I have several datasets with angular measurements, i.e. circular values from 0 to $2\pi$. These datasets tend to have peaks at 0 and/or $\pi$, and I need to tell if the peaks are detected/significant. There are several approaches to related problems I found, but they don't seem to answer the question of individual peak (mode) significance:
- Fitting a mixture model with a uniform component + 2 gaussians at 0 and $\pi$, and getting the posterior for the parameters. The posterior means for weights of each component are basically always distinct from zero , even when fitting to a uniform distribution. So this cannot be used to assess peak significance.
- Different multimodality tests: only test for the number of modes, and don't give their locations.
So I'm looking for help and suggestions - what are better ways to do this?