Probability
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18-03-2013, 07:42 AM (This post was last modified: 18-03-2013 07:57 AM by Hafnof.)
RE: Probability
So I have an infinite bag of marbles, or one so large that I could conceivably keep pulling marbles out for a lifetime without running out.

f(n) defines the colour of each marble I will pull out in sequence from zero to infinity. I do not know what this function is. I can only find out by pulling marbles out.

With no information at hand all possible functions are eligible to be the function in question. It is advisable to pull out a few marbles to eliminate as many options as possible with as little effort as possible. The first few marbles are a mixture of white marbles and marbles of other colours.

Since we know that these coloured marbles exist and are distributed in a particular way we can form a hypothesis that the remaining marbles are of the same colours and are distributed in the same fashion. This is a hypothesis we can test by continuing to pull out marbles an examine their statistical distribution. Choosing this hypothesis as the working hypothesis is reasonably consistent with Occam's razor. There is no reason to consider a more complex hypothesis as being likely to be true without some evidence to support those more complex hypotheses. See also: http://en.wikipedia.org/wiki/Inductive_inference

Still, pulling out marble after marble we could find new colours. We could find the frequency distribution changing over time. We could find regular patterns that don't conform to random selection, or to random selection alone. In fact for any f(n) we hypothesise based on our past experience there still remain an infinite variety of f(n) that fit the data and make differing future predictions.

In order to move past this impasse it becomes necessary to consider the origins of the bag and what other experiments we might be able to do rather than the simple direct sampling. Until we have a working hypothesis of how the bag came to be it is difficult to have any great certainty about what its contents are. As we dig deeper into the physics behind a particular phenomenon we'll tend to arrive at a more fundamental theory that consistently explains a number of different phenomenon and which we can test directly without having to rely only on testing the physics of the resulting phenomenons. For example we might find the machine that is sorting the marbles. We might carefully weigh each marble we have so far extracted and measure its volume or electrical conductivity - then we might do the same the bag to see if we can make some overall judgement about the distribution that might be helpful. We might investigate the machines that formed the marbles and the machines that filled the bag. With this additional information we can come to a more reliable conclusion about the nature of the marble-colour-defining-function to improve the fidelity of our predictions and our confidence in those predictions.

So yes, doing the same experiment every day doesn't necessarily tell us what will happen when we perform the experiment tomorrow. To deal with this we have Occam's razor which tells us a little about what is likely - that future results will likely be consistent with the function that most simply explains past results - and more importantly we have the ability to perform more and different experiments to discover the underlying physics that are driving a particular phenomenon. Having faith that the sun will rise again tomorrow because that's what it has always done is one thing, but having faith that the sun will rise again because the angular momentum of the earth is preserved in an orbital system is quite another. The deeper we dig and the more and different the experiments we run the more opportunities we open up to falsify our current understanding and therefore to deepen it, or fail to falsify our understanding and therefore to gain additional confidence in it.

Give me your argument in the form of a published paper, and then we can start to talk.
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18-03-2013, 07:50 AM (This post was last modified: 18-03-2013 03:11 PM by Full Circle.)
RE: Probability
I'm about to lose my marbles.


I've been following this thread with interest. I'm no math wizard but even and I, after all these posts, think I finally understand Vosur and Chas and The BeardedDude's (et al) points.

Would it be accurate to say that the whole key in this ad infinitum argument is that no one knows how many marbles are in the fucking barrel, what color or colors there are until all are pulled out or how big the barrel is or even if the barrel is infinitely large?

In my head I envision the following: A barrel of non-ascertained size, is filled with marbles, how many? No fucking way to know. I'm blindfolded and ask to draw one out. It is white. I do this (a la HJ) let's say one million times. All fucking marbles are white. I assume this will go on forever but later I find out that when I'm finally finished pulling all of them out of the barrel the barrel had been filled with 12 quadrillion black marbles first and then topped off with 1 million white ones.

In this example, during the first million draws, I am absofuckinglutely sure there are nothing but white marbles but I would be wrong by a factor of 1∧9 (or some other big fucking number). Is that correct?

I also found 1 Cat's eye that Tartarus Sauce snuck in there but that's neither here nor there Big Grin

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18-03-2013, 12:00 PM (This post was last modified: 18-03-2013 12:45 PM by Heywood Jahblome.)
RE: Probability
(18-03-2013 07:50 AM)Full Circle Wrote:  I'm about to lose my marbles.


