I am trying to create an observed variable in PyMC3 which has a multivariate normal distribution. I want the covariance matrix whose elements are other random variables. As an example, consider the following code:
import pymc3 as pm
with pm.Model() as model:
a = pm.Normal('a', mu=0, sigma=10)
b = pm.Normal('a', mu=0, sigma=10)
c = pm.Normal('a', mu=0, sigma=10)
# I recognize that the matrix is not positive definite
# with this parameterization. This is just a toy example.
# The main point is that I want the elements of the matrix
# to be random variables.
cov = [[a, b]
data = pm.MvNormal('data', mu=[0, 0],
This does not work. Neither does using
np.array(cov). I imagine the solution is to use Theano tensors somehow. I am unable to figure out how to use them.
I’d appreciate any help with this. Thanks.
You can use
import theano.tensor as tt
tt.concatenate([a, b, b, c]).reshape((2, 2))
If you want priors on covariance matrices, you probably want to look into
tt.stack worked. Thank you. Now, I am getting the following future warning:
/usr/local/lib/python3.6/dist-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
result[diagonal_slice] = x
Do you know why this warning is being thrown and how I can remedy this?
Yeah it’s a classical and harmless warning. Usually we just get rid of it with:
Can someone provide an example of what this would look like using tt.stack? I tried tt.concatenate(…) like this answer suggests but I’m getting a “TypeError: Join cannot handle arguments of dimension 0”. Since the OP replied using “tt.stack worked”, I’m wondering if @awareeye ran into the same problem?