The strengths of future carbon dioxide (CO2) sinks are highly uncertain. A sound methodology to characterize current and predictive uncertainties in carbon cycle models is crucial for the design of efficient carbon management strategies. We demonstrate such a methodology, Markov Chain Monte Carlo (MCMC), by performing a Bayesian calibration of a simple global-scale carbon cycle model with historical carbon cycle observations to (1) estimate probability density functions (PDFs) of key carbon cycle parameters, (2) derive statistically sound probabilistic predictions of future CO2 sinks, and (3) assess the utility of hypothetical observation systems to reduce prediction uncertainties. We find that the PDFs of model parameter estimates are not normally distributed, and the residuals show statistically significant temporal autocorrelation. The assumption of normally distributed PDFs likely causes biased results, and the neglect of autocorrelation in the residual of the annual CO2 time series causes overconfidence in parameter estimates and predictions. Using interannually varying global temperature observations as forcing provides important information: terrestrial parameter PDFs are shifted and are more sharply constrained when compared to PDFs estimated when forcing the carbon cycle with a simple energy-balance model. Although CO2 observations provide a strong constraint on the total carbon sink, adding independent observations of terrestrial and oceanic fluxes has the potential to reduce uncertainty in predictions of this total sink more rapidly. Assimilating hypothetical annual observations of terrestrial and oceanic CO2 fluxes with realistic uncertainties reduces predictive uncertainties about CO2 sinks in the year 2050 by as much as a factor of 2 compared to assimilating CO2 concentrations alone.