Optimised conjugate prior for model structure estimation in the exponential family

Abstract

Model structure estimation has gained attention owing to the challenge of analysing large, scarce, and poorly informative data. Bayesian hypothesis testing formally addresses this issue. For nested model structures, an efficient search method provides the maximum a posteriori (MAP) estimate, even in extensive hypothesis spaces. However, estimation quality highly depends on prior probability densities of unknown, hypothesis-specific parameters. Existing solutions mitigate this issue by estimating multivariate hyperparameters of these priors; however, these solutions restrict the hyperparameter space, limiting estimation quality. This study enhances model structure estimation for exponential family models by imposing minimal constraints on the selected hyperparameter. For Gaussian models with linearly weighted auto-regression and regression variables, the MAP hyperparameter estimate is analytic and requires solving only one equation for a scalar variable. Experiments, including a complex simulation and multi-step forecasting of futures prices, confirm the solution quality gains.