Exercise 14.12 [multivalued-probit-exercise]

The probit distribution defined on page probit-page describes the probability distribution for a Boolean child, given a single continuous parent.

1. How might the definition be extended to cover multiple continuous parents?

2. How might it be extended to handle a multivalued child variable? Consider both cases where the child’s values are ordered (as in selecting a gear while driving, depending on speed, slope, desired acceleration, etc.) and cases where they are unordered (as in selecting bus, train, or car to get to work). (Hint: Consider ways to divide the possible values into two sets, to mimic a Boolean variable.)