I've been following this thread with interest. I'm no math wizard but even and I, after all these posts, think I finally understand Vosur and Chas and The BeardedDude's (et al) points.

Would it be accurate to say that the whole key in this ad infinitum argument is that no one knows how many marbles are in the fucking barrel, what color or colors there are until all are pulled out or how big the barrel is or even if the barrel is infinetely large?

In my head I envision the following: A barrel of non-ascertained size, is filled with marbles, how many? No fucking way to know. I'm blindfolded and ask to draw one out. It is white. I do this (a la HJ) let's say one million times. All fucking marbles are white. I assume this will go on forever but later I find out that when I'm finally finished pulling all of them out that the barrel had been filled with 12 quadrillion black marbles first and then topped off with 1 million white ones.

In this example, during the first million draws, I am absofuckinglutely sure there are nothing but white marbles but I would be wrong by a factor of 1∧9 (or some other big fucking number). Is that correct?

I also found 1 Cat's eye that Tartarus Sauce snuck in there but that's neither here nor there Big Grin

A probability is quantatative description of the likely occurrence of a particular event. It is not necessarily a calculation which is where Chas and Vosur are going wrong. They have taken the position that you cannot tell if P(X|An) is increasing or decreasing without being able to calculate X. Your example shows they are wrong. The moment you draw your first black marble( or tigers eye) P(X) decreases from being some quantity between 0 and 1, down to 0. You know the probability has decreased even without knowing how many marbles where in the barrel and not preforming a calculation.

Suppose you drew all the marbles in the barrel and they were all white. P(X) would equal 1.....by definition and not some calculation. Now according to Vosur and Chas, you would need to calculate that. Their position implys you could not say P(X) = 1 unless you actually kept track of how many marbles you drew. The implications of their statements in this thread are absurd so it should be obvious they are wrong.

From what I can see Bearded Dude goes wrong by confusing the quantatative description of a likely occurrence of a particular event with the eventual outcome. If the weatherman says there's a fifty percent chance the coin toss will result in heads, he wasn't wrong if the actual coin toss comes up tails.
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18-03-2013, 01:13 PM
RE: Probability
(18-03-2013 07:33 AM)pgrimes15 Wrote:  
(09-03-2013 01:50 PM)Heywood Jahblome Wrote:  [This is more than the mind creating some pattern. Observing only white marbles does increase the chance that all the marbles are white.

Let X = the probability that all the marbles are white.
Let An = n observations of white marbles without ever observing a non white marble.


With the given scenario, P(An) is either 1 if there are no non-white balls, or 0 if there are 1 or more non-white balls.

No.....remember what An is....I bolded it for you
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18-03-2013, 01:18 PM
RE: Probability
(18-03-2013 12:00 PM)Heywood Jahblome Wrote:  
(18-03-2013 07:50 AM)Full Circle Wrote:  I'm about to lose my marbles.


I've been following this thread with interest. I'm no math wizard but even and I, after all these posts, think I finally understand Vosur and Chas and The BeardedDude's (et al) points.

Would it be accurate to say that the whole key in this ad infinitum argument is that no one knows how many marbles are in the fucking barrel, what color or colors there are until all are pulled out or how big the barrel is or even if the barrel is infinetely large?

In my head I envision the following: A barrel of non-ascertained size, is filled with marbles, how many? No fucking way to know. I'm blindfolded and ask to draw one out. It is white. I do this (a la HJ) let's say one million times. All fucking marbles are white. I assume this will go on forever but later I find out that when I'm finally finished pulling all of them out that the barrel had been filled with 12 quadrillion black marbles first and then topped off with 1 million white ones.

In this example, during the first million draws, I am absofuckinglutely sure there are nothing but white marbles but I would be wrong by a factor of 1∧9 (or some other big fucking number). Is that correct?

I also found 1 Cat's eye that Tartarus Sauce snuck in there but that's neither here nor there Big Grin

A probability is quantatative description of the likely occurrence of a particular event. It is not necessarily a calculation which is where Chas and Vosur are going wrong. They have taken the position that you cannot tell if P(X|An) is increasing or decreasing without being able to calculate X. Your example shows they are wrong. The moment you draw your first black marble( or tigers eye) P(X) decreases from being some quantity between 0 and 1, down to 0. You know the probability has decreased even without knowing how many marbles where in the barrel and not preforming a calculation.

