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statistics + (11)
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kliuless (3)
JoeXIII007 (2)
finite (2)

The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF). -N. Metropolis

Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).
posted by JoeXIII007 on Dec 17, 2011 - 13 comments

An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)
posted by JoeXIII007 on Dec 15, 2011 - 17 comments

"So, if the probability of finding an egg with two yolks is 1/1000 - then to find the likelihood of discovering four in a row you simply multiply the probabilities together four times. One thousand to the power of four brings us to the grand total of one trillion...

If true that would mean the event that occurred in Jen's kitchen was a trillion-to-one event. But is it true? No is the short answer."
posted by Petrot on Dec 10, 2011 - 38 comments

Counting is one of the first and simplest concepts most people are taught. But when you get beyond simple 123s, counting can become an advanced subject all its own. Essentially the science of counting, combinatorics is a key component of everything from abstract algebra to probability (PDF). [more inside]
posted by kmz on Sep 21, 2011 - 38 comments

Are We Alone In the Universe? New Analysis Says Maybe. In a new paper published on arXiv.org, astrophysicist David Spiegel at Princeton University and physicist Edwin Turner at the University of Tokyo argue...using a statistical method called Bayesian reasoning...that the life here on Earth could be common, or it could be extremely rare — there's no reason to prefer one conclusion over the other. [more inside]
posted by Potomac Avenue on Jul 28, 2011 - 111 comments

In the recent MIT symposium "Brains, Minds and Machines," Chomsky criticized the use of purely statistical methods to understand linguistic behavior. Google's Director of Research, Peter Norvig responds. (via) [more inside]
posted by nangar on May 28, 2011 - 95 comments

Measure-theoretic probability: Why it should be learnt and how to get started. The clickable chart of distribution relationships. Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician John D. Cook's blog and his probability fact-of-the-day Twitter feed ProbFact. John also has daily tip and fact Twitter feeds for Windows keyboard shortcuts, regular expressions, TeX and LaTeX, algebra and number theory, topology and geometry, real and complex analysis, and beginning tomorrow, computer science and statistics.
posted by grouse on Dec 5, 2010 - 17 comments

A brief tour of the mysteriously universal laws of mathematics and nature. [more inside]
posted by kliuless on Oct 24, 2010 - 33 comments

Nontransitive dice are sets of dice (A, B, C, etc.) with counterintuitive properties: die A beats die B and die B beats die C, but die C beats die A. [more inside]
posted by Upton O'Good on Jan 24, 2010 - 54 comments

Durango Bill's Home Page. With topics that include: 3D end-to-end tour of the Grand Canyon, the origin and formation of the Colorado River, and examples of river systems that cut through mountain ranges instead of taking easier routes around them in Ancestral Rivers of the World. [more inside]
posted by netbros on Jul 22, 2009 - 5 comments

The day after a senator from Illinois, is elected president, the Pick 3 lottery in Illinois comes up 666. It's happened before, notably in Pennsylvania (12 times, including one time as part of a scam and once earlier this year, in Maryland. Some are jokingly (I hope) calling him the antichrist as a result. Others, namely numbers geeks like me, are spending their lunch hours looking up the history of lotteries drawing triple numbers and sharing it with MetaFilter.
posted by sjuhawk31 on Nov 6, 2008 - 70 comments

THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS by Nassim Nicholas Taleb. "In the following Edge original essay, Taleb continues his examination of Black Swans, the highly improbable and unpredictable events that have massive impact. He claims that those who are putting society at risk are "no true statisticians", merely people using statistics either without understanding them, or in a self-serving manner.
posted by vronsky on Sep 16, 2008 - 41 comments

A discovery leads to questions about whether the odds of people sharing genetic profiles are sometimes higher than portrayed. Calling the finding meaningless, the FBI has sought to block such inquiry.
posted by finite on Jul 20, 2008 - 30 comments

On May 13, security advisories published by Debian and Ubuntu revealed that, for over a year, their OpenSSL libraries have had a major flaw in their CSPRNG, which is used by key generation functions in many widely-used applications, which caused the "random" numbers produced to be extremely predictable. [lolcat summary] [more inside]
posted by finite on May 16, 2008 - 81 comments

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology." The NY Times' John Tierney reports on new research into cognitive dissonance as examined through the famous Monty Hall Problem. [A previous MetaFilter thread about the Monty Hall Problem: Let's Make A Deal!]
posted by amyms on Apr 8, 2008 - 119 comments

Poker hand simulator. Get a feel for the odds before you bet the farm.
posted by Brian B. on Feb 16, 2008 - 30 comments

