= Posterior covariance matrix
{title2=$\Sigma_y=\mathbb E[(\theta-m_y)(\theta-m_y)^T\mid y]$}
For a vector parameter with finite second moments and <posterior mean> $m_y$, the posterior covariance matrix records its uncertainty and linear dependence after conditioning on the observations. Its diagonal entries are <posterior variances>. In a regular locally flat-prior <normal distribution> approximation it is the inverse observed information. A <quadratic form> has posterior expectation equal to the form at the posterior mean plus the trace of its matrix times this covariance.
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