Dear all,
Running monte-carlo simulations for two different models, we obtain their \chi^2. Now, if you have two different models, m_{1} and m_{2} and their likelihood L_{1} and L_{2}, is there an easy way to interpret the differences in the likelihood between these models ? For example, does it exist a value, below which the difference is such that one could say that the models are equally good fits ?
References are welcome.
Thanks,
Marc
cosmological models and likelihood
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marc vonlanthen
- Posts: 11
- Joined: May 29 2009
- Affiliation: university of geneva
cosmological models and likelihood
Keywords for the general topic are "model selection criteria", and there's a wealth of literature available. Some things to start looking at might be:
http://en.wikipedia.org/wiki/Bayesian_i ... _criterion
http://en.wikipedia.org/wiki/Akaike_inf ... _criterion
http://arxiv.org/abs/astro-ph/0602378
The latter has a statistic which is nicely calculable from MCMC chains and the authors demonstrate how it works in a cosmological context, so it might be particularly useful to you.
http://en.wikipedia.org/wiki/Bayesian_i ... _criterion
http://en.wikipedia.org/wiki/Akaike_inf ... _criterion
http://arxiv.org/abs/astro-ph/0602378
The latter has a statistic which is nicely calculable from MCMC chains and the authors demonstrate how it works in a cosmological context, so it might be particularly useful to you.