Work out what to do when calling `do` on a node with shared predecessors

[mscroggs]

Consider the following graph:

A --> B1
|      |
v      v
B2 --> C

If we call do on the node B1, then it is unclear what we should do with the node A: it's a predecessor of B1 so should be removed, but it's a predecessor of B2 so can't be removed.

[willGraham01]

I think this is one of those "more complex" situations that Ricardo alluded to when we met him a couple months ago. We probably need to check with Ricardo what the appropriate behaviour is here.

But once Node.sample uses the Graph.model to draw samples, we might be able to get away with using numpyro.handlers.do if we're convinced it does what we're looking for. In which case the Graph.do method could just be

class Graph:

  ...

  def do(self, node_label, value):
    return numpyro.handlers.do(self.model, data={node_label: value})

(which can then be sampled from in the same way as any other Graph (or Node within the Graph).

[mscroggs]

I think this is one of those "more complex" situations that Ricardo alluded to when we met him a couple months ago. We probably need to check with Ricardo what the appropriate behaviour is here.

Agreed. For now, it throws an exception in this case which is probably the most sensible thing temporarily.