Slow sampling rate for pymc3 model

Questions v3
1

I am using the following pymc3 model.

model.verbose = 0

with model:
    # top-level prior
    gamma = []
    
    alpha = 1. / numberOfRatingLevels
    
    for k in range(numberOfRatingLevels):
        gamma_k = pm.Gamma("gamma_%i" % k, alpha=alpha, beta=rate)
        
        gamma_k = gamma_k * concentration
        
        gamma.append(gamma_k)
        
    # each movie
    for m in range(numberOfMovies):
        # sample the Dirichlet by sampling from gammas and normalizing
        theta_m = []
        
        for k in range(0, numberOfRatingLevels):
            theta_mk = pm.Gamma("theta_%i%i" % (m, k), alpha=gamma[k], beta=1.)
        
            theta_m.append(theta_mk)
            
        theta_m = theta_m / np.sum(theta_m)

        # rating counts for the movie
        ratingCounts = serviceans_cnt_lst[m]
        
        # use a multinomial to achieve repeated categorical draws
        phi_m = pm.Multinomial("phi_%i" % m, n=ratingCounts.sum(), p=theta_m, observed=ratingCounts)
    
    step = pm.Metropolis()
    trace = pm.sample(3000, step=step)

The sampling takes more than 2 hours. Can someone help me?