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Statistics Question

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Re: Statistics Question

Unread postby emailking » Mon 12 Jan 2009, 21:39:42

$this->bbcode_second_pass_quote('jbeckton', '
')
$this->bbcode_second_pass_quote('emailking', 'I')t doesn't matter what the numbers are as long as all are less than 1.


No?

Say for example with all numbers less than 1:

P(A)=0.5
P(B)=0.005
P(B|A)=0.05

Treating them as independent:

P(A)*P(B)=0.0025 (or 1:400)

Treating them as dependent:

P(A)*P(B|A)=0.025 (or 1:40)

The answer is off by an entire order of magnitude because we used the wrong probability.


Well, that wasn't what I was saying for which it doesn't matter. You acknowledged the point I thought you were disputing.
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Re: Statistics Question

Unread postby jbeckton » Mon 12 Jan 2009, 21:42:09

$this->bbcode_second_pass_quote('emailking', '
')Well, that wasn't what I was saying for which it doesn't matter.


Perhaps I misunderstood, what were you refering to?
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Re: Statistics Question

Unread postby emailking » Mon 12 Jan 2009, 23:20:40

I was saying P(A and B) <= P(A), P(B) doesn't depend on in/dependent or the size of P(A) or P(B).
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Re: Statistics Question

Unread postby jbeckton » Tue 13 Jan 2009, 18:02:01

$this->bbcode_second_pass_quote('emailking', 'I') was saying P(A and B) <= P(A), P(B) doesn't depend on in/dependent or the size of P(A) or P(B).



Sure, I agree with that only that, I was just saying that P(B) not = P(B|A)
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Re: Statistics Question

Unread postby jbeckton » Tue 13 Jan 2009, 18:03:24

$this->bbcode_second_pass_quote('Carlhole', '')$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Carlhole', '')$this->bbcode_second_pass_quote('jbeckton', 'P')erhaps you are refering to a point of contention between he and Carlhole. Forgive me but I tend to skim through Carlhole's posts at this point....


What a kunt.


Need I say more?......


Yeah, say some more kunty stuff.


Me?....nah, you seem to be on top of that!

:lol:
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Re: Statistics Question

Unread postby Carlhole » Tue 13 Jan 2009, 18:10:01

***yawn***
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Re: Statistics Question

Unread postby Koyaanisqatsi » Tue 13 Jan 2009, 20:27:41

$this->bbcode_second_pass_quote('emailking', '')$this->bbcode_second_pass_quote('jbeckton', ' ')...


Well, that wasn't what I was saying for which it doesn't matter. You acknowledged the point I thought you were disputing.


This is jbeckton's tactic - once he is pinned down on an argument he plays naive and claims that that wasn't what he was saying at all, and then shifts the debate to a new point (in this case, to the issue of how small must a probability be to constitute very small). Your characterization of my position above is 100% correct. If that wasn't what JBeckton meant, then why would he respond to

$this->bbcode_second_pass_quote('jbeckton', '
')$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability. As an engineer I think you would know that.

:lol: You are incorrect; the probability of a collapse increases exponentially after the fire has started because the events are not independent. Do you really not see this?

link

by repeating

$this->bbcode_second_pass_quote('jbeckton', '
')Yes, the probability of collapse increases after the building is set on fire, therefore:
P(B) does not equal P(B|A)


I have clearly been saying - multiple, multiple times - that "P(A and B) < P(B)" and JBeckton responds each time with "P(B|A) > P(B)", which is a strawman, because I have never said otherwise. The issue is, it's September 10, what is the probability of a major terrorist attack and fire induced-progressive collapse? The probability of interest is P(A and B), not P(B|A), because the terrorist incident (and consequent office fires) has not yet occurred.
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Re: Statistics Question

Unread postby Koyaanisqatsi » Tue 13 Jan 2009, 20:34:59

$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '
'):lol: You are incorrect; the probability of a collapse increases exponentially after the fire has started because the events are not independent. Do you really not see this?


Yes, the probability of collapse increases after the building is set on fire, therefore:

P(B) does not equal P(B|A)


That's not the claim. For the thousandth time, you are confusing P(A and B) with P(B|A). See my response to emailking.


