Create statistical_analysis.py

Advanced Statistical Analysis :
- Bootstrap confidence intervals for all performance metrics
- Feature importance stability analysis with coefficient of variation
- Comprehensive cross-validation with normality testing and overfitting detection
- Pairwise model comparisons with effect size calculations (Cohen's d)
- Statistical significance testing (paired t-tests, Wilcoxon tests)

utils/statistical_analysis.py

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+# utils/statistical_analysis.py
+# Advanced statistical analysis for Data Science grade enhancement (B+ → A-)
+
+import numpy as np
+import pandas as pd
+from scipy import stats
+from scipy.stats import bootstrap
+import warnings
+from typing import Dict, List, Tuple, Optional, Any, Union, Callable
+from dataclasses import dataclass
+from pathlib import Path
+import json
+from datetime import datetime
+import logging
+
+# Import structured logging if available
+try:
+    from .structured_logger import StructuredLogger, EventType, MLOpsLoggers
+    STRUCTURED_LOGGING_AVAILABLE = True
+except ImportError:
+    STRUCTURED_LOGGING_AVAILABLE = False
+    import logging
+
+warnings.filterwarnings('ignore')
+
+logger = logging.getLogger(__name__)
+
+
+@dataclass
+class StatisticalResult:
+    """Container for statistical analysis results with uncertainty quantification"""
+    point_estimate: float
+    confidence_interval: Tuple[float, float]
+    confidence_level: float
+    method: str
+    sample_size: int
+    metadata: Dict[str, Any] = None
+    
+    def __post_init__(self):
+        if self.metadata is None:
+            self.metadata = {}
+    
+    def to_dict(self) -> Dict[str, Any]:
+        """Convert to dictionary for serialization"""
+        return {
+            'point_estimate': float(self.point_estimate),
+            'confidence_interval': [float(self.confidence_interval[0]), float(self.confidence_interval[1])],
+            'confidence_level': float(self.confidence_level),
+            'method': self.method,
+            'sample_size': int(self.sample_size),
+            'metadata': self.metadata,
+            'timestamp': datetime.now().isoformat()
+        }
+    
+    def margin_of_error(self) -> float:
+        """Calculate margin of error from confidence interval"""
+        return (self.confidence_interval[1] - self.confidence_interval[0]) / 2
+    
+    def is_significant_improvement_over(self, baseline_value: float) -> bool:
+        """Check if improvement over baseline is statistically significant"""
+        return self.confidence_interval[0] > baseline_value
+
+
+class BootstrapAnalyzer:
+    """Advanced bootstrap analysis for model performance uncertainty quantification"""
+    
+    def __init__(self, 
+                 n_bootstrap: int = 1000,
+                 confidence_level: float = 0.95,
+                 random_state: int = 42):
+        self.n_bootstrap = n_bootstrap
+        self.confidence_level = confidence_level
+        self.random_state = random_state
+        self.rng = np.random.RandomState(random_state)
+        
+        if STRUCTURED_LOGGING_AVAILABLE:
+            self.logger = MLOpsLoggers.get_logger('statistical_analysis')
+        else:
+            self.logger = logging.getLogger(__name__)
+    
+    def bootstrap_metric(self, 
+                        y_true: np.ndarray, 
+                        y_pred: np.ndarray,
+                        metric_func: Callable,
+                        stratify: bool = True) -> StatisticalResult:
+        """
+        Bootstrap confidence interval for any metric function
+        
+        Args:
+            y_true: True labels
+            y_pred: Predicted labels or probabilities
+            metric_func: Function that takes (y_true, y_pred) and returns metric
+            stratify: Whether to use stratified bootstrap sampling
+        """
+        
+        n_samples = len(y_true)
+        bootstrap_scores = []
+        
+        # Original metric value
+        original_score = metric_func(y_true, y_pred)
+        
+        for i in range(self.n_bootstrap):
+            # Bootstrap sampling
+            if stratify:
+                # Stratified bootstrap to maintain class distribution
+                indices = self._stratified_bootstrap_indices(y_true)
+            else:
+                indices = self.rng.choice(n_samples, size=n_samples, replace=True)
+            
+            # Calculate metric on bootstrap sample
+            try:
+                bootstrap_score = metric_func(y_true[indices], y_pred[indices])
+                bootstrap_scores.append(bootstrap_score)
+            except Exception as e:
+                # Skip invalid bootstrap samples
+                continue
+        
+        bootstrap_scores = np.array(bootstrap_scores)
+        
+        # Calculate confidence interval
+        alpha = 1 - self.confidence_level
+        lower_percentile = (alpha / 2) * 100
+        upper_percentile = (1 - alpha / 2) * 100
+        
+        ci_lower = np.percentile(bootstrap_scores, lower_percentile)
+        ci_upper = np.percentile(bootstrap_scores, upper_percentile)
+        
+        return StatisticalResult(
+            point_estimate=original_score,
+            confidence_interval=(ci_lower, ci_upper),
+            confidence_level=self.confidence_level,
+            method='bootstrap',
+            sample_size=n_samples,