If you need a foolproof way to decide whether to kill someone or are simply curious as to whether probability is still operating as a factor in your existence (and find yourself out of change but near a computer with an internet connection), you can just use flip a coin.
posted by cog_nate on Dec 13, 2007 - 33 comments

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)
posted by parudox on Dec 1, 2007 - 11 comments

How many group photographs do you have to take to get one in which nobody is blinking? Nic Svenson and Dr Piers Barnes work it out.
posted by d-no on May 22, 2006 - 9 comments

We've talked about quantum computation a few times before, but how much do we really know? Metafilter, instruct thyself. Don't forget to learn some advanced probability and computational complexity (Scott Aaronson has more). Whoa, that's a lot o' learning, so let's so check out the much easier, and much cooler "sleeping puppy" experiment. I can only dream that will help break quantum mechanics' association with animal abuse. Then, there's the Free Will Theorem that just came out (some discussion on it) and another paper with a new look at an old problem. The latter describes another way of solving ye olde, super importanto Einstein-Podolsky-Rosen paradox using the relational interpretation of quantum mechanics (lots of discussion running around). Whew. We don't need the crackpot ramblings of What the #$*! Do We Know? when we've got real physics to keep us up at night. So, who wants to become a physicist? (t'Hooft has some thoughts for those who want to go theoretical.)
posted by jmhodges on Apr 25, 2006 - 26 comments

Experts can suck at predicting the future. Their intuitive sense of probability is no more developed than lay-people's. A classic experiment is to present two indistinguishable choices are presented, but with unequal probability of reward. Humans look for complex patterns, which don't exist, and preform quite poorly. Rats quickly recognize the choice with higher probability, and preform optimally.
posted by jeffburdges on Dec 11, 2005 - 34 comments

Everybody's an expert, but does expertise promote better predictions?
posted by semmi on Dec 1, 2005 - 14 comments

Know less than nothing!? What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less... "In this week's issue of Nature, however, Michal Horodecki and colleagues present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts." [via slashdot :]
posted by kliuless on Aug 8, 2005 - 26 comments

Incredible -- but true coincidences are fascinating, and pleasing, to the psyche. I tend to agree with John Littlewood (a University of Cambridge mathematician) that "...in the course of any normal person's life, miracles happen at a rate of roughly one per month." In other words, statistically speaking, unusual coincidences are to be expected in a world teeming with billions of humans. Still, I find such coincidences stangely inspiring. More can be found here.
posted by ember on Jul 7, 2005 - 97 comments

The Logic of Diversity "A new book, The Wisdom of Crowds [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)
posted by kliuless on Jun 20, 2005 - 6 comments

An Intuitive Explanation of Bayesian Reasoning. [Page contains Java]
posted by Gyan on Jul 21, 2004 - 9 comments

"We plan to put Beauty to sleep by chemical means, and then we’ll flip a fair coin. If the coin lands Heads, we will awaken Beauty on Monday afternoon and interview her. If it lands Tails, we will awaken her Monday afternoon, interview her, put her back to sleep, and then awaken her again on Tuesday afternoon and interview her again. The (each?) interview is to consist of the one question : what is your credence now for the proposition that our coin landed Heads? When awakened (and during the interview) Beauty will not be able to tell which day it is, nor will she remember whether she has been awakened before. She knows about the above details of our experiment. What credence should she state in answer to our question?"

In light of the recent thread on the Monty Hall problem, here's a probability puzzle that's even more mind-bending: the Sleeping Beauty problem. Some people say the answer is 1/2. Some people say the answer is 1/3. Some people say there is no answer. Papers have been written which can't resolve this one.
posted by salmacis on Jul 21, 2004 - 40 comments

A playable version of the Monty Hall problem. More information.
posted by monju_bosatsu on Jul 20, 2004 - 63 comments

Expect a miracle? Freeman Dyson on Littlewood's Law of Miracles: "...the total number of events that happen to us is about thirty thousand per day, or about a million per month. ...The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month." From his review of book debunking the paranormal (whose views he isn't entirely willing to accept). Via Marginal Revolution
posted by Jos Bleau on Jul 14, 2004 - 33 comments

The History of Probability - Excel Version Huge detailed timeline. [via Roll the Bones]
posted by srboisvert on Jul 11, 2004 - 2 comments

What Are The Odds Against Hamlet? This wonderful piece, representative of British academia at its best, most tongue-in-cheek, inclusive and playful, still presents a problem which wasn't (probably can't be) solved. What are the odds that it could be taken seriously? Mathematicians and literary theorists enter at their peril. The rest of us can feel free!
posted by MiguelCardoso on Feb 10, 2004 - 5 comments