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20 posts tagged with statistics *and* probability.

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## How likely is it that birth control could let you down?

The NYT calculates the probability of pregnancy using 15 common birth control methods, for up to 10 years of both "typical" and "perfect" use. Protip: the graphs do slidey comparison things on mouseover!

## The observer at the end of time: Of immortal watchers and imaginary data

In a Multiverse, What Are the Odds? "Testing the multiverse hypothesis requires measuring whether our universe is statistically typical among the infinite variety of universes. But infinity does a number on statistics." (previously) [more inside]

## Calculus without limits

Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]

## John Baez on the maths of connecting everyone (and everything) on earth

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of

*understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)## Math with Bad Drawings

## Card tricks...

...to leave a smile on your face, by Helder Guimarães: Individual vs Crowd | Chaos | Freedom | Trick [more inside]

## Intelligence Tests

Is Psychometric

*g*a Myth? - "As an online discussion about IQ or general intelligence grows longer, the probability of someone linking to statistician Cosma Shalizi's essay*g, a Statistical Myth*approaches 1. Usually the link is accompanied by an assertion to the effect that Shalizi offers a definitive refutation of the concept of general mental ability, or psychometric*g*." [more inside]## direct realism

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

## Tails of the unexpected

Tails of the Unexpected: "Normality has been an accepted wisdom in economics and finance for a century or more. Yet in real-world systems, nothing could be less normal than normality. Tails should not be unexpected, for they are the rule." An eminently human-readable explanation of why normal models fail to describe the uncertainties of our abnormal world. [more inside]

## Monte Carlo

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).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

## Two PDFs about PDFs

An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)

## You must be yolking...

*"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."

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."

## Simulated Language

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]

## Never tell me the odds.

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.

## from complexity, universality

## Black Swans and The Fourth Quadrant

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.

## Probability senses tingling batman!

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.

## Incredible -- but true coincidences

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.

## The Complexity of a Controversial Concept

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)## Dyson On The Paranormal or Expect A Miracle

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

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