How to model/deal with weighted binary outcomes

Questions
10

Updated solution after this topic How to perform weighted inference

import numpy as np
import pymc3 as pm
import theano.tensor as T

N = 1000
P = 0.2

data = np.zeros(N)
data[:int(N * P)] = 1.0
weights  = np.ones(N)
weights[:int(N * P)] = 4.0

with pm.Model() as model:
    
    p_ = pm.Normal('p_',
                  mu=0.0,
                  sd=1000.0)
    p = pm.Deterministic('p', pm.math.invlogit(p_))
        
    pm.Potential('weights', 
             weights * pm.Bernoulli.dist(p=p).logp(data))

    trace = pm.sample(10000, cores=1, random_seed=1)
    
trace['p'].mean()  # 0.50019413
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