Bimodal posterior distribution interpretation/clustering

I am estimating several model parameters from a limited set of measurements. The mean value of the model is given a physically-based model, since this is an inverse scattering problem in the microwaves regime. We are also assuming a zero-mean normal distribution with known variance for the observation process.

Since the physical model has 7 parameters and we only have access to 4 observations, we expect the problem to be ill-posed and therefore we want to study which parameters are compatible with the observations. A typical posterior distribution for a given set of observations is presented below,

As seen, there are a lot of combinations of model parameters that can explain the observations. Moreover, it seem that the posterior is bimodal for some parameters. Therefore, we believe that informing a mean value and a confidence interval is misleading for this kind of posteriors. Which is the standard way to go in this cases (bimodal posterior)?

We explored several alternatives,

  1. Since there are parameters which have similar behaviors, we can manually identify several scenarios (e.g. tita1 large & tita2 small) in order to separate the zones of large probability in disjoint solutions. This solutions of course corresponds to different sets of model parameters with appropriate mean values and confidence intervals.

  2. We were thinking if it is possible to automatically identify the zones of large probability by clustering the posterior with a non-supervised algorithm. Is this a common practice?

Any feedback is welcome