The advantage is obvious as you concentrate on the situation rather than method so that you look more practical. The disadvantage is also equally appealing.. though you understand the significance of the physical problem at your hand.. you will feel very less about the underlying abstract and generalised concept. In other words, you don't feel the full power on anlysis method that gave you the result.
When I frist read about the Monte-carlo simulations.. I used to think, where the hell these things really work. My mistake was simple.. I thought about the physical situation.. but not about the method that powered Monte-Carlo..
What the hell I'm talking about?
For those of you who doesn't know.. about this.. let me tell you simply... We have different different states in phase space. You can define a probability to get a specific state from another specific state. Where this probability only depends on the two states of interest and it doesn't depend on history.
How can we use this.. if you know the probability associated with different states, then you can generate these states starting from any single given state. This is used in monte-carlo..
where we know the probability as function energy of the given state.
There is another thing called Hidden Markov Model.. which is used in continuous voice recongition applications. The idea is simple. You don't know which state you are in.. but you see the output (or result ) of the state. There results can be possible with any state with some given probability. In continuous voice recognition applications.... the output is the word and the state is the vocal state. You train your system to get the asssociated probabilities.. and find out the words from previous words. It is much more involved than this.. I should be correct with the theme..
variations of HMM are used for a lot of pattern recoginition techniques.. for little more detials wikipedia is helpful.
There one more thing called.. LZMA compression.. if you guys know about zip compression utility.. this LZMA is also.. a data compression algoritm based on some sort of Markov-Chains..
I'm not really sure about the internals of this.. but should be interesting!!
Anyways... lot more to learn and understand..
ps: Though I don't regret my being with this company, my progress in the tech. side makes me sad.. :(
Update (input from a friend) : skipping the italicised portion of this post should make more sence :)