Sunday, August 14, 2005

Village of the Twins and probability bounds

In the Telegraph Magazine, dated 23rd July 2005, by Peter Foster (I searched their website, but I couldn't find an internet reference), there was an article about a village in India which has seen an explosion in the birth of identical twins. The rate of identical twin birth there is ten times the global average - since 1967, 34 sets of identical twins have been born in a village of 900 people.
The molecular biologists think it might be a miracle twinning gene, the social scientists suggest the common practice of inter-marrying might be the cause. Others say there is something strange in the water, while the rest are content to ascribe it to a 'blessing from God' or, for the Hindus, perhaps a gift from Lord Ram, who had twin boys.

What interested me about this was the level of improbability. After all, the world is very big - there are doubtless much larger communities which have no identical twins in - does this lie within statistically reasonable bounds?

So I sat down with a pen and paper (to revise the probability theory) and a spreadsheet (to do the calculations!). If the probability of identical twins arising from a pregnancy are 1 in 300, and there have been 850 births in the village (for the sake of argument) we can determine the probability of exactly a specific number of twins being born - and hence by addition, the probability of this number of identical twins or less being born. The probabilities of 0 sets of twins through to 7 sets of twins being born are as follows: 0.0585; 0.17; 0.24; 0.22; 0.16; 0.09; 0.04; 0.02. The most likely outcome is two sets of identical twins. The probability of there being less than 10 sets of identical twins is 0.9993.

So for there to be 10 sets of identical twins in a population of 900 is not that improbable, really. Seven in every 10000 communities of this size will have this number of identical twins.

However, there is less than one in 1013 chance - the limit of my computer's accuracy, calculating in a simplistic way - of there being more than 22 sets of twins. If there are about 7x109 people in the world, there is less than a one in a million chance that a group of 900 people anywhere in the world will have 22 sets of twins. For each additional pair of identical twins, the probability drops by an order of magnitude. We are nowhere near the 10-150 universal improbability bound - and yet scientists are (rightly!) confident that there is a phenomenon here that requires explaining.

An inference is taking place here, based on low probability. Nobody has any doubt that this is a reasonable mathematical and scientific process. It is reasonable for the same process to be carried out for other specified events of low probability.