Title: Bayesian model comparison and optimisation
Authors: Dan Zhu - Monash University (Australia)
Liana Jacobi - University Melbourne (Australia) [presenting]
Joshua Chan - Australian National University (Australia)
Abstract: The marginal likelihood is the gold standard for Bayesian model comparison. We develop a general framework to automatically compute the sensitivities of marginal likelihood, obtained via simulation-based methods, with respect to any prior hyperparameters, which sets the basis for robustness checks and optimisation routines in Bayesian analysis. Large Bayesian VARs with the natural conjugate prior are now routinely used for forecasting and structural analysis. It has been shown that selecting the prior hyperparameters in a data-driven manner can often substantially improve forecast performance. Using a large US dataset, we show that using the optimal hyperparameter values leads to substantially better forecast performance. Moreover, the proposed method is much faster than the conventional grid-search approach, and is applicable in high-dimensional optimization problems. The new method thus provides a practical and systematic way to develop better shrinkage priors for forecasting in a data-rich environment.