Simon,
I think that mixture models, eg of univariate normal distributions, may
give you plenty of examples. Such models have unbounded likelihood where
a component is used to fit a sample point with mean equal to the point
and sigma tending to zero. I'm guessing that putting priors on the
sigmas which prevent them from becoming too small could change the
infinite likelihood to a finite posterior mode, with well-separated data
points leading to a posterior with as many modes as there are data points.
Cheers, Murray Jorgensen
Simon Wilson wrote:
> Dear Allstat,
>
> I am looking for some examples (can be as simple or as complicated as they want) of where fitting a
> model to data give multi-modal posterior distributions. This is to try out a couple of different
> procedures for exploring such posterior distributions.
>
> Coming across such examples is harder than I thought it was going to be when I started to look.
>
> Any suggestions gratefully received.
>
> Regards,
>
> Simon Wilson
--
Dr Murray Jorgensen http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: [log in to unmask] Fax 7 838 4155
Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 1395 862
|