'stretching' a binomial variable

Hi,

Im carrying out some Bayesian analysis using a binomial response variable
(proportion: 0 to 1), but most of my observations have a value of 0 and many
have very small values (i.e. 0.001).  I'm having troubles getting my MCMC
algorithm to converge, so I have decided to try normalising my response
variable to see if this helps.

I want it to stay between 0 and 1 but to have a larger range of values, or
just for them all to be slightly higher.

Does anyone know the best way to acheive this?  I could just add a value to
each observation (say 10 to increase the proportion a bit, but ensuring it
would still be between 0 and 1) - would that be ok?  Or is there a better
way to stretch the values up?

Sorry - i know its not really an R specific question, but I have never found
a forum with as many stats litterate people as this one :-)

Cheers - any advice much appreciated!

nicola

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