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<p>. Suppose one wants to approximate the joint density of outputs and parameters . Bayes' formula reads:</p>

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:</p>

<p>The joint is equal to the product of the likelihood and the prior and by <a href="page.php?w=Bayes%27_theorem">Bayes' rule</a>, equal to the product of the <a href="page.php?w=marginal_likelihood">marginal likelihood</a>  and <a href="page.php?w=Posterior_probability">posterior</a> . Seen as a function of  the joint is an un-normalised density.</p>

<p>In Laplace's approximation, we approximate the joint by an un-normalised</p><p>
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