Probability
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19-03-2013, 02:10 PM
RE: Probability
So... Drinking Beverage ...I get ignored and passed over again. Perhaps you are rereading my rarefaction example?

“Science is simply common sense at its best, that is, rigidly accurate in observation, and merciless to fallacy in logic.”
—Thomas Henry Huxley
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20-03-2013, 12:47 AM
RE: Probability
(19-03-2013 05:54 AM)pgrimes15 Wrote:  
(19-03-2013 12:59 AM)Heywood Jahblome Wrote:  X is there are no black marbles(and here black means any color(s) other than white).
P(X) is the probability of X

An is n observations of white marbles while never observing a black one.
P(An) is the probability of An.

If you draw a black marble P(X) = 0. P(An) is always going to be greater than 0 because by definition at least one white marble is observed and black ones never are observed.


If you draw a black marble, then P(An) also equals 0.

Therefore the expression P(X l An) = P(X n An) / P(An) is undefined with zero in the denominator and therefore this situation cannot be analysed as you are attempting.

What you are doing is trying to make a leap between objective probability ( or frequentist probability which assigns precise liklihoods to the various outcomes of an activity such as throwing a dice ) and subjective probability which is synonymuos with "degree of belief".

Incidentally, with 3 binary activities such as throwing a coin, the possible outcomes are :

BBB, BWW, BBW, WWW.

The probabilities of these are :

BBB and WWW - 0.125

BWW and BWW - 0.375

not 0.25 each as you persist in stating. This is schoolboy maths and suggests to me that you are not especially rigorous when dealing with mathematical probability .

Regards

Grimesy

Grimesy, you are in error. An is always greater than 0 by definition. Think about it this way, An is n white marble draws in a row. P(An) is the probability of n white marbles in a row. As long as it is logically possible to draw a white P(An) is greater than 0 for any n. Is the probability of drawing 5 white marbles in a row greater than 0? Or 10 white marbles in a row? Or a billion? Yes, if the composition of the bin is unknown to you then the assumption that it is logically possible to draw another white marble is reasonable.

Also regarding the .25. You are wrong about that too. It is true that the probability of flipping 3 heads in a row is .125. It would be true that drawing 3 white marbles in a row has a probability of .125 but only if drawing a white marble itself had a probability of .5. However you don't know anything about the composition of the bin. In the example you are told there are 3 marbles in the bin, but no information is given to you regarding the distribution of colors. So you can't say there is a .5 probability of drawing a white. The only reasonable assumption is that all distributions are equally likely. In fact the example says that. Since there are only 4 possible distributions of the colors, and each distribution is equally likely, it stands to reason that each distribution has a .25 probability.
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20-03-2013, 12:59 AM
RE: Probability
(19-03-2013 02:10 PM)TheBeardedDude Wrote:  So... Drinking Beverage ...I get ignored and passed over again. Perhaps you are rereading my rarefaction example?

Your rarefaction provides a sound description of the likely number of colors in the system. Most of the time it is going to be right however in this contrived circumstance it wasn't accurate. Remember just because something is probable, doesn't mean it is a sure thing. The next miracle proclaimed might indeed turnout to only have a supernatural explanation, but I wouldn't bet on it. Would you?
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20-03-2013, 05:26 AM
Re: Probability
You've shown no examples of miracles with or without natural explanations. All you have done is mess up statistics and probabilities.

And probabilities are our estimates of our observations. Occurrences are either 1 or 0 in reality. So either something does or does not exist. Trying to argue statistics leaves you nowhere since you have given 0 observations to back up any claim.
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20-03-2013, 05:27 AM
Re: Probability
You have also never answered my question for how many colors were in my example and to prove you are correct.
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20-03-2013, 05:38 AM
RE: Probability
The assumption that a newly observed phenomenon has a natural explanation is an excellent candidate for the null hypothesis. The burden of proof is on the supernaturalist to effectively prove a supernatural explaination for the event... and to explain what supernatural even means in this context.

Give me your argument in the form of a published paper, and then we can start to talk.
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20-03-2013, 07:43 AM
RE: Probability
(20-03-2013 12:47 AM)Heywood Jahblome Wrote:  
(19-03-2013 05:54 AM)pgrimes15 Wrote:  If you draw a black marble, then P(An) also equals 0.

Therefore the expression P(X l An) = P(X n An) / P(An) is undefined with zero in the denominator and therefore this situation cannot be analysed as you are attempting.

What you are doing is trying to make a leap between objective probability ( or frequentist probability which assigns precise liklihoods to the various outcomes of an activity such as throwing a dice ) and subjective probability which is synonymuos with "degree of belief".

Incidentally, with 3 binary activities such as throwing a coin, the possible outcomes are :

BBB, BWW, BBW, WWW.

The probabilities of these are :

BBB and WWW - 0.125

BWW and BWW - 0.375

not 0.25 each as you persist in stating. This is schoolboy maths and suggests to me that you are not especially rigorous when dealing with mathematical probability .

Regards

Grimesy

Grimesy, you are in error. An is always greater than 0 by definition. Think about it this way, An is n white marble draws in a row. P(An) is the probability of n white marbles in a row. As long as it is logically possible to draw a white P(An) is greater than 0 for any n. Is the probability of drawing 5 white marbles in a row greater than 0? Or 10 white marbles in a row? Or a billion? Yes, if the composition of the bin is unknown to you then the assumption that it is logically possible to draw another white marble is reasonable.

Also regarding the .25. You are wrong about that too. It is true that the probability of flipping 3 heads in a row is .125. It would be true that drawing 3 white marbles in a row has a probability of .125 but only if drawing a white marble itself had a probability of .5. However you don't know anything about the composition of the bin. In the example you are told there ar 3 marbles in the bin, but no information is given to you regarding the distribution of colors. So you can't


say there is a .5 probability of drawing a white. The only reasonable assumption is that all distributions are equally likely. In fac t th e example says that. Since there are only 4 possible distributions of the colors, and each distribution is equally likely, it stands to reason that each distribution has a .25 probability.

This feels a bit like pigeon chess . Mathematical probability cannot be applied to an infinite series of unknowns like your white/black ball scenario. Your assertion that P(X) decreases as n increases cannot be justified mathematically
Is this the heart of your strategy ? Get established that the probability of a black ball (miracle?) decreases over time, then suddenly invert this to "prove" the probability of God existing increases over time .

Regards

Grimesy
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20-03-2013, 09:35 AM
RE: Probability
Sorry. Should have said "infinite sequence" not "infinite series".

Regards

Grimesy
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20-03-2013, 10:54 AM
RE: Probability
(20-03-2013 05:27 AM)TheBeardedDude Wrote:  You have also never answered my question for how many colors were in my example and to prove you are correct.

The longer your simulation ran the probability that there were only 4 colors increased. This is true because the longer the simulation ran the fewer ways it became possible additional colors could be present. Since you told us there were more than 4 colors, I disregard the estimate of 4 colors and answer that the number of colors is 5 or more.
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20-03-2013, 10:57 AM
RE: Probability
(20-03-2013 05:26 AM)TheBeardedDude Wrote:  You've shown no examples of miracles with or without natural explanations. All you have done is mess up statistics and probabilities.

And probabilities are our estimates of our observations. Occurrences are either 1 or 0 in reality. So either something does or does not exist. Trying to argue statistics leaves you nowhere since you have given 0 observations to back up any claim.

Tell Chas the probabilities are estimates. When I told him that he was adamant they are not.
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