I had initially (last week) tended to ascribe the misinterpretation of the 600:1 odds calculation to Dr. Feuerverger. However, after carefully weighing Dr. Feuerverger's words on the Sunday show and after our e-mail exchange (posted above), I feel reasonably certain that the massaging of the interpretation (as it appears on the Discovery webpage and as depicted on the show) is the handiwork of the show's leadership, and not Dr. Feuerverger. On Ted Koppel's panel discussion it became very clear (to me at least) that several experts were misquoted and that expert opinion was stretched, to say the least. I feel pretty certain that Dr. Feuerverger was also misquoted and the significance of his 600:1 odds distorted without this consent.

Actually, I have no problem with Dr. Feuerverger's computation if it is INTERPRETED CORRECTLY. He has made an honest attempt to use simple enumerative mathematics to perform a very basic calculation founded on the (perhaps flawed) assumptions given him. Yes, we can debate those assumptions and claim that different assumptions would yield different probabilities. Fine! But the truth of the matter is that if we interpret Dr. Feuerverger's 600:1 odds correctly (as I suggested to him and he agreed - see my post above) we can get a far more relevant probability that the show's leadership just can't refute and which demolishes their statistical argument!

In fact, I think this approach may be a better one initially because it does not challenge the 600:1 odds but clarifies and builds upon it to make a point that the show's leadership will be compelled to accept - because their own statistician will support it! How can they suddenly disagree with their own statistician?

In the email exchange above, Dr. Feuerverger agreed that the 600:1 odds are to be interpreted as follows:

Suppose A is the event that the particular tomb in question is that of the NT Jesus family, and suppose B is the event that the NT Jesus family had a tomb (among the roughly 1,000 tombs found to date in the area). Then, Feuerverger's 600:1 odds claim means (per his agreement) that

P(A|B) = 599/600

(This is to be read, "The probability of A, given that B has occurred is 599/600", i.e., almost certain.) The symbol "P" represents the probability of the event following it in parentheses. A basic theorem in probability states that

P(A and B) = P(A|B) x P(B) (x is multiplication)

(Here, P(A and B) is the probability that BOTH A and B occurred.)

Note that Simcha and the media are either confusing P(A and B) with P(A|B) or they are claiming "strategic ignorance" by choosing to not acknowledge the difference - which is common sense to mathematicians and statisticians.

Now, let's try to calculate P(B). I'll make the following roughly right assumptions here based on my readings to date (correct me if you have more precise numbers):

Assumption 1: There were roughly 150,000 Jews (men and women) who lived in the time period in question in the geographic area in question

Assumption 2: The average Jewish family size at the time was 5

Assumption 3: There are about 1,500 family tombs (I recollect that 1,000 were found, so let us assume that there are another 500 not found) belonging to the population referenced in Assumption 1 above.

This means that there were roughly 150,000/5 = 30,000 Jewish families of whom only 1,500 had family tombs. So, a family PICKED AT RANDOM would have only a 1,500/30,000 = 1/20 chance of having a family tomb. Since Dr. Feuerverger has used "randomness" in all his calculations to date, we can use his very approach to claim then that the chance that the Jesus family had a family tomb to begin with is 1/20, and this is the P(B) we are after!

Now we can get back to our theorem:

P(A and B) = P(A|B) x P(B) = 599/600 x 1/20 = 599/12,000 = 4.99% or 5% approximately.

This means that the probability that the NT Jesus family had a family tomb which is the one is question is approximately 5%. Or, there is only a 1 in 20 chance that this is the NT Jesus family tomb - per Dr. Feuerverger's own 600:1 result and his own interpretation of it. How can Discovery refute it? If they do, they would be disagreeing with their own statistician!

Of course, even if the three assumptions above need some adjustments, the conclusion won't change significantly. We should not really quibble over whether there is a 1% or 2% or 5% or 15% chance because these numbers are ALL low enough to demolish the show's claim. Let's say the actual numbers in Assumptions 1, 2 and 3 above were off by a factor of two, and that we wound up with a 10% (1 in 10 chance) instead of 5% (1 in 20 chance) that the NT Jesus family had a family tomb which is the one is question. There's no damage done because any number below 35% or so would be inconclusive anyway, since it would show that there could have been three or more families whose tomb was the one found, and that shatters the show's claim.

Your opinions?

Joe