To try to fix my little issue (2012 05 17) with using all the papers I printed out to learn hidden markov models and because I had to sit in a presentation (that really only contained about 10 minutes of material) for 4 hours yesterday I figured I'd give them a shot. Problem is, I took the wikipedia route which sent me to simple markov models which made me realize I didn't understand those enough. I dug in. Here is a free textbook that starts with some very practical applications of markov models in the real world. It's a great intro! Reading that made me realize that I keep forgetting what stochastic means so I thought I'd review today (by typing it out here) to see if I still understand it.
Something is stochastic when it isn't deterministic, meaning it can't be described by a solid equation and always end with the same value. Instead, it will take on a range of values described by some sort of distribution because it is affected by random forces or outside actions.
Think of it as the result of a function.. something like y=mx+b. in a deterministic model, plugging in x and b always gives the same y. in a stochastic model, x and b are not just numbers, they're distributions so the Y is kind of random but it should typically lie within some range. That range can be calculated given the distributions of y and b.
What does that mean for markov models? They're a way to model these sort of non-deterministic problems that vary over time. That is, a stageful model where the current thing moves from state to state with a known probability. I'd try to type out an example, but I couldn't do it justice (just yet) have a look at the first chapter of that book I linked to above if you're interested.
How does this apply to hidden markov models? Well, those are models that you use when you are pretty sure there are hidden, or unknown "states" but you are unable to find the probability distribution of reaching those states.
Reasons why I'm interested: This is a graph based problem which i sort of love. It's rooted deep in probabilities which I am trying to get a handle on because, well, they're useful. And, finally, I have no idea why I'm working on this. I just am. There is this intersection between stats, probability, finance, machine learning, computer modeling and analysis that I'm trying to crack.