Re: [Help-mcsim] R?p. : MCSim and mixture models

[Bill Harris]

"Frederic BOIS" <address@hidden> writes:

> Hi Bill,
>
> I assume that by mixture you mean "model A" with probability P(A),
> "model B" with probability P(B) etc., and in an MCMC context.

That's correct, Frederic.  See section 13 of
http://mc-stan.org/manual.html for examples.  Stan has a simplex type,
so you can define a vector of length k ≥ 2 and know it will sample it in
ways that ensure that the sum of its components is always 1.  

> I have never done that. I would setup an indicator variable, condition
> the code on its value... 

In your work, I might imagine setting up a mixture model to model
outliers and good data or perhaps even a diseased and a healthy state,
but that may never come up.

In my case, I'm modeling electrical power flow into a building as
measured, say, once per hour.  I'll draw a picture of possible data with
words. 

  In state 1, the power is lognormally distributed around a low level.
  This represents base level lighting, electronics, and the like.

  In state 2, the power jumps up to a very high level and then decays
  exponentially to a medium high level.  This may represent an air
  conditioning system turning on and drawing a lot of current at the
  start and then less as the building cools to a more normal
  temperature.

  At some time, the air conditioning turns back off, and power declines
  rather quickly to state 1 conditions.  (In my case, I might often have
  more than 2 states.)

I'd like to have a model that

- Captures the switching between the states.

- Accommodates the autocorrelation in the data.

- Tracks the exponential decay.

I could model the thermostat or control system that runs the air
conditioning, but it may be controlled by a clock, and I'd like to be
able to detect the timing rather than enter it by hand.

I'll try what you showed soon, I hope.

Thanks,

Bill
-- 
Bill Harris                  
Facilitated Systems
http://makingsense.facilitatedsystems.com/