What business cases are there for using Markov chains? I've seen the sort of play area of a markov chain applied to someone's blog to write a fake post. I'd like some practical examples though? E.g. useful in business or prediction of stock market, or the like...
Edit: Thanks to all who gave examples, I upvoted each one as they were all useful.
Edit2: I selected the answer with the most detail as the accepted answer. All answers I upvoted.
I've seen spam email that was clearly generated using a Markov chain -- certainly that qualifies as a "business use". :)
We use log-file chain-analysis to derive and promote secondary and tertiary links to otherwise-unrelated documents in our help-system (a collection of 10m docs).
This is especially helpful in bridging otherwise separate taxonomies. e.g. SQL docs vs. IIS docs.
Hidden Markov models are based on a Markov chain and extensively used in speech recognition and especially bioinformatics.
I know AccessData uses them in their forensic password-cracking tools. It lets you explore the more likely password phrases first, resulting in faster password recovery (on average).
There is a class of optimization methods based on Markov Chain Monte Carlo (MCMC) methods. These have been applied to a wide variety of practical problems, for example signal & image processing applications to data segmentation and classification. Speech & image recognition, time series analysis, lots of similar examples come out of computer vision and pattern recognition.
If commercial graphics software counts, there are some Ray Tracing systems that implement Metropolis Light Transport (invented by Eric Veach, basically he applied metropolis hastings to ray tracing), and also Bi-Directional- and Importance-Sampling- Path Tracers use Markov-Chains.
The bold texts are googlable, I omitted further explanation for the sake of this thread.
We plan to use it for predictive text entry on a handheld device for data entry in an industrial environment. In a situation with a reasonable vocabulary size, transitions to the next word can be suggested based on frequency. Our initial testing suggests that this will work well for our needs.
I recently stumbled on a blog example of using markov chains for creating test data...
http://github.com/emelski/code.melski.net/blob/master/markov/main.cpp
Markov chains are used by search companies like bing to infer the relevance of documents from the sequence of clicks made by users on the results page. The underlying user behaviour in a typical query session is modeled as a markov chain , with particular behaviours as state transitions... for example if the document is relevant, a user may still examine more documents (but with a smaller probability) or else he may examine more documents (with a much larger probability).