply plant a link to
highly specialized lectures/books that likely take months to work through
(given a sufficient mathematical background) come from. Especially since the
material at hand isn't relevant unless you work in certain specialized
subfields.

Don't get me wrong, the resources posted here are often good and learning is
great, but I doubt anyone who sees them here actually follows through and
starts studying.

~~~
logicallee
as a hacker news reader it's your responsibility to become an expert in the
basics of things like computer vision, machine learning, wavelet algorithms
(even if it becomes irrelevant) and so forth.

at the end of the day, _someone_ has to build something using all this, and
that someone is us.

I mean what else are you going to do while waiting for another javascript
framework to appear? surely we can't _all_ write new front-end frameworks. It
just doesn't make sense.

 _(note: this comment might be at least partly sarcastic, but I 'm not sure
which part and how much.)_

~~~
_e
I am glad you added a disclaimer stating your post is meant to be sarcastic
because my automated deep learning HN voting bot has not learned sarcasm,
opencv or angular6 yet.

I don't know how or why but it has mastered memory management in spark.

~~~
logicallee
>it has mastered memory management in spark.

that's really only half of learning something, though, isn't it? it needs to
write a blog article about its experience.

~~~
_e
I just hope it is just a matter of time before it learns to do that!

