Bayesian method for the correlated competitive bidding model

A multivariate competitive bidding model takes into account the correlation among competitors in determination of markup size. However, parameter estimation for the multivariate model is a challenging issue. A simplified, piecemeal style statistical method was proposed for low-dimension problems. However, this method may cause significant estimation errors when applied to complex bidding situations. A refined Bayesian statistical method based on Markov chain Monte Carlo (MCMC) simulation is developed that can be employed in practical bidding problems. To deal with missing values in bid data, a data augmentation technique is integrated in the MCMC process. The proposed Bayesian method is shown through case studies to be robust for complex bidding situations and also insensitive to the selection of the prior models of the correlation matrix. An important feature of the proposed Bayesian method is that it allows a project manager to quantify statistical uncertainties of parameter estimation and their effects on markup decisions. The optimal markup is represented by a posterior distribution which paints a complete picture of the uncertainties involved in the markup size decision.