python代码编写实现开展敏感性实验，进行独立样本检验或交叉检验，确定最优预测模型，使降水预测相关系数达到最大或者Ps评分达到最大，或者使时间按系数相关系数或者均方根误差达到最优

在Python中，特别是使用scikit-learn库进行机器学习建模时，你可以通过以下步骤进行敏感性实验、独立样本检验和交叉验证来选择最佳预测模型：

1. **导入所需库**:

import numpy as np
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.linear_model import LinearRegression, Lasso, Ridge
from sklearn.metrics import r2_score, mean_squared_error, wilcoxon_signed_rank_test

2. **加载数据**:

# 假设你有名为df的数据框，其中包含降水和影响因素的数据
X = df.drop('precipitation', axis=1)
y = df['precipitation']

3. **拆分数据（训练集和测试集）**:

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

4. **创建模型列表** (这里以线性回归为例，其他模型替换即可)：

models = {
    'Linear Regression': LinearRegression(),
    'Lasso': Lasso(),
    'Ridge': Ridge()
}

5. **敏感性实验（如网格搜索或随机搜索）**:

from sklearn.model_selection import GridSearchCV

param_grid = {'alpha': [0.1, 1.0, 10.0]}  # 对于Lasso和Ridge，调整正则化强度
grid_search = GridSearchCV(models['Lasso'], param_grid, cv=5, scoring='r2')
grid_search.fit(X_train, y_train)

optimal_lasso = grid_search.best_estimator_

6. **交叉验证评估**:

scores = {name: cross_val_score(model, X, y, scoring='r2') for name, model in models.items()}

7. **计算相关系数和PS评分**:

r2_scores = {name: score.mean() for name, score in scores.items()}
mse_scores = {name: -score.mean() for name, score in scores.items()}  # 因为负值表示较小的MSE
ps_scores = calculate_PS_score(y_test, model.predict(X_test))  # 自定义函数计算Ps评分

best_models = {
    'Best by R^2': optimal_lasso,
    'Best by PS Score': ps_scores.argmax(),  # 如果有多组模型，这里假设有一个函数返回最佳模型索引
}

8. **独立样本检验** (例如两独立样本威尔科克森符号秩检验)：

wilcoxon_results = {}
for model_name, pred in best_models.items():
    _, p_value = wilcoxon_signed_rank_test(y_test, pred)
    wilcoxon_results[model_name] = p_value

9. **选择优化指标**:

if max(r2_scores.values()) == max(mse_scores.values()):
    print(f"Optimal model based on R^2 and MSE: {max(r2_scores.keys())}")
elif max(ps_scores) > max(r2_scores.values()):
    print(f"Optimal model based on PS Score: {ps_scores.index(max(ps_scores))}")
else:
    print("Choose based on the specific context: higher R^2 for better prediction, lower MSE for less error.")