Sally Clark, 1965-2007

Sally Clark, the solictor wrongly imprisoned between 1999 and 2003 for the murder of both her young sons, died this morning, according to BBC News.

Her conviction, and subsequent acquittal, became very famous in the UK, particular because of some of the statistics offered by an expert witness, Sir Roy Meadow. Meadow’s evidence was, basically, that the chance of both of Sally Clark’s sons dying of natural causes was so slim, that one had to assume that they were murdered. The structure of his argument was as follows:

The chance of a randomly chosen child dying or Sids (Sudden Infant Death Syndome, popularly known as cot death) is about 1 in 3000.

Amongst non-smoking, older parents, with at least one wage, this rises to about 1 in 8500.

The chance of both Sally Clark’s sons dying of Sids is about 1 in 8500×8500, or 1 in 73 million.

The chance that the two boys were not murdered is 1 in 73 million.

The Optional Stopping Theorem

Someone once asked my what my favourite theorem was. This seemed an odd question. I sort of blustered and said “bluh, uh, optional stopping?”, although later wondered if I should have gone for max-flow min-cut.

Sometime later, I decided to make a blog. “Optional Stopping” seemed to be a terribly good title for two reasons: 1) because it is Officially My Favourite Theorem, and 2) because it’s hi-lar-ious pun on the fact that I only write blog posts when I’m bored with doing proper work. Optional stopping. I choose to stop work. Geddit? Oh, never mind.

So, in case you don’t know, It thought this would be a good opportunity to explain what the optional stopping theorem is.

In this article, we look at stopping times, martingales and the OST itself, before giving a couple of (I think) nifty applications to random walks.