There are some issues with your wording. I assume when you say $\tau_\text{best}$ you are referring to the Bayes estimator (posterior mean) or perhaps the posterior mode. Also, the min max subscripts would best be defined by lower and upper limits of the credible set.

Regardless, what you want is called the highest posterior density interval (HPDI) which is unique under most conditions. This posting should answer your question.

The R package "coda" contains an algorithm to compute the HPDI from a sample. Also, SAS will compute this interval as part of any Bayesian analysis.

There are some issues with your wording. I assume when you say $\tau_\text{best}$ you are referring to the Bayes estimator (posterior mean) or perhaps the posterior mode. Also, the min max subscripts would best be defined by lower and upper limits of the credible set.

Regardless, what you want is called the highest posterior density interval (HPDI) which is unique under most conditions. This posting should answer your question.

The R package "coda" contains an algorithm to compute the HPDI from a sample. Also, SAS will compute this interval as part of any Bayesian analysis.