rvern | 7 years ago | on: People Aren’t Dumb, the World Is Hard
rvern's comments
rvern | 7 years ago | on: Thomas Bayes and the crisis in science
Let A be the event that the car is behind door 1, B that the car is behind door 2, and C that the car is behind door 3. Let E be the event that the host opens door 3. We assume that the car is initially equally likely to be behind each door and that the host opens a door with a goat at random, never opening the door we picked.
Since A, B, and C are exhaustive and mutually exhaustive propositions, we can calculate the marginal probability of E by using the law of total probability:
P(E) = P(E ∧ A) + P(E ∧ B) + P(E ∧ C).
Bayesians like to define joint probability from conditional probability instead of the reverse; that is, define P(A ∧ B) as P(A | B) P(B) instead of P(A | B) as P(A ∧ B) / P(B).
So P(E ∧ A) = P(E | A) P(A). P(E | A) is 1/2 because we picked door 1, the car is behind door 1, and the host chooses at random a door that has a goat, of which there are two: 2 and 3. P(A) is 1/3. Therefore P(E ∧ A) is 1/2 × 1/3 = 1/6.
Similarly, P(E ∧ B) = P(E | B) P(B). P(E | B) is 1 because we picked door 1 so the host will not open door 1 and we assume the car is behind door 2 so the host will not open door 2, leaving only door 3 to be opened. P(B) is 1/3. Therefore P(E ∧ B) is 1 × 1/3 = 1/3.
P(E ∧ C) = P(E | C) P(C). P(E | C) is 0 because the host will never open the door the car is behind. P(C) is 1/3. Therefore P(E ∧ C) is 0 × 1/3 = 0.
So P(E) = 1/6 + 1/3 + 0 = 1/2. We know that the host opened door 3 (this is E), so the car cannot be behind door 3. How likely is it to be behind door 1? By Bayes’ theorem,
P(A | E) = P(E | A) P(A) / P(E).
We said earlier that P(E | A) is 1/2, P(A) is 1/3, and P(E) is 1/2. So P(A | E) = (1/2 × 1/3) / (1/2) = 1/3.
Given E, the car must be behind door 1 or door 2 since the host opened door 3. Therefore the sum of P(A | E) and P(B | E) must be 1. P(A | E) is 1/3, so P(B | E) is 2/3. The car is more likely to be behind door 2 than door 1. We initially picked door 1, so, if we want the car, we should switch.
rvern | 7 years ago | on: Thomas Bayes and the crisis in science
rvern | 7 years ago | on: Forced Labor in Malaysia's Electronics Industry
rvern | 7 years ago | on: Former Equifax Manager Charged with Insider Trading
rvern | 7 years ago | on: Former Equifax Manager Charged with Insider Trading
rvern | 7 years ago | on: Former Equifax Manager Charged with Insider Trading
rvern | 7 years ago | on: Former Equifax Manager Charged with Insider Trading
rvern | 7 years ago | on: GitLab Ultimate and Gold now free for education and open source
rvern | 7 years ago | on: A new study of the rules of spacing in English sentences
rvern | 8 years ago | on: Best-selling introductory psychology books give misleading view of intelligence
That's where you make a mistake. Whatever the reason, the Wikipedia articles on the g factor, the intelligence quotient and Cattell–Horn–Carroll theory represent better what is widely accepted in the field than any other source. This somehow also turns out to be true for other academic fields.
Anyway, when source A says explicitly that source B is wrong but source B makes no such claim about source A, you should usually believe source A. But in this case you can know that the study is right by just learning for yourself what does happen to be widely accepted in the field and why it is widely accepted.
rvern | 8 years ago | on: Beverly Clock
rvern | 8 years ago | on: Visa confirms Coinbase wasn’t at fault for overcharging users
rvern | 8 years ago | on: An American served a year in prison for copyright conduct that is legal in EU
rvern | 8 years ago | on: The Rise of China and the Fall of the ‘Free Trade’ Myth
rvern | 8 years ago | on: The Rise of China and the Fall of the ‘Free Trade’ Myth
This should be completely obvious.
It also refutes the author’s argument. Why has a market economy directed by a Communist state become the world’s second-largest?! Would Friedman find it hard to explain why China, run by a Communist Party, has emerged as central to the global capitalist economy!? China has 19% of the world population but roughly 10% of the world GDP. It is 79th in GDP per capita at purchasing power parity. We should not evaluate a country’s economic policies by looking at its nominal GDP without also looking at its population—this is nothing Friedman would have difficulty explaining.
rvern | 8 years ago | on: The Rise of China and the Fall of the ‘Free Trade’ Myth
rvern | 8 years ago | on: The Rise of China and the Fall of the ‘Free Trade’ Myth
rvern | 8 years ago | on: Just 8 men own same wealth as half the world
http://marginalrevolution.com/marginalrevolution/2008/07/xxx...
rvern | 8 years ago | on: The Case Against Education: Why the Education System Is a Waste
“At this point, one could object, ‘Though education teaches few practical skills, that hardly makes it wasteful. By your own admission, education serves a vital function: certifying the quality of labor. That’s useful, isn’t it?’ Indeed. However, this is a dangerous admission for the champion of education. If education merely certifies labor quality, society would be better off if we all got less. Think about it like this: A college degree now puts you in the top third of the education distribution, so employers who seek a top-third worker require this credential. Now imagine everyone with one fewer degree. In this world, employers in need of a top-third worker would require only a high school diploma. The quality of labor would be certified about as accurately as now—at a cost savings of four years of school per person.
[…]
Suppose you agree society would benefit if average education declined. Is this achievable? Verily. Government heavily subsidizes education. In 2011, U.S. federal, state, and local governments spent almost a trillion dollars on it. The simplest way to get less education, then, is to cut the subsidies. This would not eliminate wasteful signaling, but at least government would pour less gasoline on the fire.
The thought of education cuts horrifies most people because ‘we all benefit from education.’ I maintain their horror rests on what logicians call a fallacy of composition—the belief that what is true for a part must also be true for the whole. The classic example: You want a better view at a concert. What can you do? Stand up. Individually, standing works. What happens, though, if everyone copies you? Can everyone see better by standing? No way.”