Posterior=prior

[Jean]

Hi,

I've tried PopABC to estimate migration rates between 3 pops (using
microsat data). I've set fairly wide priors for all parameters (not
knowing much a priori), except the mutation rate so that the simulated
data had realistic levels of heterozygosity. My intention was to
adjust the priors after test runs.

After runs of 1 million steps, discarding 99% of the simulated data
(rejection rate 0.01), the posterior distributions look like the prior
for basically all the parameters.

It seems odd that I can't get any information for any parameter. I
can't adjust the prior, since the posteriors are not informative.

Any ideas?

Thanks.

Jean

[Joao Sollari Lopes]

Hi Jean,

Sorry that I have been a bit absent from the Google Group.
Regarding your study, in my early work I notice that you can get away
with using as few as 1000 simulations and still use the regression-
step mentioned in Beaumont et al (2002). That means you can use a
rejection rate of 0.001. The regression-step is also quite a big help,
although close examination of the distributions should be performed.
More recently there has been suggestions of using sequential methods,
which allowed one to reuse the posterior distribution as the new
prior, thus increasing the efficiency on the use of the simulations.
However careful use of a weighting scheme is necessary so that you are
not overestimating your parameters.

More importantly though is to look at the heterozygosity and pairwise
differences of your own data to have a feeling of whether the data
contains enough information to perform parameter estimations. In any
case I think it is worth playing a bit with the regression-step and
tolerance intervals.

You can take a look at some recent and not so recent reviews to
understand better the possibilities and caveats of the method:

Lopes and Beaumont (2009) "ABC: A useful Bayesian tool for the
analysis of population data". Infect Genet Evol
Beaumont (2010) "Approximate Bayesian Computation in Evolution and
Ecology". Annu Rev Ecol Evol Syst
Lopes (2010) "10 years of Software development for approximate
Bayesian computation" in Int J Comput Res
Bertorelle et al (2010) "ABC as a flexible framework to estimate
demography over space and time: some cons, many pros". Mol Ecol
Csillery et al (2010) "Approximate Bayesian Computation (ABC) in
practice" Trends Ecol Evol

Hope that helps,
Joao