My background is in applied math, not stats, so forgive my nontechnical terms throughout. For a work presentation on Monday I have to prepare a brief example of forecasting time-series data with Bayesian techniques. In the past I did some probability on networks, percolation theory etc. and I've reread a lot of material on random walks on graphs, and Markov theory, and MCMC etc. I think I want to use OpenBUGS or JAGS or something similar (it's supposed to be using MCMC techniques).
I'm stuck on how to model this load data. Essentially I have hourly usage data that peaks at certain times during the day. There are some obvious trends in the data, like peaks during morning or night, but not middle of the day when people aren't home, or at night when everyone's asleep. That's on the day-scale. On the week-scale there are for example, those who have higher usage on the weekends, and maybe they're not home on Monday and Tuesdays so usage is particularly low. There are seasonal scales (so usage averages are lower/higher depending on the month of the year), and all sorts of random variations in the data, like when people are on vacation for example.
I might not manage to capture all of those phenomena. But in general, how should I model this? I mean, there's inherent state in the system, so I feel I might want to model load on Monday as a separate variable to load on Tuesday, etc. assuming the usage is a function of some weekly routine. But then I might be decoupling things that I shouldn't. I don't know how to go about this at all. I don't see where the Markov chain that I might model the system with (since the number of states seems to be small) can be coded into BUGS. I'm pretty lost here.
I was looking for a basic example that I can build on. I don't have time to read an entire book, so I'm kind of just looking to hack together something reasonable based off existing examples. I just need some nice plots and to show that the Bayesian approach can be better than just averaging (or something similar). It would also be nice to understand Bayesian modelling a bit better.
Any pointers would be appreciated.