ABSTRACT

This research presented a new systematic approach that helped overcome the problem of 2^k models in the Bayesian statistics. This study introduced a new method henceforth called Sampling Without Replacement Bayesian Model Averaging (SWR-BMA). K independent variables were considered and a random sample of size  was taken without replacement at a time. This process of sampling was replicated r times, each time ensuring that all K variables were considered in the sampling process. In this study the Nigerian Gross Domestic Product (GDP) was used as the response variable while 19 other variables were used as predictor variables. Simulation was also carried out leading to a generated data of size 90 with k = 30 and k = 60. These data were analyzed using the SWR-BMA and MCMC. The results showed that SWR-BMA is a good alternative to MCMC when k is large. A new g-prior was also proposed and it was used to compare with some popular g-priors in literature, namely, uniform information prior (UIP), Hannan-Quinn criterion (HQ) and benchmark prior, in the light of different model priors. The results showed that the proposed prior produced posterior means and posterior standard deviation similar to those given by the benchmark prior for most of the variables used in the analysis. However, in some variables, the proposed prior produced a smaller posterior standard deviation than that produced by benchmark prior. Furthermore, the proposed prior gave a smaller posterior standard deviation for all the variables in the analysis than those produced by the UIP and HQ, indicating dominance. In addition, the proposed prior showed a higher posterior inclusion probability in most variables than the benchmark prior. The SWR-BMA overcomes the problem of summing over all possible 2^k models when k is very large as it reduces the number of models to be summed over and also achieve a good result.