# Complex demo: Load Iris, simulate probability distributions (normal, binomial), compute Bayes' theorem for class probability, visualize with SciPy/NumPy/Matplotlib, integrate with classification
import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score
from scipy.stats import norm, binom
from scipy.special import logsumexp
import matplotlib.pyplot as plt
import seaborn as sns

def advanced_iris_probability_demo():
    # Load and prep
    iris = load_iris()
    df = pd.DataFrame(iris.data, columns=iris.feature_names)
    df['Target'] = iris.target
    
    # Feature engineering
    df['Petal_Ratio'] = df['petal length (cm)'] / (df['petal width (cm)'] + 1e-5)
    
    # Simulate probability distributions
    # Normal distribution for petal length (mean=4.8, std=1.76 for class 0)
    x = np.linspace(1, 7, 100)
    y_normal = norm.pdf(x, loc=4.8, scale=1.76)
    
    # Binomial distribution for simulated class probability (n=10, p=0.5)
    y_binomial = binom.pmf(np.arange(0, 11), n=10, p=0.5)
    
    # Bayes' theorem simulation for class probability
    # P(Class|Feature) = P(Feature|Class) * P(Class) / P(Feature)
    prior = np.array([0.33, 0.33, 0.34])  # Prior P(Class)
    likelihood = np.array([0.4, 0.3, 0.3])  # Simulated P(Feature|Class)
    evidence = np.sum(likelihood * prior)
    posterior = (likelihood * prior) / evidence
    print(f"Posterior Probabilities: {posterior}")
    
    # Classification integration
    X = df.drop('Target', axis=1)
    y = df['Target']
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
    model = RandomForestClassifier(n_estimators=50, random_state=42)
    model.fit(X_train, y_train)
    y_pred = model.predict(X_test)
    acc = accuracy_score(y_test, y_pred)
    print(f"Accuracy with Probability Integration: {acc:.2f}")
    
    # Visualize distributions
    fig, axes = plt.subplots(1, 2, figsize=(12, 5))
    axes[0].plot(x, y_normal, label='Normal PDF (Petal Length)')
    axes[0].set_title('Probability Distribution for Iris Feature')
    axes[0].set_xlabel('Value')
    axes[0].set_ylabel('Probability Density')
    axes[0].annotate('Peak at Mean', xy=(4.8, norm.pdf(4.8, loc=4.8, scale=1.76)), xytext=(5, 0.2), arrowprops=dict(facecolor='black', shrink=0.05))
    axes[0].legend()
    axes[1].bar(np.arange(len(posterior)), posterior, label='Bayes Posterior')
    axes[1].set_title('Bayes\' Theorem for Class Probability')
    axes[1].set_xlabel('Class')
    axes[1].set_ylabel('Posterior Probability')
    axes[1].annotate('Highest Prob Class', xy=(0, posterior[0]), xytext=(1, posterior[0] + 0.05), arrowprops=dict(facecolor='black', shrink=0.05))
    axes[1].legend()
    plt.tight_layout()
    plt.show()

advanced_iris_probability_demo()