敏感性分析

Python 中的蒙特卡洛模拟

Izzy Weber

Curriculum Manager, DataCamp

敏感性分析

帮助理解输入范围的影响
当用表或图汇总时，展示模式或趋势

如果使用蒙特卡罗模拟增减 bmi 与 hdl 的取值，预测的 y（疾病进展）将如何变化？

定义参数

cov_dia = dia[["age", "bmi", "bp", "tc", "ldl", "hdl", "tch", "ltg", "glu"]].cov()
mean_dia = dia[["age", "bmi", "bp", "tc", "ldl", "hdl", "tch", "ltg", "glu"]].mean()

定义模拟函数

def simulate_bmi_hdl(cov_dia, mean_list):

    list_ys = []
    for i in range(50):
        simulation_results = st.multivariate_normal.rvs(mean=mean_list, 
                                                        size=500, cov=cov_dia)
        df_results = pd.DataFrame(simulation_results, 
                                  columns=["age","bmi","bp","tc","ldl","hdl","tch","ltg","glu"])
        predicted_y = regr_model.predict(df_results)
        df_y = pd.DataFrame(predicted_y, columns=["predicted_y"])
        df_summary = pd.concat([df_results, df_y], axis=1)
        y = np.mean(df_summary["predicted_y"]) 
        list_ys.append(y)

    return(np.mean(list_ys))

在参数范围内执行模拟

hdl = []
bmi = []
simu_y = []
for mean_hdl_inc in np.arange(-20, 50, 30): 
    for mean_bmi_inc in np.arange(-7, 11, 3):

        mean_list = mean_dia + np.array([0, mean_bmi_inc, 0, 0, 0, mean_hdl_inc, 0, 0, 0])
        hdl.append(mean_hdl_inc)
        bmi.append(mean_bmi_inc)

        mean_y = simulate_bmi_hdl(cov_dia, mean_list)

        simu_y.append(mean_y)

df_sa = pd.concat([pd.Series(hdl), pd.Series(bmi), pd.Series(simu_y)], axis=1)

df_sa.columns = ["hdl_inc", "bmi_inc", "y"]

敏感性分析结果的样式化数据框

df_sa.sort_values(by=['hdl_inc', 'bmi_inc']).pivot(index='hdl_inc',
                                             columns='bmi_inc',
                                             values='y').style.background_gradient(
                                             cmap=sns.light_palette("red", as_cmap=True))

排序、透视并设置样式后的 df_sa

敏感性分析结果的六边形箱图

df_sa.plot.hexbin(x='hdl_inc',y='bmi_inc', C='y',
                    reduce_C_function=np.mean,
                    gridsize=10, cmap="viridis",
                    sharex=False)

df_sa 的六边形箱图

致密参数空间的六边形箱图

Vamos praticar!

Python 中的蒙特卡洛模拟