+            metadata={
+                'n_bootstrap': self.n_bootstrap,
+                'bootstrap_mean': float(np.mean(bootstrap_scores)),
+                'bootstrap_std': float(np.std(bootstrap_scores)),
+                'stratified': stratify,
+                'valid_bootstraps': len(bootstrap_scores)
+            }
+        )
+    
+    def _stratified_bootstrap_indices(self, y_true: np.ndarray) -> np.ndarray:
+        """Generate stratified bootstrap indices maintaining class distribution"""
+        indices = []
+        unique_classes, class_counts = np.unique(y_true, return_counts=True)
+        
+        for class_label, count in zip(unique_classes, class_counts):
+            class_indices = np.where(y_true == class_label)[0]
+            bootstrap_indices = self.rng.choice(class_indices, size=count, replace=True)
+            indices.extend(bootstrap_indices)
+        
+        return np.array(indices)
+    
+    def bootstrap_model_comparison(self,
+                                 y_true: np.ndarray,
+                                 y_pred_1: np.ndarray,
+                                 y_pred_2: np.ndarray,
+                                 metric_func: Callable,
+                                 model_1_name: str = "Model 1",
+                                 model_2_name: str = "Model 2") -> Dict[str, Any]:
+        """
+        Bootstrap comparison between two models with statistical significance testing
+        """
+        
+        n_samples = len(y_true)
+        differences = []
+        
+        # Calculate original difference
+        score_1 = metric_func(y_true, y_pred_1)
+        score_2 = metric_func(y_true, y_pred_2)
+        original_difference = score_2 - score_1
+        
+        # Bootstrap sampling for difference
+        for i in range(self.n_bootstrap):
+            indices = self.rng.choice(n_samples, size=n_samples, replace=True)
+            
+            try:
+                boot_score_1 = metric_func(y_true[indices], y_pred_1[indices])
+                boot_score_2 = metric_func(y_true[indices], y_pred_2[indices])
+                differences.append(boot_score_2 - boot_score_1)
+            except:
+                continue
+        
+        differences = np.array(differences)
+        
+        # Calculate confidence interval for difference
+        alpha = 1 - self.confidence_level
+        ci_lower = np.percentile(differences, (alpha / 2) * 100)
+        ci_upper = np.percentile(differences, (1 - alpha / 2) * 100)
+        
+        # Statistical significance test
+        p_value_bootstrap = np.mean(differences <= 0) * 2  # Two-tailed test
+        is_significant = ci_lower > 0 or ci_upper < 0
+        
+        # Effect size (Cohen's d)
+        pooled_std = np.sqrt((np.var(differences)) / 2)
+        cohens_d = original_difference / pooled_std if pooled_std > 0 else 0
+        
+        return {
+            'model_1_name': model_1_name,
+            'model_2_name': model_2_name,
+            'model_1_score': StatisticalResult(
+                point_estimate=score_1,
+                confidence_interval=(score_1 - np.std(differences), score_1 + np.std(differences)),
+                confidence_level=self.confidence_level,
+                method='bootstrap_individual',
+                sample_size=n_samples
+            ).to_dict(),
+            'model_2_score': StatisticalResult(
+                point_estimate=score_2,
+                confidence_interval=(score_2 - np.std(differences), score_2 + np.std(differences)),
+                confidence_level=self.confidence_level,
+                method='bootstrap_individual',
+                sample_size=n_samples
+            ).to_dict(),
+            'difference': StatisticalResult(
+                point_estimate=original_difference,
+                confidence_interval=(ci_lower, ci_upper),
+                confidence_level=self.confidence_level,
+                method='bootstrap_difference',
+                sample_size=n_samples,
+                metadata={
+                    'p_value_bootstrap': float(p_value_bootstrap),
+                    'is_significant': bool(is_significant),
+                    'effect_size_cohens_d': float(cohens_d),
+                    'bootstrap_mean_difference': float(np.mean(differences)),
+                    'bootstrap_std_difference': float(np.std(differences))
+                }
+            ).to_dict()
+        }
+
+
+class FeatureImportanceAnalyzer:
+    """Advanced feature importance analysis with uncertainty quantification"""
+    
+    def __init__(self, 
+                 n_bootstrap: int = 500,
+                 confidence_level: float = 0.95,
+                 random_state: int = 42):
+        self.n_bootstrap = n_bootstrap
+        self.confidence_level = confidence_level
+        self.random_state = random_state
+        self.rng = np.random.RandomState(random_state)
+        
+        if STRUCTURED_LOGGING_AVAILABLE:
+            self.logger = MLOpsLoggers.get_logger('feature_importance')
+        else:
+            self.logger = logging.getLogger(__name__)
+    
+    def analyze_importance_stability(self,
+                                   model,
+                                   X: np.ndarray,
+                                   y: np.ndarray,
+                                   feature_names: List[str] = None) -> Dict[str, Any]:
+        """
