Instruction and Periodic Accountability Assessment (IPAA) model.

We need to support a verison of the MML algorithm for temporal models.

Assume we have 

X[,,t-1] - f(X[,,t-1],U[,,t],CGMP[t],Z[,,t],deltaT) -> X[,,t] 
   |                                                    |
h(X[,,t-1],Q[t-1],EMP[t-1],Z[,,t])               h(X[,,t],Q[t],EMP[t],Z[,,t])
   |                                                    |
   V                                                    V
Y[,,t-1]                                              Y[,,t]

X[,,t] is a multivariate latent variable.  Dimensions are persons,
competency and time.

Y[,,t] is a multivariate observable variable (may be missing values).
Dimensions are person, observable, and time.

Z[,,t] is a multivariate collection of background variables.
Dimensions are person, variable and time.  Note that some of these
variables may be constant over the time period involved.

f is the competency growth process.
f0 is a special process which takes only a set of parameters as inputs
and gives the initial distribuiton of the latent variables X[,,0].

CGMP[] is a list of Proficiency Model parameters.  The parameters at
time 0 have special interpretation (and probably a different
structure).

To support Bayesian estimation, we will define a proficiency model
prior distribution 
CGMP[t] ~ g(CGMHP) for t>0
CGMP[0] ~ g0(CGMHP)

U is the "action" taken at each time point.

As a simplifying assumption, we will assume that the process is time
invariant, except for the constants U which act as a driver function.

-------------------

h is the evidence model.

It gives the distribuiton of the observable Y, as a function of the
latent variable X, a set of parameters, and a constant Q which
describes the assessment design at each time point.  This setup
essentially allows for a different Q-Matrix describing the design at
each time point.

EMP[t] ~ c(EMHP)

-----------------

The variables Q, U are decision variables and are set by the
curriculum designers.

Three classes of problem arise in this framework:

1) Filtering/Forecasting --- Given a set of observables Y, and
   decision variables Q and U, and parameters, EMP, CGMP, estimate
   X[t].  This problem is "filtering" if Y[t] is observed and
   forecasting if Y[t] is not yet observed.

2) Parameter estimation.  Given a set of observables Y, and decision
   variables Q and U, estimate EMP and CGMP.

Note that given a realization of X, EMP[t] and CGMP[t] are all rendered
independent.  This supports EM and MCMC like algorithms over this
space.

3) Decision optimization.  Find U and Q to maximize some reward
   generally subject to some constraints.

Note that we must generally by able to sample and calculate
likelihoods (up to a constant) from f and h (as well as c and g).