How does PyMC3 interpret von Mises boundaries?

[Paul_Scotti]

If I wanted to have a von Mises distribution that is bounded with a lower bound of 350 degrees and an upper bound of 30 degrees (so encompassing 40 degrees on a 0-359 continuous scale), how would I implement that? It looks like the documentation says that von Mises go from a scale of -np.pi to np.pi, so what happens if I enter a value outside of that? Does it automatically get converted into the -np.pi to np.pi scale?

For example would the following code work correctly?

a = pm.Uniform('a', lower = np.deg2rad(-10.), upper = np.deg2rad(30.))
b = pm.VonMises('b', mu=a, kappa = 30.)

[amit]

Would http://docs.pymc.io/api/bounds.html work for what you are trying to do?

[Paul_Scotti]

It seems the von Mises is already bounded to support -np.pi to np.pi according to the documentation. But it’s unclear, even with that documentation, how I can further bound the von Mises such that I want the upper to be -2.96 (equivalent to -170 deg.) and the lower to be 2.62 (equivalent to 150 deg.) but I don’t want pymc3 to interpret the boundaries as the reverse such that 0 would be allowed but -3 would not be allowed. I also want to know whether I need to transform/bound any distribution that is the prior for the mu in the von Mises distribution (such that the prior only inputs values between -np.pi to np.pi) or whether it will automatically get converted within the values that von Mises supports.

[amit]

The distribution is periodic in 2pi. So any ‘mu’ you specify (directly or through a prior) will get folded into the -pi to pi interval modulo 2pi. You can check this by sampling with mu = mu0, mu0+2pi, mu0+4pi etc.

If I understand your question correctly, you are not trying to alter the period. You are just trying to bound the draws and then flip the interval. A combination of pm.Bound and pm.Deterministic should do it for you. If you are just trying to alter the period and the phase for the distribution, you could still use pm.Deterministic.

[Paul_Scotti]

Oh I see. Thanks for the help about how ‘mu’ gets folded into the interval. That solves several problems but leaves me with one last concern. If I want to use a mixture of von Mises distributions, I have to specify VonMises.dist, but the use of .dist means that I can’t use pm.Deterministic to fix the folding issue. For instance,

dists = [
    pm.VonMises.dist(mu=3, kappa=10),
    pm.VonMises.dist(mu=-3, kappa=10),
]
y = pm.Mixture('y', w=p, comp_dists=dists, observed=obs)

Is there a way for me to use a Deterministic function or to otherwise transform the dists so that both von Mises components are within the interval -pi to pi?

[Paul_Scotti]

For anyone wondering how to fix the von Mises between -pi and pi (given that you are not using a mixture), the easiest way I could think of was to create a custom function:

from theano.compile.ops import as_op
@as_op(itypes=[tt.dscalar], otypes=[tt.dscalar])
def within_pi_op(k):
while (k<-np.pi or k>np.pi):
k[k>np.pi] -= np.pi2
k[k<-np.pi] += np.pi2
return k

and then

vm = pm.VonMises(‘vm’,mu=3,kappa=10)
a = pm.Deterministic(‘a’, within_pi_op(vm))

The problem is I can’t use pm.Deterministic.dist so I can’t transfer this to using a mixture of von Mises.

[Paul_Scotti]

Ok, so I think I have it working now. But it required monkey patching which I realize is bad coding practice. I’d love any ideas on how to get this implemented without monkey patching.

Here’s how PyMC3 currently deals with a mixture of von Mises distributions (using pm.Bound does not fix it and instead removes the values outside the boundaries):

And here’s what I wanted it to do and what it currently does after monkey patching:

The patch I did was to go inside the class VonMises(Continuous) and change the “def random” so that its output of generate_samples is now within_pi(generate_samples), where within_pi just takes all the values lower than -pi and all the values greater than pi and adds 2pi or subtracts 2pi respectively.