You were right, if I introduce a second peak, sometimes the model works and find both and sometimes not.

Here is the reason for the discrete grid:

What I observe are noisy projections of a unknown 3D object. The goal is to reconstruct the 3D volume from the 2D projections. In the beginning you start with some kind of initial of low resolution inital 3D model, then you find the likelihood of the orientations + shift (on a coarse grid) of the observed projections, backproject them (weighted by likelihood) and get a better resolved 3D reconstruction. Then you restart the process (expectation maximization) with the new reconstructed volume and a finer grid. In the end you get a reconstruction which has a high resolution.

There are already software packes who implement bayesian appraoches for this problem ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3690530/ ), but I entered the world of bayes with the rethinking book and STAN and was wondering if I can implement similar things with STAN.

Best,

Thorsten