The minimal model of glucose kinetics, in conjunction with an insulin-modified intravenous glucose tolerance test, is widely used to estimate insulin sensitivity (S_I). Parameter estimation usually resorts to nonlinear least squares (NLS), which provides a point estimate, and its precision is expressed as a standard deviation. Applied to type 2 diabetic subjects, NLS implemented in MINMOD software often predicts S_I=0 (the so-called "zero" S_I problem), whereas general purpose modeling software systems, e.g., SAAM II, provide a very small S_I but with a very large uncertainty, which produces unrealistic negative values in the confidence interval. To overcome these difficulties, in this article we resort to Bayesian parameter estimation implemented by a Markov chain Monte Carlo (MCMC) method. This approach provides in each individual the S_I a posteriori probability density function, from which a point estimate and its confidence interval can be determined. Although NLS results are not acceptable in four out of the ten studied subjects, Bayes estimation implemented by MCMC is always able to determine a nonzero point estimate of S_I together with a credible confidence interval. This Bayesian approach should prove useful in reanalyzing large databases of epidemiological studies.