Top Japanese scientists disagree with Global Warming

Yes and between 12,000 and 10,000 years ago, Wooly Mammoths paid dearly for farting too much and urinating in the world's rivers leading to catastrophic global warming that wiped them out.
After they were wiped out, the rest of the creatures on earth, including early man, signed a deal with Gaia that the Earth's climate be stable since the main perpetrators were no more and everyone else learned the lesson.
Then modern man learned to harness the power of fire/combustion. Gaia got angry.
 
Call me Smart ass any time, no offense taken...

Interestingly nobody is posting what his estimates were... :rock:

Rattler
 
rattler said:
Call me Smart ass any time, no offense taken...

Interestingly nobody is posting what his estimates were... :rock:

Rattler
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Way out! about ten times too high the the steel balls, and ten times too low for the cork thing, until I threw a few numbers around in my head then you can get quite near.

However, policy decisions often need an understanding of statistics to assess risk from unlikely events or potentially unreliable data. Take the following medical problem for example.

A test of a disease wrongly indicates a positive result 5% of the time (false positive). The disease strikes 1/1000 of the population. People are tested at random, regardless of whether they are suspected of having the disease. A patient’s test is positive. What is the probability of the patient having the disease?

Most Doctors get this completely wrong!

Slightly less relevant but even more interesting is the Monty Hall problem which was part of a genuine American game show.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice, or doesn't it matter?

http://math.ucsd.edu/~crypto/Monty/monty.html

Many professional statisticians get the answer wrong!
 
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perseus said:
-snip- Take the following medical problem for example.

A test of a disease wrongly indicates a positive result 5% of the time (false positive). The disease strikes 1/1000 of the population. People are tested at random, regardless of whether they are suspected of having the disease. A patient’s test is positive. What is the probability of the patient having the disease?

Most Doctors get this completely wrong!
Click to expand...

Not calculating I would intuitively argue 95% probablity that he has got the disease as I think it has othing to do with the probability towards society just of the test... I will research it a bit after the cup final... (1:1 currently at half time for Barca-Atletic Bilbao :cheers:).

perseus said:
Slightly less relevant but even more interesting is the Monty Hall problem which was part of a genuine American game show.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice, or doesn't it matter?

http://math.ucsd.edu/~crypto/Monty/monty.html

Many professional statisticians get the answer wrong!
Click to expand...

This one was clear as after showing one door one door has the higher probabilty than the one I chose (33% win first chosen door, 50% for the not opened door by host)

Thanks for sharing, interesting.

Rattler
 
Rattler

Strangely enough you got the difficult Monty Hall one right, and for the right reasons, well done. However, you were way out on the first one.

(actually it is 2/3 not 50%, but you are right you should switch)
 
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perseus said:
Rattler

Strangely enough you got the difficult Monty Hall one right, and for the right reasons, well done. However, you were way out on the first one.
Click to expand...

Ok, now that Barca has won (4:1 :jump:), let me take another intuitive take at the prob:

Of 1000 persons, one is ill.

I test all 1000, so I get 50 positive results, 1 of those is correct of cause, the others not.

So, my next guess is that a positivly tested person has a chance of 1:50 = 2% of being ill...?

Am I getting closer?

Rattler
 
The one iwth the doors feels like a case of the inverted cups with a ball underneath one, except you don't get to see the guy mix it around. What's the point?

Rattler, if the 1/1000 is an absolute fact I think you're about right. I was thinking the same thing... if the test is wrong 5% of the time, then 1/1000 is FAR less than 5% of 1000, which would be 50. So his odds of having a disease would then be 1/50, so 2%.
I dunno, it could be wrong but that's where my thinking got me.
 
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Yes it is around 2%, most Doctors thought it was 95% (probably gut feeling though rather than considered opinion)

The one iwth the doors feels like a case of the inverted cups with a ball underneath one, except you don't get to see the guy mix it around. What's the point?
Click to expand...

It isn't a trick, there is no mixing around. So your gut feeling is that is makes no difference? if so you are in very good company, but wrong.

Sources of confusion
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When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999). Out of 228 subjects in one study, only 13% chose to switch (Granberg and Brown, 1995:713). In her book The Power of Logical Thinking, vos Savant (1996:15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."

... nearly all people still think each of the two unopened doors has an equal probability and conclude switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption is a deeply rooted intuition (Falk 1992:202). People strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not (Fox and Levav, 2004:637).

A competing deeply rooted intuition at work in the Monty Hall problem is the belief that exposing information that is already known does not affect probabilities (Falk 1992:207). This intuition is the basis of solutions to the problem that assert the host's action of opening a door does not change the player's initial 1/3 chance of selecting the car. For the fully explicit problem this intuition leads to the correct numerical answer, 2/3 chance of winning the car by switching, but leads to the same solution for other variants where this answer is not correct (Falk 1992:207).
Click to expand...

