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Nobody Understands Probability

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Re: Nobody Understands Probability

#51

Post by Dn_Ab »

Tichy wrote: post #42
Dn_Ab wrote: post #38

Earlier quoted context omitted.

I thought on this a bit. And I do believe you are correct. Because as you note, he did in fact condition the space such that 1/3 is the correct answer and is stretching. He goes on to say "Now this means that if we want to claim that the probability that the man has two boys is , what we are really claiming is that he is equally likely to inform us that he has at least one boy, in all situations where it is true, ind…

Can't read your code, but aren't (F,M,1) and (M,F,2) impossible? Not sure what exactly you are calculating.

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two kids ordered by age.

Re: Nobody Understands Probability

#54

Post by [deleted] »

Eliezer wrote: post #37
frossie wrote: post #2

For those who didn't make it all the way down: People often intuitively think of probabilities as a fact about the world, when in reality probabilities are a fact about our model of the world.

Not an exact quote, but E. T. Jaynes: "If I am ignorant about a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon."

[deleted]

Re: Nobody Understands Probability

#55

Post by iliketosleep »

thwarted wrote: post #47
abeppu wrote: post #46

Earlier quoted context omitted.

1/3 would be correct if you set aside the issues about 'given' information addressed in the post. And I think the post has a valid point, that we have to be careful to appropriately understand biases and uncertainties in our data sources. But your reading of it, I think, demonstrates the real weakness of this part of the OP's discussion, namely that he's started with, and trying to expand from, a basic, 'classic' pro…

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox has interesting content in the sections Second Question and Ambiguous Problem Statements. I'll accept that I'm wrong and that the answer is 1/3 and that I just don't understand it and that I'm supporting the point that "no one understands probability, especially me", but there has been little explanation why the birth order is even a factor. Even that Wikipedia entry l…

i think it's like this.... interpretation 1.. we select a random FAMILY from the set of all families with two children.one of the children happens to be a boy. {BB, BG, GB} are possibilities. P(BB) = 1/3

interpretation 2.. we select a random CHILD from the set of all families with two children. one of the children happens to be a boy. in this case we have the following possible combinations [B1B2, G1B3, B4G2]. we know it's a boy, so what's the probability that B1 or B2 was selected? 1/4+1/4 = 1/2.

Re: Nobody Understands Probability

#56

Post by Tichy »

Dn_Ab wrote: post #51
Tichy wrote: post #42

Earlier quoted context omitted.

Can't read your code, but aren't (F,M,1) and (M,F,2) impossible? Not sure what exactly you are calculating.

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two kids ordered by age.

I see - I thought the first child you meet is always a boy in your example. So I am still not sure what you are calculating, but at least I understand the tuple notation :-)

Re: Nobody Understands Probability

#57

Post by tome »

scott_s wrote: post #45
tome wrote: post #39

Earlier quoted context omitted.

There are at least two interpretations of probability. Firstly the epistemological, as you say, represents our lack of knowledge about the world. Secondly the aleatory truly represents the phenomenon of chance in the world. The best interpretation of quantum theory for example (as I understand it) takes the latter view that randomness is genuinely physically manifested, and does not simply represent our inability to…

I think you're confusing concepts. The original point is about the difference between the map and the territory . And, because I'm (finally) systematically going through Eliezer's sequences: http://wiki.lesswrong.com/wiki/Map_and_Territory_(sequence) Your second paragraph is about a particular map: quantum theory. Quantum theory has probabilities in it. The dominant interpretation of quantum theory is that the probab…

No I don't think so. Unlike statistical physics, where probabilities are simply a mathematical technique for dealing with uncertainty, quantum mechanics actually postulates that randomness is inherent to the universe.

If you disagree with me, please describe how your concept of "maps and territories" applies to the StatPhys/QM distinction.

Re: Nobody Understands Probability

#58

Post by scott_s »

tome wrote: post #57
scott_s wrote: post #45

Earlier quoted context omitted.

I think you're confusing concepts. The original point is about the difference between the map and the territory . And, because I'm (finally) systematically going through Eliezer's sequences: http://wiki.lesswrong.com/wiki/Map_and_Territory_(sequence) Your second paragraph is about a particular map: quantum theory. Quantum theory has probabilities in it. The dominant interpretation of quantum theory is that the probab…

No I don't think so. Unlike statistical physics, where probabilities are simply a mathematical technique for dealing with uncertainty, quantum mechanics actually postulates that randomness is inherent to the universe. If you disagree with me, please describe how your concept of "maps and territories" applies to the StatPhys/QM distinction.

Suppose I accurately map the coastline, and every relevant part of the coastline is depicted in my map. But the map is not the same as the coastline itself.

If my coastline has some feature that blips in and out of existence in a predictable way, I can integrate that into my map. My map then has uncertainty in it. That uncertainty is an accurate reflection of the coastline itself - but there is still a distinction between the map and the coastline.

I don't disagree with your second sentence. But there is still a difference between our theory of quantum mechanics and the universe itself.

Re: Nobody Understands Probability

#59

Post by jodrellblank »

thwarted wrote: post #48
Tichy wrote: post #41

Earlier quoted context omitted.

You picked that 0.5 out of thin air, though. You forgot about BG.

I didn't "forget" about it, I contend that case is already handled by GB; "one child is a boy and one child is a girl" is the same as "one child is a girl and one child is a boy" and can be expressed as either GB or BG, making GB and BG equivalent.

GB and BG take up more area in probability space.

If you have a thousand paths in front of you, one leading to a fortune, one to a potion and the rest to a pit of death, you can't say the 998 paths are together equal to the other two just because they all end at the same place. It's much more likely you'll hit the pit of death.

It's much more likely to have boy/girl children even though BG and GB look the same at the end. You get as much probability current down each of the wires BG and GB you do down the GG and BB wires, making twice as much in total for BG/GB combined.

If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. You dont get to say there are three colours because I can class the two gray buildings as the same the chances are 1/3rd for each colour.

Re: Nobody Understands Probability

#60

Post by Dn_Ab »

Tichy wrote: post #56
Dn_Ab wrote: post #51

Earlier quoted context omitted.

(F,M,1) means met daughter (who is older) first. (M, F, 2) is met son who is younger than his sister first. These is the space of possible ways to meet his two kids ordered by age.

I see - I thought the first child you meet is always a boy in your example. So I am still not sure what you are calculating, but at least I understand the tuple notation :-)

I was trying to make a point that two problems that look the same actually lead to different results based on what information you are given. For example, being told someone has 2 kids and at least one is a girl then the space for this is S = {(M,F), (F,M), (F,F)}. However if I were to run into someone with two kids and saw a daughter then the information I have doesn't allow me to construct the space S above if I wanted to find the chance of say, 2 girls while accounting for age.

Instead I must consider S X {1,2} because instead of knowing that there is at least one daughter I just know that I have met one daughter whose age (whether older) is unknown to me. I know nothing of her sibling. So I am calculating the possible ways I could have met her and then the chance of 2 daughters conditioned on that space. This is a very tricky differentiation. Distinctions like this and thinking about what to condition on is what makes probability so tricky.

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