Implement MaskedTensorVariables and operations

PyTensor doesn't have a type that behaves like masked arrays. It's not just a problem of wrapping a masked array.

In your example, as soon as you try to do some operation, you will get incorrect values:

import pytensor
import numpy as np

X = np.ma.masked_greater(np.array([1, 2, 3, 4]), 3)
sh_val = pytensor.shared(X)
print(sh_val.eval()) # [1,2,3,4]
sh_val.set_value(X)
print(sh_val.eval()) # [1,2,3,--]
print((sh_val + 1).eval())  # [2 3 4 5]

We can raise explicitly when a user tries to pass a masked array. To actually support numpy-like behavior, we would need to implement something like MaskedTensorVariables and write all the operations to support those types. Similar to how we handle SparseTensorVariables.

Originally posted by @ricardoV94 in https://github.com/pymc-devs/pytensor/issues/258#issuecomment-1488040890

Start with the pytensor.shared example and compare the proposed MaskedTensorVariables design with the existing SparseTensorVariables approach. Trace how the masked array behaves through an operation such as addition. Done means masked values are preserved correctly across supported operations, rather than producing unmasked numeric results.