Suppose you drew all the marbles in the barrel and they were all white. P(X) would equal 1.....by definition and not some calculation. Now according to Vosur and Chas, you would need to calculate that. Their position implys you could not say P(X) = 1 unless you actually kept track of how many marbles you drew. The implications of their statements in this thread are absurd so it should be obvious they are wrong.

From what I can see Bearded Dude goes wrong by confusing the quantatative description of a likely occurrence of a particular event with the eventual outcome. If the weatherman says there's a fifty percent chance the coin toss will result in heads, he wasn't wrong if the actual coin toss comes up tails.

No. What changed was your perception of the probability.

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18-03-2013, 01:34 PM
RE: Probability
(18-03-2013 01:18 PM)Chas Wrote:  
(18-03-2013 12:00 PM)Heywood Jahblome Wrote:  A probability is quantatative description of the likely occurrence of a particular event. It is not necessarily a calculation which is where Chas and Vosur are going wrong. They have taken the position that you cannot tell if P(X|An) is increasing or decreasing without being able to calculate X. Your example shows they are wrong. The moment you draw your first black marble( or tigers eye) P(X) decreases from being some quantity between 0 and 1, down to 0. You know the probability has decreased even without knowing how many marbles where in the barrel and not preforming a calculation.

Suppose you drew all the marbles in the barrel and they were all white. P(X) would equal 1.....by definition and not some calculation. Now according to Vosur and Chas, you would need to calculate that. Their position implys you could not say P(X) = 1 unless you actually kept track of how many marbles you drew. The implications of their statements in this thread are absurd so it should be obvious they are wrong.

From what I can see Bearded Dude goes wrong by confusing the quantatative description of a likely occurrence of a particular event with the eventual outcome. If the weatherman says there's a fifty percent chance the coin toss will result in heads, he wasn't wrong if the actual coin toss comes up tails.

No. What changed was your perception of the probability.

So you are saying my perception of the quantitative description of the likely occurrence of a particular event is changing?

That makes no sense Chas.

What makes sense is my quantatative description of the likely occurrence of a particular event is changing.
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18-03-2013, 01:52 PM
RE: Probability
(18-03-2013 01:34 PM)Heywood Jahblome Wrote:  
(18-03-2013 01:18 PM)Chas Wrote:  No. What changed was your perception of the probability.

So you are saying my perception of the quantitative description of the likely occurrence of a particular event is changing?

That makes no sense Chas.

What makes sense is my quantatative description of the likely occurrence of a particular event is changing.
No, your qualitative perception of the quantitative facts is changing. You are basing your argument on too little information.

You don't know what the distribution is, so you can't tell what your samples mean. The more white balls you draw, the more likely you think it is that there is a preponderance of white balls.

If there are any black balls, then each time you draw only white balls, it is a less and less likely event. But that's really all you can say. If that's all you are trying to say, fine.

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18-03-2013, 02:01 PM
RE: Probability
(18-03-2013 01:34 PM)Heywood Jahblome Wrote:  
(18-03-2013 01:18 PM)Chas Wrote:  No. What changed was your perception of the probability.

So you are saying my perception of the quantitative description of the likely occurrence of a particular event is changing?

That makes no sense Chas.

What makes sense is my quantatative description of the likely occurrence of a particular event is changing.

A "likely occurrence" is an assumption.
Your perception can change if you assume anything about a "quantitative description" of a particular event.

A new type of thinking is essential if mankind is to survive and move to higher levels. ~ Albert Einstein
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18-03-2013, 02:05 PM
RE: Probability
At this point, you guys have to realize that this troll knows exactly what you're saying, probably agrees with it, and just keeps on bickering to see how long he can get you guys to keep on bickering with him? You know, troll stuff...

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18-03-2013, 03:21 PM
RE: Probability
(18-03-2013 01:13 PM)Heywood Jahblome Wrote:  
(18-03-2013 07:33 AM)pgrimes15 Wrote:  With the given scenario, P(An) is either 1 if there are no non-white balls, or 0 if there are 1 or more non-white balls.


No.....remember what An is....I bolded it for you


Sorry . . bit confused

what is P(An) or P(X) ?
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