In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?
Those mathematicians know to be cautious when working with their models. Because they know that no matter how useful and interesting their model, no matter how compelling the evidence they collect, there might be something out there about elliptic curves that they didn’t quite imagine. And if you can’t imagine it, your model can’t capture it, and that means the evidence won’t reflect it.
Mathematics professor Jason Brown spent 10 years working with statistics to solve the magical mystery. Brown’s the findings were presented on Aug. 1 at the Joint Statistical Meeting in a presentation called “Assessing Authorship of Beatles Songs from Musical Content: Bayesian Classification Modeling from Bags-Of-Words Representations.”
When our brains don’t have a good intuition for reasoning with numbers, explicit probabilistic thinking can lead to improved decision-making.
This is an interesting case of how numbers get reported and what they mean. Often the numbers that get reported reflect a desire to grab people’s attentions or simply to tell the story the media outlet wants to tell. If you report 26% or 3% neither one is necessarily lying though the two numbers are referring to two different things. (Here is a link to an earlier post about how an Illinois tax increase was reported)
12% of respondents to a recent survey said they watched fewer NFL games and of those 26% said that the main reason was Colin Kaepernick’s protest during the national anthem. How should that get reported? And what impression gets left in people’s minds based on the wording?
Another way to think about it is this: 12% of the 26% who watched fewer games comes out to about 3% of the total number of people who watched football. Hmm. That leaves a very different impression than 26%.
Here is the original, misleading ESPN article whose headline has since changed I believe.
“National anthem protests were the top reason that NFL fans watched fewer games last season, according to a new survey released by J.D. Power.
“The pollster said it asked more than 9,200 people who attended either one football, basketball or hockey game whether they tuned into fewer games and why. Twenty-six percent of those who watched fewer games last season said that national anthem protests, some of which were led by Colin Kaepernick, were the reason.”
And here is a link to a Huffington Post article discussing the issue with how the numbers are reported: