Monte Carlo theory, methods and examples (2013)
statweb.stanford.edu
statweb.stanford.edu
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.
At the same time, you know, I didn't even think to use Monte Carlo let alone design the damned thing...
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.
How was this done before computers?
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"?
The current chapters are done enough to post. They could change somewhat later but only to another 'done' state.
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.
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...
or just email to some of the authors to get the pdf ...
If you roll two dice you get 7 most often, 6 and 8 slightly less, 5 and 9 even less, etc.
Say you only have 1 die and want to generate the random number distribution that 2 dice give. Easy, just roll twice, and add them.
But what if you only have the output from 2 dice, and want to pretend to roll 1 die. You need a more general way of converting one random distribution to another.
A "random" process is one in which every outcome is independent and unrelated to every other outcome. Drawing "random numbers" doesn't always mean drawing them uniformly at random, where every number in some range, like 0 to 1, is equally likely. You can draw random numbers according to a probability distribution, which is a mathematical expression describing the probability of drawing one number or another.
One very popular distribution is called the "normal distribution" (named for the "normal equations" of physics) or the "Gaussian distribution" (named for Karl Gauss). Normally-distributed random numbers tend to follow a "bell curve" pattern, with values closer to the peak of the bell curve being more probable than numbers further away.
That's a continuous distribution. You can also have a discrete distribution. Some examples of physical processes that can be moseled with discrete probability distributions:
- Coin toss: do I get a Heads?
- A sequence of coin tosses: how many Heads do I get?
- A die roll: do I get a 5?
- A sequence of die rolls: do I get at least one 5? Is the sum of the die rolls at most 30?
- A poker hand: will I get a flush on my next draw?
- Traffic accidents at an intersection: will there be more than 2 accidents in the next 5 days?
These are all "stochastic" questions, meaning that there is uncertainty, in their answers. So we use probability, and therefore randomness, usually non-uniform, to model these scenarios.
Sometimes you need to generate new random numbers from these distributions as part of your analysis, or for generating predictions. In those cases, you need to take a continuous stream of uniform random numbers, like /dev/random, and turn them into a sequence of numbers that follows one of these distributions.
Someone here suggested extending to finding the volume of the Steinmetz solid which I must get round to.
Did the author finish the book and leave this draft online, or was it never finished?
Conversely, there are not so many situations where getting the correct answer within some probabilistic time is particularly useful, because humans live short lives, and need to get things done.
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.
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.)
If you're a JS dev, it's your job to do this every 3 months
I don't know how or why but 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.
Probabilistic programming, Monte Carlo methods, and other complex topics are back in vogue these days. Because programmers who only can do simpler coding tasks will be soon replaced by robots, that are programmed probabilistically. And if you want to have one of those really rare jobs of maintaining said robots, you have to be prepared.
Fear and learn.