A number of studies have shown that time-lapse crosshole geophysical data can provide valuable information regarding the hydraulic properties of the unsaturated zone. The stochastic inversion of such data can yield estimates of uncertainties in such properties, which are valuable for hydrological characterization. Here, we investigate the effect on output parameter uncertainties of accounting for realistic correlation between the hydraulic model parameters in the inversion procedure. We do this within a Bayesian framework using a Markov-chain-Monte-Carlo (McMC) strategy, and we investigate the particular problem of estimating vadose zone hydraulic properties from ground-penetrating radar (GPR) data collected during a 1-D infiltration experiment. Our results clearly indicate that prior information on the correlation between model parameters has the effect of noticeably reducing posterior parameter uncertainties and hence, if available, should be included in such inversions.