Freethought & Rationalism Archive

Doug Shaver · 12-29-2011, 01:20 AM

Quote:

Originally Posted by tanya

Put the mathematics books away. They are useless for this inquiry.

Sarah Palin couldn't have said it any better.

tanya · 12-29-2011, 08:30 AM

Quote:

Originally Posted by Doug Shaver

Your point is erroneous. Bayes' Theorem does not predict probabilities. It calculates them. And like any calculator, it is susceptible to GIGO. You can't get the right numbers out if you don't put the right numbers in.

Well written, Doug. I should have furnished a link, and written more precisely. My effort was sloppy.

Quote:

Originally Posted by tanya

My point then, was simple: Bayes' theorem is very useful in predicting probabilities

As Doug noted, above, this sentence is flawed. Let's try to fix it.

Quote:

Originally Posted by Oracle Data Mining Concepts

The Naive Bayes algorithm is based on conditional probabilities. It uses Bayes' Theorem, a formula that calculates a probability by counting the frequency of values and combinations of values in the historical data.

Bayes' Theorem finds the probability of an event occurring given the probability of another event that has already occurred. If B represents the dependent event and A represents the prior event, Bayes' theorem can be stated as follows

Prob(B given A) = Prob(A and B)/Prob(A)

To calculate the probability of B given A, the algorithm counts the number of cases where A and B occur together and divides it by the number of cases where A occurs alone.

I should have written, Bayes' theorem permits computation of the probability of a particular outcome, based upon assessment of historical data. The user of Bayes' theorem is thus able to predict, more objectively, the likelihood of a particular outcome attaining fruition.

Quote:

Originally Posted by tanya

Put the mathematics books away. They are useless for this inquiry.

Quote:

Originally Posted by Doug Shaver

Sarah Palin couldn't have said it any better.

I think you may have missed an earlier post, in which I had recommended that Toto get out her old mathematics books, if she wished to learn something about Bayes' theorem. I was teasing myself in the suggestion to remove the very books I had just encouraged Toto to read.

Doug Shaver · 12-30-2011, 12:54 AM

Quote:

Originally Posted by tanya

I think you may have missed an earlier post, in which I had recommended that Toto get out her old mathematics books, if she wished to learn something about Bayes' theorem. I was teasing myself in the suggestion to remove the very books I had just encouraged Toto to read.

Then I'll retract my insult. Please excuse me.

Quote:

Originally Posted by tanya

Quote:

Originally Posted by Oracle Data Mining Concepts

The Naive Bayes algorithm is based on conditional probabilities. It uses Bayes' Theorem, a formula that calculates a probability by counting the frequency of values and combinations of values in the historical data.
. . . . If B represents the dependent event and A represents the prior event, Bayes' theorem can be stated as follows

Prob(B given A) = Prob(A and B)/Prob(A)

To calculate the probability of B given A, the algorithm counts the number of cases where A and B occur together and divides it by the number of cases where A occurs alone.

I should have written, Bayes' theorem permits computation of the probability of a particular outcome, based upon assessment of historical data. The user of Bayes' theorem is thus able to predict, more objectively, the likelihood of a particular outcome attaining fruition.

You should also be more critical when evaluating your sources. ODMC calls it "Naïve Bayes" for a reason. Notice the statement "Bayes' theorem can be stated as follows [emphasis added]." The version of the Bayes formula they use may work fine for the purpose to which that company applies it, but for many other applications it is hopelessly oversimplified.

In particular, it cannot work for calculating probabilities of historical events because we're not working with numbers of "cases where A and B occur together" and "cases where A occurs alone." In those cases we have measureable frequencies of occurrences. All we have in history are unique events where frequency metrics are useless.

tanya · 12-30-2011, 01:14 AM

Quote:

Originally Posted by Doug Shaver

You should also be more critical when evaluating your sources. ODMC calls it "Naïve Bayes" for a reason. Notice the statement "Bayes' theorem can be stated as follows [emphasis added]." The version of the Bayes formula they use may work fine for the purpose to which that company applies it, but for many other applications it is hopelessly oversimplified.

In particular, it cannot work for calculating probabilities of historical events because we're not working with numbers of "cases where A and B occur together" and "cases where A occurs alone." In those cases we have measureable frequencies of occurrences. All we have in history are unique events where frequency metrics are useless.

http://betterexplained.com/articles/...bayes-theorem/

Here's another link:

Quote:

Originally Posted by Richard Lowry

Bayes' theorem describes the relationships that exist within an array of simple and conditional probabilities. Although its primary application is to situations where "probability" is defined according to the strict relative- frequency construction of the concept, it is sometimes also applied to situations where "probability" is constructed as an index of subjective confidence. In this latter form of application, the subjective confidence that one has in the truth of some particular hypothesis is computationally adjusted upward or downward in accordance with whether an observed outcome is confirmatory or disconfirmatory of the hypothesis.

My point then, is this: if "frequency metrics are useless", how can one employ Bayes' theorem?

Doug Shaver · 12-31-2011, 05:48 AM

Quote:

Originally Posted by tanya

My point then, is this: if "frequency metrics are useless", how can one employ Bayes' theorem?

As Carrier explains, for historical issues, one uses epistemic probabilities.

ApostateAbe · 12-31-2011, 11:06 AM

Quote:

Originally Posted by Doug Shaver

Quote:

Originally Posted by tanya

My point then, is this: if "frequency metrics are useless", how can one employ Bayes' theorem?

As Carrier explains, for historical issues, one uses epistemic probabilities.

Epistenic probabilities. Shucks, why didn't I think of that?

aa5874 · 12-31-2011, 11:40 AM

Quote:

Originally Posted by Doug Shaver

.....You should also be more critical when evaluating your sources. ODMC calls it "Naïve Bayes" for a reason. Notice the statement "Bayes' theorem can be stated as follows [emphasis added]." The version of the Bayes formula they use may work fine for the purpose to which that company applies it, but for many other applications it is hopelessly oversimplified.

In particular, it cannot work for calculating probabilities of historical events because we're not working with numbers of "cases where A and B occur together" and "cases where A occurs alone." In those cases we have measureable frequencies of occurrences. All we have in history are unique events where frequency metrics are useless.

Remarkably, this is the same Doug Shaver who declared "Bayes Theorem Rules".

Quote:

Originally Posted by Doug Shaver

..I have no idea what Abe will say, but Bayes' Theorem rules. Whatever contradicts it, is wrong.

Doug Shaver · 01-01-2012, 05:43 AM

Quote:

Originally Posted by aa5874

Remarkably, this is the same Doug Shaver who declared "Bayes Theorem Rules".

Not the least bit remarkably, you appear unable to distinguish "Bayes" from "Naive Bayes."

aa5874 · 01-01-2012, 06:20 AM

Quote:

Originally Posted by Doug Shaver

Quote:

Originally Posted by aa5874

Remarkably, this is the same Doug Shaver who declared "Bayes Theorem Rules".

Not the least bit remarkably, you appear unable to distinguish "Bayes" from "Naive Bayes."

Please, do not compound your error. Your posts are recorded.

Quote:

Originally Posted by Doug Shaver

You should also be more critical when evaluating your sources. ODMC calls it "Naïve Bayes" for a reason. Notice the statement "Bayes' theorem can be stated as follows [emphasis added]." The version of the Bayes formula they use may work fine for the purpose to which that company applies it, but for many other applications it is hopelessly oversimplified.

In particular, it cannot work for calculating probabilities of historical events because we're not working with numbers of "cases where A and B occur together" and "cases where A occurs alone." In those cases we have measureable frequencies of occurrences. All we have in history are unique events where frequency metrics are useless....

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