$this->bbcode_second_pass_quote('Koyaanisqatsi', 'I')t doesn't matter whether one uses the equation for dependent or independent events if P(B) or P(B|A) is sufficiently small:


$this->bbcode_second_pass_quote('', '
')This is an assumption you have made (you know what happens when you make assumptions). I have done probability (PRA) studies for nuclear power plants that have probabilities 10^(-6) and smaller which is certainly <<1, are you saying we should ignore them? The NRC says they are significant, I agree.

Have you made any attempt to quantify P(B) and P(B|A) before assuming the difference is negligible? I bet you haven’t.

Guess you are just going with “since the probability <<1 it must be impossible".

Well sorry to say that events with a probability <<1 occur everyday. For instance you chances of dying in a plane crash are 11 million to 1 or 9.1e-8

Guess we can assume that no one ever dies in a plane crash since P<<1 right? I wonder what the probability of dying in a office building from an airplane impact would be?

Guess its impossible?


Perfectly valid to discuss what are realistic probabilities for what goes into the equation. But first we need to agree on what equation to use. The equation is

P(A and B) = P(A)*P(B|A)

which means that, given values of P(A) and P(B|A):

$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability.

which you continually claim is invalid because the events are dependent.
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Re: Statistics Question

Unread postby ROCKMAN » Wed 14 Jan 2009, 11:48:41

I love debates about statistics! It allows me to ask my favorite stat question: if you flip a quarter 19 times and it comes up heads every time, what are the odds that it will come up heads on the 20th flip? This was the question asked the first day of class by my first stat instructor.
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Re: Statistics Question

Unread postby jbeckton » Wed 14 Jan 2009, 20:01:48

$this->bbcode_second_pass_quote('ROCKMAN', 'I') love debates about statistics! It allows me to ask my favorite stat question: if you flip a quarter 19 times and it comes up heads every time, what are the odds that it will come up heads on the 20th flip? This was the question asked the first day of class by my first stat instructor.


50/50
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Re: Statistics Question

Unread postby jbeckton » Wed 14 Jan 2009, 20:09:47

$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')I have clearly been saying - multiple, multiple times - that "P(A and B) < P(B)" and JBeckton responds each time with "P(B|A) > P(B)", which is a strawman, because I have never said otherwise.


Nor have I ever claimed that P(A and B)>P(B) or P(A) which you keep implying.

I only claimed "P(B|A) > P(B)"
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Re: Statistics Question

Unread postby GoghGoner » Wed 14 Jan 2009, 20:27:04

$this->bbcode_second_pass_quote('ROCKMAN', 'I') love debates about statistics! It allows me to ask my favorite stat question: if you flip a quarter 19 times and it comes up heads every time, what are the odds that it will come up heads on the 20th flip? This was the question asked the first day of class by my first stat instructor.


I guess we would have to prove you aren't using a rigged coin :)

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Re: Statistics Question

Unread postby ROCKMAN » Thu 15 Jan 2009, 08:05:58

You’re the winner Goner. Most would answer 50/50 (including me). He would make the point that regardless what the charts say, it’s highly unlikely anyone in the class would ever see such a run. It would be much more likely that it was a double headed coin. It was a serious point: don’t get so wrapped up the mechanics of statistical analysis that you forget the critical importance of understand the population you’re evaluating. More important: understand the assumptions being made (i.e. an honest coin). He felt that saying my stats were wrong just because my assumptions about the population were wrong was the biggest sin a statistician could make.

I’ve used that point many times during my career to debunk the work of others. This is the main reason I tend to put little value in any stats someone throws out unless it includes a very clear picture of the assumptions and population parameters. As soon as you start questioning the assumptions the battle usually begins.

It really wasn’t a trick question IMO. It is THE question for every stat analysis as far as I’m concerned.
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Re: Statistics Question

Unread postby Koyaanisqatsi » Thu 15 Jan 2009, 20:24:58

$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')I have clearly been saying - multiple, multiple times - that "P(A and B) < P(B)" and JBeckton responds each time with "P(B|A) > P(B)", which is a strawman, because I have never said otherwise.


Nor have I ever claimed that P(A and B)>P(B) or P(A) which you keep implying.

