I have a setup where 2 sine waves (each parametrised by amplitude and frequency) are added together and I want to recover the original 4 parameters. Data is blue dots and red line is the ‘true’ function:

My model is as follows:

```
# True values
#freq1 = 20
#ampl1 = 2
#freq2 = 10
#ampl2 = 3
# Define priors
_noise = pm.HalfNormal("sigma", sigma=50)
_freq1 = pm.HalfNormal("freq1", sigma=10)
_ampl1 = pm.HalfNormal("ampl1", sigma=10)
_freq2 = pm.HalfNormal("freq2", sigma=10)
_ampl2 = pm.HalfNormal("ampl2", sigma=10)
# Define likelihood
temp = (
(_ampl1 * pm.math.sin((2*np.pi/_freq1) * x)) +
(_ampl2 * pm.math.sin((2*np.pi/_freq2) * x))
)
likelihood = pm.Normal("liklihood", mu=temp, sigma=_noise, observed=y)
```

and it learns the overall function pretty well. Showing many reconstructed functions from the posterior parameter

distributions:

However, if I look at the posterior distributions themselves the true values for both frequencies are showing up in both frequency parameter distributions:

Is there any way to get around this symmetry issue? Perhaps by specifying that freq1 is greater than freq2 as a constrain or is the only way to play with the priors so their support doesn’t overlap?