测试环境：

pymc3==3.10.0

代码部分:

import pymc3 as pm
from scipy import stats

class variational_method(object):

    def __init__(self):
        pass
    
    def fit(self,data,sigma_true,mu_prior_mu,sigma_prior_mu,samples,iter_num):
        with pm.Model() as variational_model:
            mu = pm.Normal('mu', mu=mu_prior_mu, sigma=sigma_prior_mu)
            pm.Normal('x', mu=mu, sigma=sigma_true, observed=data)
            approx = pm.fit(n=iter_num,method=pm.ADVI(),obj_optimizer=pm.adam(learning_rate=0.01))
        trace = approx.sample(draws=samples)
        pm.plot_trace(trace)
        return pm.summary(trace)

### 样本分布的假设 正态
mu_true = 1.5
sigma_true = 2
data = stats.norm.rvs(mu_true, sigma_true, size=200)

### mu的先验分布设置 正态
mu_prior_mu = 0.5
sigma_prior_mu = 1

### mu更新的初始值设置
mu_init = 0  

### 变分法其它参数
samples = 120
iter_num = 50000

vm = variational_method()
vm.fit(data,sigma_true,mu_prior_mu,sigma_prior_mu,samples,iter_num)

输出结果：