Extracting Log of Marginal Likelihood — compute

Compute log of marginal likelihood of Bayesian Fit

Usage

compute_logml(object, ...)

# S3 method for class 'bvarmn'
compute_logml(object, ...)

# S3 method for class 'bvharmn'
compute_logml(object, ...)

Arguments

object: Model fit
...: not used

Value

log likelihood of Minnesota prior model.

Details

Closed form of Marginal Likelihood of BVAR can be derived by

$$p(Y_0) = \pi^{-mn / 2} \frac{\Gamma_m ((\alpha_0 + n) / 2)}{\Gamma_m (\alpha_0 / 2)} \det(\Omega_0)^{-m / 2} \det(S_0)^{\alpha_0 / 2} \det(\hat{V})^{- m / 2} \det(\hat{\Sigma}_e)^{-(\alpha_0 + n) / 2}$$

Closed form of Marginal Likelihood of BVHAR can be derived by

$$p(Y_0) = \pi^{-ms_0 / 2} \frac{\Gamma_m ((d_0 + n) / 2)}{\Gamma_m (d_0 / 2)} \det(P_0)^{-m / 2} \det(U_0)^{d_0 / 2} \det(\hat{V}_{HAR})^{- m / 2} \det(\hat{\Sigma}_e)^{-(d_0 + n) / 2}$$

References

Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. Review of Economics and Statistics, 97(2).