model = pm.Model()
with model:
    posnormal = pm.Bound(pm.Normal,lower = 0.0)
    negnormal = pm.Bound(pm.Normal,upper = 0.0)
    
    #Varying Intercept:-
    mu_intercept = pm.Normal('mu_intercept',mu = 0.0,sigma = 1e5)
    sigma_intercept = pm.HalfNormal('sigma_intercept',sigma = 1)
    intercept = pm.Normal('intercept',mu = mu_intercept,sigma = sigma_intercept, shape = asins_num)
    
    #Common slope:-
    brand_slope = posnormal('brand_slope',mu = 0.0, sigma = 1e5, shape = x2.shape[1])
    
    #Varying slope:-
    mu_slope = posnormal('mu_slope',mu = 0.0,sigma = 1e5)
    sigma_slope = pm.HalfNormal('sigma_slope',sigma = 1)
    slope = pm.Normal('slope',mu = mu_slope,sigma = sigma_slope, shape = asins_num)
    slope1 = pm.Normal('slope1',mu = mu_slope,sigma = sigma_slope, shape = asins_num)
    slope2 = pm.Normal('slope2',mu = mu_slope,sigma = sigma_slope, shape = asins_num)
    
    sigma_y = pm.HalfNormal('sigma_y',sigma = 1)
    
    mu = intercept[asin_idx] + pm.math.dot(x2,brand_slope) + slope[asin_idx] * x1['Discount'] \
    slope1[asin_index] * x1['SB_Impressions'] + slope2[asin_index] * x1['SNB_Impressions']

    Y = pm.Normal('Y',mu = mu,sigma = sigma_y,observed = Y_Act)

with model:
    trace = pm.sample(500,tune = 500,init = 'advi',n_init = 10000,cores = 4,progressbar = True)
    #start = pm.find_MAP()
    #step = pm.NUTS(scaling = start)
    #trace = pm.sample(500,tune = 500,step = step,start = start,cores = 4,progressbar = True)