Enhanced conditional Co-Gibbs sampling algorithm for data imputation

The Gibbs sampler is an iterative algorithm for data imputation of a random vector at locations where values of the variable of interest are missing. In this algorithm, the simulated values converge to a Gaussian random vector distribution with zero mean and a given covariance matrix obtained by solving a simple kriging system through several iterations. In a bivariate dataset, if the principal variable for imputation depends on an auxiliary variable that is more abundant at the sample locations, this algorithm fails to produce the local and spatial cross-correlation structures. To overcome this impediment, a variant of the Gibbs sampler, the conditional Co-Gibbs sampler, has been proposed in this study, where simple kriging is replaced by three alternative cokriging paradigms: multicollocated cokriging, collocated cokriging, and homotopic cokriging. The algorithm was examined for an actual case study to statistically evaluate its performance. The results indicate that the conditional Co-Gibbs sampler with multicollocated cokriging outperformed the alternatives, including simple kriging where data imputation occurred as a consequence of ignoring the influence of the auxiliary variable, partially or totally. In addition, a computer software, provided as an open-source executable file, was used to implement the proposed algorithm for data imputation in bivariate cases.