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# Posts

### May 15, 2013

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On Monday, Harald Helfgott of the École Normale Supériure in Paris posted a proof of one of the oldest open problems in number theory to the preprint repository arxiv. The ternary Goldbach conjecture, like so many questions in number theory, is easy to state but hard to prove. Every odd number greater than 5 can [...]
Editor's Pick
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Local middle school students took their learning beyond the bounds of their classroom on a visit to NIMBioS last week. Fifty students from Gresham Middle School‘s Beta Club, along with teachers and parent chaperones, visited the institute and participated in … Continue reading →
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Several months ago, Mike Betancourt and I wrote a discussion for the article, Can quantum probability provide a new direction for cognitive modeling?, by Emmanuel Pothos and Jerome Busemeyer, in Behavioral and Brain Sciences. We didn’t say much, but it was a milestone for me because, with this article, BBS became the 100th journal I’d [...]The post Does quantum uncertainty have a place in everyday applied statistics? appeared first on Statistical Modeling, Causal Inference, and […]
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The single most lucrative single day prize for any contestant in Jeopardy’s history was indirectly based on data mining and simulation. Roger Craig, who has a PhD in computer science, used data-mining algorithms to train himself on a database of training questions. His source data was The Jeopardy Archive, which has every question and answer […]
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David Kessler, Peter Hoff, and David Dunson write: Marginally specified priors for nonparametric Bayesian estimation Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions about all aspects of such a parameter, but may [...]The post Reputations changeable, situations tolerable appeared first on Statistical […]
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An article in yesterday’s Science Times explained that limiting the salt in your diet doesn’t actually improve health, and could in fact be bad for you. That’s a huge turn-around for a public health rule that has run very deep. How can this kind of thing happen? Well, first of all epidemiologists use crazy models to […]
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Udacity today announced that it is partnering with AT&T and Georgia Tech to offer an online Master's degree in computer science. This is an important and exciting development, but it's not without concerns.
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For over twenty-three hundred years, at least since the publication of Euclid’s Elements, the conjecture and proof of new theorems has been the sine qua non of mathematics. The method of proof is at “the heart of mathematics, the royal road to creating analytical tools and catalyzing growth” (Rav, 1999; pg 6). Proofs are not […]

Rav, Y. (1999). Why Do We Prove Theorems?, Philosophia Mathematica, 7 (1) 5-41. DOI:

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How does the scientific method really work? It's probably more complicated than you think. In this article, we apply it rigorously to "prove" $\pi=3$. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!

### May 14, 2013

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The current puzzle is… puzzling: Given the set {1,…,N} with N<61, one iterates the following procedure: take (x,y) within the set and replace the pair with the smallest divider of x+y (bar 1). What are the values of N such that the final value in the set is 61? I find it puzzling because the […]
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Report on recent work of Yi Tang Zhang, taking us a step closer to a proof of the Twin Primes Conjecture.
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This is yet another post about the intersection of operations research and my frugality. I occasionally stop by Jimmy John’s to pick up some day-old bread for \$0.50 per loaf. I purchase a loaf for each one of my kids and then let them do whatever they want with it for dinner. They love it. […]
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Cash register at Catalina Coffee: It’s a wooden frame for an iPad. The cashier flips the top over to let customers paying with a credit card to sign. Register frame created by Tinkering Monkey.
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I’m in London, where according to the Guardian we’re supposed to get half a month’s rain today. Sounds scary, doesn’t it?  That makes it sound like it’s going to rain fifteen times what it does on a typical rainy day; of course it means that we’re supposed to get fifteen times what London gets on a […]
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(Cross-posted at NewAPPS)A few days ago Eric had a post about an insightful text that has been making the rounds on the internet, which narrates the story of a mathematical ‘proof’ that is for now sitting somewhere in a limbo between the world of proofs and the world of non-proofs. The ‘proof’ in question purports to establish the famous ABC conjecture, one of the (thus far) main open questions in number theory. (Luckily, a while back Dennis posted an extremely helpful and precise […]
Editor's Pick
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I think it’s part of my duty as a blogger to intersperse, along with the steady flow of jokes, rants, and literary criticism, some material that will actually be useful to you. So here goes. Jarno Vanhatalo, Jaakko Riihimäki, Jouni Hartikainen, Pasi Jylänki, Ville Tolvanen, and Aki Vehtari write: The GPstuff toolbox is a versatile [...]The post GPstuff: Bayesian Modeling with Gaussian Processes appeared first on Statistical Modeling, Causal Inference, and Social Science.
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Suppose you want to know when your great-grandmother was born. You can’t find the year recorded anywhere. But you did discover an undated letter from her father that mentions her birth and one curious detail:  the 13-year and 17-year cicadas…Read more ›
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Every odd integer greater than 5 is the sum of three primes, says Harald Helfgott. And there are infinitely many prime gaps less than seventy million, says Yitang Zhang. (As Dan Goldston quips in this blog post from Nature, this is within a factor of thirty-five million of the target.
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A week ago I wrote about Perrin numbers, numbers Pn defined by a recurrence relation similar to Fibonacci numbers. If n is prime, Pn mod n = 0, and the converse is nearly always true. That is, if  Pn mod…Read more ›
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I’ve discussed the broken business model that is the credit rating agency system in this country on a few occasions. It directly contributed to the opacity and fraud in the MBS market and to the ensuing financial crisis, for example. And in this post and then this one, I suggest that someone should start an […]

