When 2 + 2 = 5...

Check Dembski’s Explanatory Filter Delivers a False Positive at the Panda's Thumb. Matt Young criticizes Bill Dembski's explanatory filter methodology for determining intelligent design:

Dembski’s vaunted explanatory filter is no more than a flow chart designed to distinguish events of low probability. If the probability of an event is low enough and if Dembski can discern a pattern, then he concludes that the event must have been the product of design. Dembski admits that the explanatory filter may produce a false negative (fail to infer design where design exists) but claims it will never produce a false positive (infer design where none exists). In this article, I will give a real example wherein the explanatory filter could have yielded a false positive. According to an article in Science [Quinn Eastman, “Crib Death Exoneration Could Usher in New Gene Tests,” Science, 20 June 2003, p. 1858], a British woman lost three babies to sudden infant death syndrome (SIDS or crib death) within four years. The Crown Prosecution Service applied the explanatory filter as follows: One death is tragic; two deaths are suspicious; three deaths are murder. The woman was prosecuted. According to the BBC, the rate of SIDS in England and Wales is less than 0.5 death per 1000 live births. In effect, prosecutors reasoned that the probability of three SIDS deaths was 0.00053, or approximately 10-10. They concluded that this probability was so small that a design inference was warranted, and the woman was charged. What the prosecutors did not know or ignored was that SIDS may be a genetic disease that runs in families. Indeed, the woman’s grandmother testified that three of her children died of unexplained causes before the ages of 6 weeks (in the 1940’s, before SIDS was recognized).

I posted a comment questioning the relevance of using an event with a probability calculated at 10^-10 as indicative of the failure of Dembski's explanatory filter. Dembski stated, in Intelligent Design,

...The French mathematician Emile Borel proposed 10^-50 as a universal probability bound below which chance could definitely be precluded - that is, any specified event as improbable as this could not be attributed to chance. ...In The Design Inference I justify a more stringent universal probability bound of 10^-150 based on the number of elementary particles in the observable universe, the duration of the observable universe until its heat death and the Planck time.

It would appear that an event with a probability of 10^-10 being falsely attributed to design falls outside the boundary of 10^-150 proposed by Dembski. Simply put, 10^-10 ≠ 10^-150. One response claimed that the probability could be met as such:

If, for example, the genetic disease makes it 100% likely that any child born from that mother will die, whereas the overall incidence of the disease is not 5 per thousand but 1 per million, and the mother had 25 babies which all died, then that meets the probability level of Dembski’s filter.

The only problem with that explanation is that the mother didn't have 25 babies (to her overwhelming joy), so the example is conjecture. Another comment was:

The 1e-150 number is Dembski’s “universal probability bound”. Probabilities smaller than this do not require justification of a “local small probability” bound.

This was a bit confusing since there was no reference I found in Dembski's book differentiating between a universal and local small boundary. The good news is that Dembski's work is being tested against data from current research.