This need not be a problem if the posterior distribution is proper.

Analytically, when the mode(s) of the posterior distribution can be given in closed form.

The posterior distribution of the parameters is proportional to the prior times the likelihood.

Also, the observed data are used both to construct the posterior distribution and to evaluate the estimated models.

These trees may be as a result of bootstrap analysis or samples from a posterior distribution.

For example, one would want any decision rule based on the posterior distribution to be admissible under the adopted loss function.

The posterior distribution can be found by updating the parameters as follows.

Only this way is the entire posterior distribution of the parameter(s) used.

See the article on the posterior predictive distribution for more information.

The posterior distribution is then used as the basis for statistical inference.