HierarchicalBVARResult.log_marginal_likelihood

HierarchicalBVARResult.log_marginal_likelihood: float

Log marginal likelihood of the sample given the prior, in closed form.

\(\log p(Y \mid Y_d) = \log p(Y, Y_d) - \log p(Y_d)\) when the prior contributes dummy observations \(Y_d\), and \(\log p(Y)\) otherwise; the dummy rows are part of the prior, so their contribution is divided out and the number stays comparable across priors with different dummy content. Differences across priors fitted to the same sample are log Bayes factors. It is exact – the matrix-variate-t normalizing-constant ratio – so marginal_likelihood() reports it with zero Monte Carlo error. It is not a log likelihood and has no parameter count attached; there is no llf on this result.