tensorflow_theta.py

theta=np.arange(0.05,1,0.05)
print(theta)
prior = 1/len(theta) #The normalizing constant of the prior

#Evaluate joint likelihood and unnormalized posterior at one specific #$\theta = 0.5$
dist = tfp.distributions.Bernoulli(probs=0.5) #one specific theta
print(np.prod(dist.prob(obs_data))) #joint likelihood
print(np.prod(dist.prob(obs_data))*prior) #unnormalized posterior

#Repeat the process for all thetas, range 0.05 - 0.95
res = np.zeros((len(theta),5))
for i in range(0,len(theta)):
  dist = tfp.distributions.Bernoulli(probs=theta[i])   
  res[i,0:4]=np.array((theta[i],np.prod(dist.prob(obs_data)),prior,np.prod(dist.prob(obs_data))*prior))

  
#Normalize posterior
import pandas as pd
res=pd.DataFrame(res,columns=["theta","jointlik","prior","unnorm_post","post"])
res["post"]=res["unnorm_post"]/np.sum(res["unnorm_post"])
res

#Plot prior and posterior for parameter θ
plt.figure(figsize=(16,6))
plt.subplot(1,2,1)
plt.stem(res["theta"],res["prior"])
plt.xlabel("theta")
plt.ylabel("probability")
plt.ylim([0,0.5])
plt.title("prior distribution")
plt.subplot(1,2,2)
plt.stem(res["theta"],res["post"])
plt.ylim([0,0.5])
plt.xlabel("theta")
plt.ylabel("probability")
plt.title("posterior distribution")