How to model problem where we see a yes/no output?

Questions
2

In general, these kind of question is formulated as a GLM with Bernoulli likelihood:

with pm.Model() as m:
    ...
    obs = pm.Bernoulli('observed', p, observed=w)

Now the trick is to come up with the formulation of p. Rearrange your initial formulation a bit, we get:

                                   p = z > y 
=>                             z - y > 0
=> (a_guess - a) + (b_guess - b) * x > 0

A direct translation would be:

with pm.Model() as model:
    
    a = pm.Uniform('a', lower=-10, upper=10)
    b = pm.Uniform('b', lower=-10, upper=10)
    p = (a_guess - a) + (b_guess - b) * x > 0
    obs = pm.Bernoulli('observed', p, observed=w)

of course, a binary p will likely makes inference pretty difficult, instead, we usually use a Sigmoid:

with pm.Model() as model:
    a = pm.Uniform('a', lower=-10, upper=10)
    b = pm.Uniform('b', lower=-10, upper=10)
    latent_p = (a_guess - a) + (b_guess - b) * x
    obs = pm.Bernoulli('observed', pm.math.sigmoid(latent_p), observed=w)
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