MCMC with user-defined LnLike

[Eric Hack]

Hi

Thanks for the documentation.  I did not have the proper translation tools.

In an earlier message, I asked:
- Can a user-defined likelihood function be easily implemented in
MCSim?
You wrote:
it depends what you want to
  do with it. Assume you want the likelihood for one data point. You
should be able to represent your data
  as an input function, taking the observed value at a prescribed
observation time. Then the likelihood
  should be representable as a standard function of the parameters,
state and output variables and that data.
  Now if you want to compute the total likelihood for a dataset you
have to find a way to (say) form the product
  of individual datapoints likelihood. To do that you can setup an
output variable to act as an accumulator:
  this_point-like = f(params, this_data)
  total_like = total_like * this_point-like
  Just make sure that it behave correctly. That should be easy for
discrete-time sims. For integration it's more difficult
  because Calc-Deriv (the "model") may be called several times within
an integration step and the product would be formed
  too often (to avoid that I tend to use control input function of the
Spikes form).
  An alternative is to code the product in the "yourcode.c" file. The
TransformPred function is called after a Monte Carlo
  simulation and can be used for that. If you are not using MC
simulations you may need to add calls to TransformPred
  elsewhere in the program.

Thanks for these helpful tips.  The accumulator was part of the question.

I am also wondering if this likelihood function can be used in MCMC 
simulations?  I have looked briefly at a paper describing this model, and I 
think it is essentially the MVK 2-stage clonal growth cancer model.  The 
likelihood contribution is different for survivors, fatal tumors, and 
incidental tumors.  I believe that the contributions work out as follows:
 S(t)=exp(-H(t)) for the survivors,
 h(t)S(t) for the fatal tumors, and
 S(t)F(t) for the incidental tumors, 
 where S(t) is the survival function, H(t) is the cumulative hazard function, 
h(t) is the instantaneous hazard, and F(t) is the cumulative probability of a 
malignant transformation.  Each type of contribution is based on H(t), a 
function of the number of 2nd stage mutations.

Is there an easy way to set this model up in MCSim to do MCMC analysis of the 
data?  My first guess was to modify the LnLikeData, or add a user distribution 
to LnDensity and put the function in 'yourcode.c' or wherever the other 
likelihoods are calculated.  The thing about adding a distribution to LnDensity 
is that I did not know if 'mod' would let me get away with an unknown 
distribution name.  Can I add it to a list of keywords someplace?

You may be aware of more appropriate distributions that I have not thought of 
for these data, so any suggestions are welcome.

Thanks again,
Eric



 
C. Eric Hack

Toxicology Excellence for Risk Assessment (TERA)
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Suite 409
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