Through a MCMC Gibbs sampler I obtain $M$ chains of the parameters vector $\mathbf{\theta}$, meaning that each component of $\mathbf{\theta}$ is the value of one parameter at a given iteration.
Since I know the likelihood and the prior I found the maximum a posteriori estimate:
$$\hat{\mathbf{\theta}}=\underset{\mathbf{\theta}^{(1)},\,...,\,\mathbf{\theta}^{(M)}}{\operatorname{argmax}}\,p(\mathbf{\theta}),$$
I'd like to have an error on each component of $\hat{\mathbf{\theta}}$.
One other estimate of the best parameters is the mode or the mean of MCMC chains for each parameter, for which I can consider the standard deviation as an error, but this is not what I'm interested in.