Downstream

Once we have defined P and Q using …, we need to actually do stuff with these distributions.

At a high level, the flow is:

Define the prior, P_plate, and approximate posterior, Q_plate, abstractly as Plate’s. Note that these do not currently have platesizes, so they can’t be initialized, and we haven’t e.g. concretely initialized any parameters.
Bind the prior and approximate posterior to platesizes and initialized the parameters, by passing P_plate and Q_plate, to BoundPlate.
Construct an inference problem, by passing P_bound_plate and Q_bound_plate into Problem, along with a dict of data.
Call problem.sample(K=10), which draws 10 samples for each random variable.
Do something with the sample (there’s lots of options, see below).

A code example for this flow is:

import alan

P_plate = alan.Plate(
    a = alan.Normal(0., 1),
    p1 = alan.Plate(
        b = alan.Normal('a', 1),
        p2 = alan.Plate(
            c = alan.Normal("b", 1),
        ),
    ),
)

Q_plate = alan.Plate(
    a = alan.Normal(0., 1),
    p1 = alan.Plate(
        b = alan.Normal('a', 1),
        p2 = alan.Plate(
            c = alan.Data(),
        ),
    ),
)

all_platesizes = {'p1': 3, 'p2': 4}
P_bound_plate = alan.BoundPlate(P_plate, all_platesizes)
Q_bound_plate = alan.BoundPlate(Q_plate, all_platesizes)

data = {'c': t.randn((3,4), names=('p1', 'p2')}
problem = alan.Problem(P_bound_plate, Q_bound_plate, data)

sample = data.sample(K=10)

Contents: