Objet : Help-mcsim digest, Vol 1 #139 - 1 msg

[Frédéric BOIS]

Hi,

If you want to do:

Distrib (Sigma_V, InvGamma, 2, 0.1823);
Distrib (Mean_V, Normal, 0.1, 1.2);  # values are abitrary
Distrib (V, TruncLogNormal, exp(Mean_V), exp(Sigma_V), 1e-6,10);

you have a problem with V, the way to do it is to define a variable Log_V and 
do:

in the model definition file, define V and compute it in the Scale section as :
V = exp(Log_V);

in the input file:
Distrib (Sigma_V, InvGamma, 2, 0.1823);
Distrib (Mean_V, Normal, 0.1, 1.2);  # values are abitrary
Distrib (Log_V, TruncNormal, Mean_V, Sigma_V, -14, 2.3);

This way, V will have the lognormal distribution you want.
Note that we used InvGamma as priors for variances, as usually made, rather 
than for SDs.
If you use a variance you would do:

Distrib (SigmaSquare_V, InvGamma, 2, 0.1823);
Distrib (Mean_V, Normal, 0.1, 1.2);  # values are abitrary
Distrib (Log_V, TruncNormal_v, Mean_V, SigmaSquare_V, -14, 2.3);

using the TruncNormal_v distribution specification.

I hope this helps.


Frederic Bois




>>> <address@hidden> Vendredi 25 octobre 2002 11:42:37 >>>
Date: Fri, 25 Oct 2002 02:46:42 -0400 (EDT)
From: Suhrid Balakrishnan <address@hidden>
To: address@hidden 
Subject: McSim query 

Hi,

I'm trying to do some analysis with McSim 4.1 and I'd like to specify
priors in a heirarchical fashion exactly as the authors of the software
did in their 1996 paper - Bois, F. Y., Gelman, A., Jiang, J., Maszle, D.,
Zeise, L. and Alexeef, G. (1996). Population toxicokinetics of
tetrachloroethylene. Archives of Toxicology 70:347-355. also used in
Gelman, A., Bois, F. Y. and Jiang, J. (1996). Physiological
pharmacokinetic analysis using population modeling and informative prior
distributions. Journal of the American Statistical Association
91:1400-1412.

The problem I'm facing is that I see no way to easily incorporate the
Lognormal hierarchical prior (mu*, Sigma*) (where mu* and Sigma* are the
geometric mean and standard deviations respectively = exp(mu) and
exp(Sigma)) with further conditional distributions on mu ~ Normal (M,S)
and Sigma as inverse-gamma(a,b) (a, b being the shape and scale
parameters, respectively) in the McSim framework. 

I've tried a number of things including toying with levels, exponents,
outputs, scaling etc. and nothing seems to work.

What one desires, I presume, is a way to specify the following
hierarchical distributions in the simulation file (which the authors used
in both references above):

Distrib (Sigma_V, InvGamma, 2, 0.1823);
Distrib (Mean_V, Normal, 0.1, 1.2); # values are abitrary
Distrib (V, TruncLogNormal, exp(Mean_V), exp(Sigma_V), 1e-6,10);

But the above formulation isn't allowed by McSim (no exponentiation
alllowed in the Distrib specification).

Or an alternative way to get the same effect - is there something obvious
that I'm not seeing? Presumably, there is a way to do this, I would be
greatly appreciative if anyone would let me know how.

Thanks in advance,

Sincerely,

Suhrid 







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