I only claimed "P(B|A) > P(B)"


Fine - I was suggesting that because I don't see how

$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability.


can be interpreted otherwise. By probability of two events occurring together, I mean P(A and B), not P(B|A). Saying that the statement is invalid because P(B|A) > P(B) is a strawman because I have never suggested that this might not be the case.

Let's start with a clean slate. If we let A=a 9/11 scale terrorist attack(+consequent fires) and B=fire-induced progressive collapse, then the probability of BOTH terrorist attack AND fire induced progressive collapse is:

P(A and B) = P(A)*P(B|A)

correct?
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Re: Statistics Question

Unread postby jbeckton » Thu 15 Jan 2009, 21:35:06

$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')Let's start with a clean slate. If we let A=a 9/11 scale terrorist attack(+consequent fires) and B=fire-induced progressive collapse, then the probability of BOTH terrorist attack AND fire induced progressive collapse is:

P(A and B) = P(A)*P(B|A)

correct?


Yes

And I would also agree that we are left with a “very unlikely event” but I do not agree that this should be enough evidence to show that 911 was in any way a conspiracy, only that a “very unlikely event” occurred.

But as we all know, “very unlikely” is open to interpretation and “very unlikely” events occur every day just as we saw in the Hudson River crash today. There is approximately a 1:11000000 chance of this occurring to any person and it happened to a few hundred just a few hours ago.

I am sure that “very very unlikely” won’t comfort them very much should they ever fly again.
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Re: Statistics Question

Unread postby Koyaanisqatsi » Mon 19 Jan 2009, 15:09:57

$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')Let's start with a clean slate. If we let A=a 9/11 scale terrorist attack(+consequent fires) and B=fire-induced progressive collapse, then the probability of BOTH terrorist attack AND fire induced progressive collapse is:

P(A and B) = P(A)*P(B|A)

correct?


Yes

And I would also agree that we are left with a “very unlikely event”


So do you agree with this or not?

$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability.
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Re: Statistics Question

Unread postby jbeckton » Mon 19 Jan 2009, 22:06:14

$this->bbcode_second_pass_quote('Koyaanisqatsi', '')$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')Let's start with a clean slate. If we let A=a 9/11 scale terrorist attack(+consequent fires) and B=fire-induced progressive collapse, then the probability of BOTH terrorist attack AND fire induced progressive collapse is:

P(A and B) = P(A)*P(B|A)

correct?


Yes

And I would also agree that we are left with a “very unlikely event”


So do you agree with this or not?

$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability.


Depends on our perceptions of "very unikely".
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Re: Statistics Question

Unread postby Koyaanisqatsi » Tue 20 Jan 2009, 04:00:28

$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '')$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', '
')Let's start with a clean slate. If we let A=a 9/11 scale terrorist attack(+consequent fires) and B=fire-induced progressive collapse, then the probability of BOTH terrorist attack AND fire induced progressive collapse is:

P(A and B) = P(A)*P(B|A)

correct?


Yes

And I would also agree that we are left with a “very unlikely event”


So do you agree with this or not?

$this->bbcode_second_pass_quote('', 'Y')ou are still left with two very unlikely events occurring together, yielding an even smaller probability.


Depends on our perceptions of "very unikely".

Well, you already agreed that the statement is false. This must mean that you have an internal standard for what constitutes "very unlikely". According to YOUR definition, is the statement true or false?
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Re: Statistics Question

Unread postby jbeckton » Wed 21 Jan 2009, 19:46:20

$this->bbcode_second_pass_quote('Koyaanisqatsi', 'A')ccording to YOUR definition


Like most engineers, I don't really like terms like ‘very’, ‘nearly’, ‘really’…etc

My definition of "very low" for this case:

P(A)*P(B|A)
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Re: Statistics Question

Unread postby Koyaanisqatsi » Fri 23 Jan 2009, 03:02:02

$this->bbcode_second_pass_quote('jbeckton', '')$this->bbcode_second_pass_quote('Koyaanisqatsi', 'A')ccording to YOUR definition


Like most engineers, I don't really like terms like ‘very’, ‘nearly’, ‘really’…etc

My definition of "very low" for this case:

P(A)*P(B|A)


Okay, from this and from your earlier statements I take it that you think that either P(A) and/or P(B|A) is not very unlikely, correct?
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