Dear Colleagues,

I am having a few problems expanding upon example 9 in Nonmem 7.2.  This is the 
one with the SDE plug-in.  I have a model with 3 differential equations and two 
observation compartments.  One of the differential equations is the parameter 
that I want the process noise on.  The SDEs look like this:
kmet = exp(A(3))
dAdt(1) = kin - kmet*A(1)
dAdt(2) = kmet*A(1) - kel*A(2)
dAdt(3) = 0 + SGW3 * dW ;

Observations are:
F(1) = A(1)/V
F(2) = A(2)/V

Can someone please provide advice on how to code this model with the SDE 
plug-in?  Here are the points as I understand them:

·         I have 3 "base ODE equations" which should be DADT(1,2,3).

·         I have 2 "prediction equations" which should be DADT(4,5).

o   e.g., DADT(4) = A(1)/V

o   the actual derivatives (dF_i / dA_j) required by the EKF will be computed 
from these equations entered in the ODEs, or so promises the commentary in the 
example

·         I need to have 9 additional compartments to house the state 
correlation matrix

o   Or is it only 6, the upper triangle?

o   What happens if I have too many?  The integrator just runs more slowly?

o   I don't need to code anything for these, the plug-in will do all the work.

·         I have 3 "SGW" parameters that get stored in a local array and sent 
into the filtering code.  One for each state.

o   Can I set the first two to zero, so I only have SGW3 as a THETA parameter?

o   Shouldn't there be 9 of these?  Or does this mechanism only handle a 
diagonal scale matrix for the independent Wiener processes?

·         I need to pass the number of ODEs and Observations into SDE_DER

o   After reviewing the FORTRAN code, it looks like the order of the parameters 
is reversed from that in the comments.
CALL SDE_DER(DADT,A,DA,IR,SGW, NDES, NOBS)

§  NDES=3, NOBS=2

§  DADT, A, and DA are reserved variables (derivatives, state variables, and 
system jacobian).

§  What is IR?

·         I'm unsure how the $ERROR block is working (Y = IPRED+W*EPS(1) + 
WS*EPS(2)):

o   Is WS a system variable?  If not, how does the SDE_CADD routine update it 
as promised in the commentary.

o   How does EPS(2) enter the fray?

o   Does it matter which EPS is assigned as the process noise term?  Must it be 
the final one, or always the second one?  Can there be more than 2 EPS in the 
model?

o   Is this a red herring since the R matrix is what really matters for the 
likelihood computation and that is being constructed by SDE_CADD?

Thanks in advance for any assistance you can render.

Jason Chittenden
Scientist

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