Incidentally rattler you are correct to change but the probability is 2/3s not 50% I have edited the previous post to make this clear

The player, having chosen a door, has a 1/3 chance of having the car behind the chosen door and a 2/3 chance that it's behind one of the other doors. It is assumed that when the host opens a door to reveal a goat, this action does not give the player any new information about what is behind the door he has chosen, so the probability of there being a car behind a different door remains 2/3; therefore the probability of a car behind the remaining door must be 2/3 (Wheeler 1991; Schwager 1994). Switching doors thus wins the car with a probability of 2/3, so the player should always switch (Wheeler 1991; Mack 1992; Schwager 1994; vos Savant 1996:8; Martin 2002).
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Yes Perseus, 2/3s.
But still, it could have gone either way.

Here's how I went about it.
When presented with three with no additional information, I guessed door 1.
When door 3 showed the goat, the situation with door 1 and 2 didn't change. So why should I pick door 1 because the host said "are you sure you don't want to open door 2?" He could have said that to either regret my decision later or to mislead me deliberately depending on what sort of person he is.
I don't see why the additional probability should be stacked onto the other door. Seems more like it would be distributed evenly among the two unopened doors. Real weird. Then again, math has never been my strength so...
 
perseus said:
Incidentally rattler you are correct to change but the probability is 2/3s not 50% I have edited the previous post to make this clear
Click to expand...

Hah! Gotcha! :biggun:

Now you got it wrong! It indeed is 2/3, but only compared to the two *leftover* doors after host has been opening one he knows has no car, the other not opened door has a straightforward 50% prob (and as there are only two left, the one you chose with 33% makes the other having 66% = 2/3):

This, of cause, assumes that the moderator knows where the cars are...

Let us say you chose a door w/o car, and that then the guy opens one more, he has opened *1 of 2* doors without a car(making the opened door for you a 50% chance), which in turn gives the not opened door another 50% chance of having a win or not (overall on three doors). Either he has two no-car doors to choose from, or only has one left, and always because he *knows* that the car is behind the other.

For you contestant, as you do not know nothing (like in real life), it means you *have to* switch if you want to play (and you actually have no other choice of strat except going for them) probabilities...!

Once you have the choice to switch, the 50% (overall) door represents 66% for you compared to your original 33% door in your original choice.

Rattler
 
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the_13th_redneck said:
Yes Perseus, 2/3s.
But still, it could have gone either way.

Here's how I went about it.
-snip-
When door 3 showed the goat, the situation with door 1 and 2 didn't change.-snip-
Click to expand...

This is where your flaw in thinking is: The situation *changes a lot* (see my post above):

The point is the knowledge differece between you and moderator, he knows where the car is an will not "accidentally" open it: FOr him, whatever *you* chose, his two doors have certainity, and you have to take that into consideration.

Any door, at start, has a 33% chance of holding a car. Now, the 2nd door opened, this is not so: It will be 100% no car (as the guy knows). this makes the ne not-touched door a 50% candidate versus your 33% starter (at point of moderator choice, after that it is even - as correctly pointed out by the author - a 66% chance you will find the car if you switch vs. your original 33% which will not change).

Switch! http://www.youtube.com/watch?v=DFt7wo02bRg

Rattler
 
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Donkey said:
Ever here of the butterfly affect?
Click to expand...

Yes, this is more concerned with short term weather, than long term changes in climate. The butterfly effect (the unpredictable way small effects can become big ones) doesn't influence IF it is going to be warmer in Summer than Winter for example, only how exactly it gets there. This is because there is a strong forcing effect with seasons (due to the orientation of polar axis towards or away from the sun) as there is a strong forcing effect with global warming over a period of centuries (due to the build up of greenhouse gases).
 
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perseus said:
Yes, this is more concerned with short term weather, than long term changes in climate. The butterfly effect (the unpredictable way small effects can become big ones) doesn't influence IF it is going to be warmer in Summer than Winter for example, only how exactly it gets there. This is because there is a strong forcing effect with seasons (due to the orientation of polar axis towards or away from the sun) as there is a strong forcing effect with global warming over a period of centuries (due to the build up of greenhouse gases).
Click to expand...

Ah but are you sure that is fact????
 
Quite interesting.
Actually I think I want to understand this one.

