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January 10 - January 16, 2019
Math is a science of not being wrong about things,
Leonard Jimmie Savage, the pioneer of decision theory
Bayesian statistics.*
Here’s an old mathematician’s trick that makes the picture perfectly clear: set some variables to zero.
A mathematician is always asking, “What assumptions are you making? And are they justified?”
survivorship bias.
Mathematics is the study of things that come out a certain way because there is no other way they could possibly be.
calculus is still derived from our common sense—Newton took our physical intuition about objects moving in straight lines, formalized it, and then built on top of that formal structure a universal mathematical description of motion.
basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe
Augustin-Louis Cauchy, who introduced the notion of limit into calculus
linear regression,
the size of the typical discrepancy* is governed by the square root of the number of coins you toss.
If you want to make the error bar half as big, you need to survey four times as many people.
the U.S. economy gained a net 27.3 million jobs. Of those, 26.7 million, or 98%, came from the “nontradable sector”:
Don’t talk about percentages of numbers when the numbers might be negative.
“Seventy-five percent” sounds like it means “almost all,” but when you’re dealing with numbers that could be either positive or negative, like profits, it might mean something very different.
improbable things happen
a lot.
“it is probable that improbable things will happen. Granted this, one might argue that what is improbable is probable.”
When you’re trying to draw reliable inferences from
improbable events, wiggle room is the enemy.
Everything you do either gives you cancer or prevents it.
“statistically noticeable” or “statistically detectable”
counsels us about the existence of an effect but is silent about its size or importance. But it’s too
Bertrand Russell,
a premier psychological
“A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.”
statistically significant finding gives you a clue, suggesting a promising place to focus your research energy.
The significance test is the detective, not the judge.
“The finding is quite interesting, and suggests that more research in this direction is needed”?
If a result is novel and important, other scientists in other laboratories ought to test and retest the phenomenon and its variants,
Registered Replication Reports.
the Many Labs project,
Facebook generally knows its users’ real names and locations, so it can use public records to generate a list of Facebook profiles belonging to people who have already been convicted of terroristic crimes or support of terrorist groups.
take a deep breath and keep your eye on the box, you can’t go wrong.
two questions you can ask.
What’s the chance that a person gets put on Facebook’s list, given that they’re not a terrorist?
What’s the chance that a person’s not a terrorist, given that they’re on Facebook’s list?
the answer to the first question is about 1 in 2,000, while the answer to the second is 99.99%. And it’s the answer to the second question that you really want.
critical prior information, which is that most people aren’t terrorists!
ignore that fact at your peril.
Upton Sinclair, the best-selling author of The Jungle, released in 1930 a whole book, Mental Radio,
Human beings are always inferring, always using observations to refine our judgments about the various competing theories that
jostle around inside our mental representation of the world.
We are very confident, almost unshakably confident, about s...
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The sum of the numbers in the bottom row is about 0.0325, so to make those numbers sum to 1 without changing their proportions to one another, we can just divide each number by 0.0325.
posterior probabilities.
Bayesian inference,
the passage from prior to posterior rests
an old formula in probabi...
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