On rereading this just now, I just had to laugh. Two reasons I suppose. First of all, the article is really about Markov chains (my original title was just that), and I spend just 3 paragraphs right at the end talking about speech recognition. I think my editor was a smidge too enthusiastic about the speech recognition part. Secondly I note that I talk about random walks in a couple of places – even Gambler’s Ruin – a topic I skirted just recently here. It certainly sounds like I knew back then what I couldn’t work out a few days ago; so maybe there’s something to all this forgetting stuff as you grow older.
Where was I? Oh, yes, Markov chains. In essence, they’re a description of a finite state machine with the transitions between states governed by some probability model. What can we determine from such a model? Well, there’s the possibility of calculating the probabilities for a steady state after a large number of transitions for a start. Using the Viterbi algorithm, you can try to determine the transition probabilities for a “hidden” model from a series of state changes. The standard (read: old) method for pricing equity options uses a Markov chain model known as the Black-Scholes algorithm (and, boy, does that take me back to the time I worked for the swaps trading desk at Deutsche Bank).
This article first appeared in issue 301, December 2010.
You can read the PDF here.
(I write a monthly column for PCPlus, a computer news-views-n-reviews magazine in the UK (actually there are 13 issues a year — there's an Xmas issue as well — so it's a bit more than monthly). The column is called Theory Workshop and appears in the Make It section of the magazine. When I signed up, my editor and the magazine were gracious enough to allow me to reprint the articles here after say a year or so.)
Bush, Kate - Top of the City
(from The Red Shoes)