So let's say I picked the first door like I did.
The presenter shows that the 3rd door doesn't contain the car.
So that means it's either in the 1st or 2nd door.
Apparently there's a 2/3 chance that it's the 2nd one. But how do you know that I picked the 1st door to start with? What if I picked the 2nd door? Then would the 2nd door still have a 2/3 chance of having the prize? Apparently in that case, the 1st door would have a 2/3 chance of having the prize, so I would switch, only to be wrong.
The choices that are presented to me after the 3rd one opens seems to be 50/50. That's what would seem logical if you consider the round to be completely over and started anew after the 3rd door is opened. So basically the two choices left to me after the 3rd door is opened is, do I stay with door 1 or move to door 2? Two choices at that one given moment in time.
If I picked door 3 at the very beginning and the presenter showed that it indeed did not have the car, then I'd have to pick between door 1 or door 2. In this case, the "other door" can't possibly be 2/3rds because then we'd have two doors worth 2/3rds the chance and that's simply not possible.
Or am I thinking of it too much like an actual game show?

rattler said:
This is where your flaw in thinking is: The situation *changes a lot* (see my post above):

The point is the knowledge differece between you and moderator, he knows where the car is an will not "accidentally" open it: FOr him, whatever *you* chose, his two doors have certainity, and you have to take that into consideration.

Any door, at start, has a 33% chance of holding a car. Now, the 2nd door opened, this is not so: It will be 100% no car (as the guy knows). this makes the ne not-touched door a 50% candidate versus your 33% starter (at point of moderator choice, after that it is even - as correctly pointed out by the author - a 66% chance you will find the car if you switch vs. your original 33% which will not change).

Switch! http://www.youtube.com/watch?v=DFt7wo02bRg

Rattler
Click to expand...
 
Lets see:

For me this reolves around knowledge.

You (the contestant) do *no* know anything, hence pick any door with 33% probability. Call this door #1

Now, either o have a car behind it or not (you *dont* know). 33% prob allright.

Now, moderator entering: He has two doors to chose, and *he knows* where the car is. Let us say you have it already, he will know. You did not hit it, he will know.

So, as it is his job to open a door *that 100% has no car behind it* he will open one he knows it is so (and not prove, as you supposed in your example, that your choice was right or wrong; indeed probabilites would be different if that were the case).

So, of door 2+3, that gives hi two choices, and the one he choses was a 100% certainity (because of his knowledge advantage).

Lets say he opened door #2, 100% sure there was no car.

Ok, so what are you (not knowing anything *except that the moderator knew* (!) ) left with?

Door#1 with its original 33% prob (you might have the car already!), and door #3 which has 50% prob compared to door #2 and you know the moderator opened #2 because he knew there was no car.

This leaves you with the following problem:

door #1 33% prob for a car
door #2 100% no car
door 3: 50% for a car (calculated between #2 and #3, i.e. 66% for calculation refering to #1)

See how the moderator changes the probabilities and why, going for probabilities, you have to switch?

Rattler
 
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rattler said:
Lets see:

For me this reolves around knowledge.

You (the contestant) do *no* know anything, hence pick any door with 33% probability. Call this door #1

Now, either o have a car behind it or not (you *dont* know). 33% prob allright.

Now, moderator entering: He has two doors to chose, and *he knows* where the car is. Let us say you have it already, he will know. You did not hit it, he will know.

So, as it is his job to open a door *that 100% has no car behind it* he will open one he knows it is so (and not prove, as you supposed in your example, that your choice was right or wrong; indeed probabilites would be different if that were the case).

So, of door 2+3, that gives hi two choices, and the one he choses was a 100% certainity (because of his knowledge advantage).

Lets say he opened door #2, 100% sure there was no car.
Click to expand...

Yes, up to here I get it completely. Obviously he will only open the door he knows is absolutely incorrect. Which leaves you with two doors. But what if he's doing it to mislead you into switching, knowing that you had picked the right door? He may want to plant a sense of doubt into your head.


rattler said:
Ok, so what are you (not knowing anything *except that the moderator knew* (!) ) left with?

Door#1 with its original 33% prob (you might have the car already!), and door #3 which has 50% prob compared to door #2 and you know the moderator opened #2 because he knew there was no car.

This leaves you with the following problem:

door #1 33% prob for a car
door #2 100% no car
door 3: 50% for a car (calculated between #2 and #3, i.e. 66% for calculation refering to #1)

See how the moderator changes the probabilities and why, going for probabilities, you have to switch?

Rattler
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That's the part that I have trouble with. Why is the additional probability awarded to the door that you did not select the first time around? What if you did select door 3 and not door 1? Then would door 1 suddenly have more probability than door 3 even though if you take all the words out of it, it looks exactly the same. What if you played this game with a friend and you chose door 1 and he chose door 3 and indeed door 2 was shown not to be the answer? Then should both of you switch?

Dunno... I'm sure there's some sense in this but I'm having trouble really getting into the part where the probability is being awarded to the other door. Yes I understand that when you first chose that door, it has a 1/3 chance. It would seem though that the other door should be awarded an additional 1/3 and become a 2/3 chance. But what if you "unselected" door 1 after door 2 was shown to be empty and in your thoughts, re-selected a door from scratch? Wouldn't that be 50/50? How would that really change things?
 
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