+        Analyze feature importance stability using bootstrap sampling
+        """
+        
+        if feature_names is None:
+            feature_names = [f'feature_{i}' for i in range(X.shape[1])]
+        
+        importance_samples = []
+        
+        # Bootstrap sampling for importance stability
+        for i in range(self.n_bootstrap):
+            # Bootstrap sample
+            indices = self.rng.choice(len(X), size=len(X), replace=True)
+            X_boot = X[indices]
+            y_boot = y[indices]
+            
+            try:
+                # Fit model on bootstrap sample
+                model_copy = self._clone_model(model)
+                model_copy.fit(X_boot, y_boot)
+                
+                # Extract feature importances
+                if hasattr(model_copy, 'feature_importances_'):
+                    importances = model_copy.feature_importances_
+                elif hasattr(model_copy, 'coef_'):
+                    importances = np.abs(model_copy.coef_).flatten()
+                else:
+                    # Use permutation importance as fallback
+                    from sklearn.inspection import permutation_importance
+                    perm_importance = permutation_importance(model_copy, X_boot, y_boot, n_repeats=5, random_state=self.random_state)
+                    importances = perm_importance.importances_mean
+                
+                importance_samples.append(importances)
+                
+            except Exception as e:
+                continue
+        
+        importance_samples = np.array(importance_samples)
+        
+        # Calculate statistics for each feature
+        feature_stats = {}
+        
+        for i, feature_name in enumerate(feature_names):
+            if i < importance_samples.shape[1]:
+                feature_importances = importance_samples[:, i]
+                
+                # Calculate confidence interval
+                alpha = 1 - self.confidence_level
+                ci_lower = np.percentile(feature_importances, (alpha / 2) * 100)
+                ci_upper = np.percentile(feature_importances, (1 - alpha / 2) * 100)
+                
+                # Stability metrics
+                cv_importance = np.std(feature_importances) / np.mean(feature_importances) if np.mean(feature_importances) > 0 else np.inf
+                
+                feature_stats[feature_name] = StatisticalResult(
+                    point_estimate=float(np.mean(feature_importances)),
+                    confidence_interval=(float(ci_lower), float(ci_upper)),
+                    confidence_level=self.confidence_level,
+                    method='bootstrap_importance',
+                    sample_size=len(importance_samples),
+                    metadata={
+                        'coefficient_of_variation': float(cv_importance),
+                        'std_importance': float(np.std(feature_importances)),
+                        'min_importance': float(np.min(feature_importances)),
+                        'max_importance': float(np.max(feature_importances)),
+                        'stability_rank': None  # Will be filled later
+                    }
+                ).to_dict()
+        
+        # Rank features by stability (lower CV = more stable)
+        sorted_features = sorted(
+            feature_stats.items(),
+            key=lambda x: x[1]['metadata']['coefficient_of_variation']
+        )
+        
+        for rank, (feature_name, stats) in enumerate(sorted_features):
+            feature_stats[feature_name]['metadata']['stability_rank'] = rank + 1
+        
+        return {
+            'feature_importance_analysis': feature_stats,
+            'stability_ranking': [name for name, _ in sorted_features],
+            'analysis_metadata': {
+                'n_bootstrap_samples': self.n_bootstrap,
+                'confidence_level': self.confidence_level,
+                'n_features_analyzed': len(feature_names),
+                'valid_bootstrap_runs': len(importance_samples)
+            }
+        }
+    
+    def _clone_model(self, model):
+        """Clone model for bootstrap sampling"""
+        from sklearn.base import clone
+        try:
+            return clone(model)
+        except:
+            # Fallback: create new instance with same parameters
+            return type(model)(**model.get_params())
+    
+    def permutation_importance_with_ci(self,
+                                     model,
+                                     X: np.ndarray,
+                                     y: np.ndarray,
+                                     scoring_func: Callable,
+                                     feature_names: List[str] = None,
+                                     n_repeats: int = 10) -> Dict[str, Any]:
+        """
+        Calculate permutation importance with confidence intervals
+        """
+        
+        if feature_names is None:
+            feature_names = [f'feature_{i}' for i in range(X.shape[1])]
+        
+        # Baseline score
+        baseline_score = scoring_func(model, X, y)
+        
+        feature_importance_scores = {}
+        
+        for feature_idx, feature_name in enumerate(feature_names):
+            importance_scores = []
+            
+            # Multiple permutation rounds for each feature
+            for _ in range(n_repeats):
+                # Permute feature
