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Posts Tagged ‘Probability

What you do know can hurt you…

From the ever-entertaining xkcd, a behavioral analog to the Monty Hall Problem (and the variation considered here a couple of weeks ago)…

As we reconsider the odds, we might recall that it was on this date in 1777 that Swiss mathematician, physicist, and astronomer Johann Heinrich Lambert died in Berlin.  Lambert, who was only 49 when he passed, made a number of contributions to scientific knowledge; but he is probably best remembered for the first proof (in 1768) that pi is irrational (that’s to say, can’t be expressed as the quotient of two integers).

Johann Heinrich Lambert

Written by (Roughly) Daily

September 25, 2010 at 12:01 am

Odds are that your bank balance is…

From Technology Review:

A computer chip that performs calculations using probabilities, instead of binary logic, could accelerate everything from online banking systems to the flash memory in smart phones and other gadgets.

Rewriting some fundamental features of computer chips, Lyric Semiconductor has unveiled its first “probability processor,” a silicon chip that computes with electrical signals that represent chances, not digital 1s and 0s.

“We’ve essentially started from scratch,” says Ben Vigoda, CEO and founder of the Boston-based startup. Vigoda’s PhD thesis underpins the company’s technology. Starting from scratch makes it possible to implement statistical calculations in a simpler, more power efficient way, he says…

Read the full story here.

As we remind ourselves that dealing with our banks was already a crap-shoot, we might recall that it was on this date in 79 CE, the feast day of Vulcan, the Roman god of fire, that Mount Vesuvius began to stir– in preparation for the eruption that, two days later, destroyed the cities of Pompeii and Herculaneum.

Fresco of Bacchus and Agathodaemon with Mount Vesuvius, as seen in Pompeii’s House of the Centenary (source)

Birdbrains…

source

Readers will recall “The Monty Hall Problem”:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

As explained in “Riddle Me This…,” the Bayesian peculiarities of the answer are not always intuitively obvious.  Indeed, as Discover reports,

Over the years, the problem has ensnared countless people, including professional mathematicians.  But not, it seems, pigeons.  Walter Hebranson and Julia Schroder showed that, after some training, the humble pigeon can learn the best tactic for the Monty Hall Problem, switching from their initial choice almost every time.  Amazingly, humans who get similar extensive practice never develop the optimal strategies that the pigeons pick up.

The original paper “Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma” from the Journal of Comparative Psychology is here… but the Discover article is a good– and for the humans among us, chastening– summary.

As we retreat to our fingers for counting, we might recall that it was on this date in 1833 that the first tax-supported public library was founded, in Peterborough, NH.  The original collection consisted of about 100 books and was kept in Smith & Thompson’s General Store, which also housed the Post Office.

Smith & Thompson’s (on left) in 1870

Playing the odds…

A P value is the probability of an observed (or more extreme) result arising only from chance.

It’s science’s dirtiest secret: The “scientific method” of testing hypotheses by statistical analysis stands on a flimsy foundation. Statistical tests are supposed to guide scientists in judging whether an experimental result reflects some real effect or is merely a random fluke, but the standard methods mix mutually inconsistent philosophies and offer no meaningful basis for making such decisions. Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous, and tests of medical dangers or treatments are often contradictory and confusing.

Replicating a result helps establish its validity more securely, but the common tactic of combining numerous studies into one analysis, while sound in principle, is seldom conducted properly in practice.

Experts in the math of probability and statistics are well aware of these problems and have for decades expressed concern about them in major journals. Over the years, hundreds of published papers have warned that science’s love affair with statistics has spawned countless illegitimate findings. In fact, if you believe what you read in the scientific literature, you shouldn’t believe what you read in the scientific literature.

“There is increasing concern,” declared epidemiologist John Ioannidis in a highly cited 2005 paper in PLoS Medicine, “that in modern research, false findings may be the majority or even the vast majority of published research claims.”

Ioannidis claimed to prove that more than half of published findings are false, but his analysis came under fire for statistical shortcomings of its own. “It may be true, but he didn’t prove it,” says biostatistician Steven Goodman of the Johns Hopkins University School of Public Health. On the other hand, says Goodman, the basic message stands. “There are more false claims made in the medical literature than anybody appreciates,” he says. “There’s no question about that.”

Nobody contends that all of science is wrong, or that it hasn’t compiled an impressive array of truths about the natural world. Still, any single scientific study alone is quite likely to be incorrect, thanks largely to the fact that the standard statistical system for drawing conclusions is, in essence, illogical. “A lot of scientists don’t understand statistics,” says Goodman. “And they don’t understand statistics because the statistics don’t make sense”…

What’s one to make of the stream of “eat this,” “avoid that” studies surfacing nearly daily?  It’s an odds-on bet that readers will find out in the complete Science News story, “Odds Are, It’s Wrong.”

As we tell Monty that we’ll take what’s behind Door #2, we might recall that it was on this date in 1905 that Albert Einstein kicked off  “Annus Mirabilis” with the publication of the first of his four epoch-making papers in Annalen der Physik— this one, proposing energy “quanta”– thus kicking off the year in which he reinvented physics and our understanding of reality.

The second of those papers, on Brownian motion, was the very first work of “statistical physics.”

Einstein, dressed for the patent office, 1905

Happy Náw-Rúz! This date in 1844 was the first day of the first year of the Bahai calendar.

Odds are…

1 in 104,600

The odds an accidental death will be due to being bitten or struck by an alligator are 1 in 104,600 (US, 1999 – 2005).

…or, roughly the same odds as that a male will be diagnosed with breast cancer (1 in 100,000), but slightly worse than the odds that a person in Maine will die of a fall from a ladder (1 in 110,000) or that a person in Nebraska will die of alcohol poisoning (also 1 in 110,000)…

To play in the pastures of probability– as pertains to Accidents & Death, Daily Life & Activities, Health & Illness, Relationships & Society– visit Book of Odds.

As we consider our chances, we might recall that it was on this date in 1741 that David Garrick made his debut at London’s Goodman’s Fields Theater in the title role in Shakespeare’s Richard III; Garrick received a standing ovation, and went on become one of the most celebrated English actors of all time (and the owner/manager of The Drury Lane Theatre, a pretty important gig in its own right)…

I do mistake my person all this while;
Upon my life, she finds, although I cannot,
Myself to be a marvellous proper man.
I’ll be at charges for a looking-glass…

Garrick, by Gainsborough

(click to enlarge)

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Written by (Roughly) Daily

October 19, 2009 at 12:01 am