This book by J.R.Norris is a classic reference for Markov Chains. It is unlikely that any paper on Markov chains in the recent times does not mention this book somewhere in the paper. I will try to attempt to summarize the main chapters of the book in this post. The book starts off by saying that Markov process are random processes that don’t retain memory. When the state-space is restricted to finite or countably many, these processes are called Markov Chains.

Via Delhi-IBSEN festival 2010 : This play is an adaptation of Henrik Ibsen’s “Lady from the sea” and is directed by Ila Arun. The story is told in the folk form as the narrative through the balladeers, Bhopa and Bhopi, traditional story-tellers from Rajasthan, who use the Phad, or a painted scroll to tell their stories. The play begins with the Bhopi telling her husband that she had discovered a new phad, called ‘Ibsenji ka phad’, in her late father-in-law’s trunk.

http://video.ted.com/assets/player/swf/EmbedPlayer.swf

I am hooked on to “Markov Chains” these days and they seem to fascinate me as the applications are in almost every field that I look at. I happened to go over Page Rank algo. From a Markov chain’s perspective, the algo can be summarized in 2 steps Step 1 : Represent a random surfer’s movement as a Markov chain Here N is the total number of pages indexed by Google, Q is a transition matrix( irreducible, a periodic) that captures the transition probability of moving from one page to another , p is the page rank of the pages on the internet and alpha is adjustment factor to take in to consideration the inherent importance of a page.

Real Statistics is not primarily about the Mathematics which underlies it: common sense and scientific judgment are more important. But, there is no excuse for not using the right Mathematics when it is available. - David Williams