### May 13, 2013

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Guy Freeman writes: I thought you’d all like to know that Stan was used and referenced in a peer-reviewed Rapid Communications paper on influenza. Thank you for this excellent modelling language and sampler, which made it possible to carry out this work quickly! I haven’t actually read the paper, but I’m happy to see Stan [...]The post Stan! appeared first on Statistical Modeling, Causal Inference, and Social Science.
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Here is the cover of the Japanese translation of our Introducing Monte Carlo methods with R book.  A few year after the French translation. It actually appeared last year in August but I was not informed of this till a few weeks ago. The publisher is Maruzen, with an associated webpage if you want to […]
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From David Mumford’s May 2013 interview in SIAM News: The applied mathematician has the difficult job of looking at a problem in context with no explicit mathematics and trying to see what kinds of mathematical ideas are under the surface…Read more ›
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Matthew Hankins and others on Twitter are making fun of scientists who twist themselves up lexically in order to report results that fail the significance test, using phrases like “approached but did not quite achieve significance” and “only just insignificant” and “tantalisingly close to significance.” But I think this fun-making is somewhat misplaced!  We should […]
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I liked this MathOverflow question, which asks:  are there two non-isogenous elliptic curves over Q, each one of which has a rational cyclic 13-isogeny, and such that the kernels of the two isogenies are isomorphic as Galois modules? This is precisely to look for rational points on the modular surface S parametrizing pairs (E,E’,C,C’,φ), where […]
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Premise is mapping the produce manifold. Airbnb is figuring out where you want to go in places you’ve never been. Joe Blitzstein figured out when The Simpsons jumped the shark. Jim Holt reviewed Mandelbrot’s memoir for the New York Review of Books. From Smithsonian magazine, Life in the city is essentially one giant math problem. […]
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Time flies! It seems to me that we have only just finished perusing the excellent Giant’s Shoulders #58 at Asylum Science and now there are only three days left to submit those history of science, history of technology and history … Continue reading →
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Ed Yong (@edyong209) is a well-known and highly respected science writer. At regular intervals he posts lists of links on his website, Not Exactly Rocket Science, of science stories that he has found interesting, a sort of one-man blog carnival. … Continue reading →
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David Jinkins writes: The objective of this paper is to measure the relative importance of conspicous consumption to Americans and Chinese. To this end, I estimate the parameters of a utility function borrowed from recent theoretical work using American and Chinese data. The main parameter of interest governs the amount that individuals care about peer [...]The post A Structural Comparison of Conspicuous Consumption in China and the United States appeared first on Statistical Modeling, Causal […]
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Dogfooding refers companies using their own software. According to Wikipedia, In 1988, Microsoft manager Paul Maritz sent Brian Valentine, test manager for Microsoft LAN Manager, an email titled “Eating our own Dogfood”, challenging him to increase internal usage of the…Read more ›