A new approach for Bayesian model averaging

Bayesian model averaging (BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models. However, successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble. Two methods, namely the Expectation-Maximization (EM) and the Markov Chain Monte Carlo (MCMC) algorithms, are widely used for BMA model training. Both methods have their own respective strengths and weaknesses. In this paper, we first modify the BMA log-likelihood function with the aim of removing the additional limitation that requires that the BMA weights add to one, and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem, thereby formulating a new approach for BMA (referred to as BMA-BFGS). Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy, and that both are superior to the EM algorithm. On the other hand, the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is almost equivalent to that for EM.