An analytical approach to Bayesian evidence computation. (arXiv:2301.13783v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Garcia_Bellido_J/0/1/0/all/0/1">Juan Garcia-Bellido</a>
The Bayesian evidence is a key tool in model selection, allowing a comparison
of models with different numbers of parameters. Its use in analysis of
cosmological models has been limited by difficulties in calculating it, with
current numerical algorithms requiring supercomputers. In this paper we give
exact formulae for the Bayesian evidence in the case of Gaussian likelihoods
with arbitrary correlations and top-hat priors, and approximate formulae for
the case of likelihood distributions with leading non-Gaussianities (skewness
and kurtosis). We apply these formulae to cosmological models with and without
isocurvature components, and compare with results we previously obtained using
numerical thermodynamic integration. We find that the results are of lower
precision than the thermodynamic integration, while still being good enough to
be useful.
The Bayesian evidence is a key tool in model selection, allowing a comparison
of models with different numbers of parameters. Its use in analysis of
cosmological models has been limited by difficulties in calculating it, with
current numerical algorithms requiring supercomputers. In this paper we give
exact formulae for the Bayesian evidence in the case of Gaussian likelihoods
with arbitrary correlations and top-hat priors, and approximate formulae for
the case of likelihood distributions with leading non-Gaussianities (skewness
and kurtosis). We apply these formulae to cosmological models with and without
isocurvature components, and compare with results we previously obtained using
numerical thermodynamic integration. We find that the results are of lower
precision than the thermodynamic integration, while still being good enough to
be useful.
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