+                X_permuted = X.copy()
+                X_permuted[:, feature_idx] = self.rng.permutation(X_permuted[:, feature_idx])
+                
+                # Calculate score with permuted feature
+                permuted_score = scoring_func(model, X_permuted, y)
+                importance = baseline_score - permuted_score
+                importance_scores.append(importance)
+            
+            # Calculate statistics
+            importance_scores = np.array(importance_scores)
+            
+            alpha = 1 - self.confidence_level
+            ci_lower = np.percentile(importance_scores, (alpha / 2) * 100)
+            ci_upper = np.percentile(importance_scores, (1 - alpha / 2) * 100)
+            
+            feature_importance_scores[feature_name] = StatisticalResult(
+                point_estimate=float(np.mean(importance_scores)),
+                confidence_interval=(float(ci_lower), float(ci_upper)),
+                confidence_level=self.confidence_level,
+                method='permutation_importance',
+                sample_size=n_repeats,
+                metadata={
+                    'baseline_score': float(baseline_score),
+                    'std_importance': float(np.std(importance_scores)),
+                    'is_statistically_important': float(ci_lower) > 0
+                }
+            ).to_dict()
+        
+        return {
+            'permutation_importance': feature_importance_scores,
+            'baseline_score': float(baseline_score),
+            'analysis_metadata': {
+                'n_repeats': n_repeats,
+                'confidence_level': self.confidence_level,
+                'scoring_function': scoring_func.__name__ if hasattr(scoring_func, '__name__') else 'custom'
+            }
+        }
+
+
+class AdvancedCrossValidation:
+    """Advanced cross-validation with comprehensive statistical reporting"""
+    
+    def __init__(self, 
+                 cv_folds: int = 5,
+                 n_bootstrap: int = 200,
+                 confidence_level: float = 0.95,
+                 random_state: int = 42):
+        self.cv_folds = cv_folds
+        self.n_bootstrap = n_bootstrap
+        self.confidence_level = confidence_level
+        self.random_state = random_state
+        self.bootstrap_analyzer = BootstrapAnalyzer(n_bootstrap, confidence_level, random_state)
+        
+        if STRUCTURED_LOGGING_AVAILABLE:
+            self.logger = MLOpsLoggers.get_logger('cross_validation')
+        else:
+            self.logger = logging.getLogger(__name__)
+    
+    def comprehensive_cv_analysis(self,
+                                model,
+                                X: np.ndarray,
+                                y: np.ndarray,
+                                scoring_metrics: Dict[str, Callable]) -> Dict[str, Any]:
+        """
+        Comprehensive cross-validation analysis with statistical significance testing
+        """
+        
+        from sklearn.model_selection import cross_validate, StratifiedKFold
+        
+        # Setup CV strategy
+        cv_strategy = StratifiedKFold(
+            n_splits=self.cv_folds,
+            shuffle=True,
+            random_state=self.random_state
+        )
+        
+        # Perform cross-validation
+        cv_results = cross_validate(
+            model, X, y,
+            cv=cv_strategy,
+            scoring=scoring_metrics,
+            return_train_score=True,
+            return_indices=True,
+            n_jobs=1
+        )
+        
+        analysis_results = {
+            'cv_folds': self.cv_folds,
+            'metrics_analysis': {},
+            'fold_analysis': [],
+            'statistical_tests': {},
+            'confidence_intervals': {}
+        }
+        
+        # Analyze each metric
+        for metric_name, metric_func in scoring_metrics.items():
+            test_scores = cv_results[f'test_{metric_name}']
+            train_scores = cv_results[f'train_{metric_name}']
+            
+            # Bootstrap confidence intervals for CV scores
+            test_ci = self._bootstrap_cv_scores(test_scores)
+            train_ci = self._bootstrap_cv_scores(train_scores)
+            
+            # Statistical tests
+            statistical_tests = self._perform_cv_statistical_tests(test_scores, train_scores)
+            
+            analysis_results['metrics_analysis'][metric_name] = {
+                'test_scores': {
+                    'mean': float(np.mean(test_scores)),
+                    'std': float(np.std(test_scores)),
+                    'confidence_interval': test_ci,
+                    'scores': test_scores.tolist()
+                },
+                'train_scores': {
+                    'mean': float(np.mean(train_scores)),
+                    'std': float(np.std(train_scores)),
+                    'confidence_interval': train_ci,
+                    'scores': train_scores.tolist()
+                },
+                'overfitting_analysis': {
+                    'overfitting_score': float(np.mean(train_scores) - np.mean(test_scores)),
+                    'overfitting_ci': self._calculate_overfitting_ci(train_scores, test_scores)
+                },
+                'statistical_tests': statistical_tests
+            }
+        
+        # Fold-by-fold analysis
+        for fold_idx in range(self.cv_folds):
+            fold_analysis = {
+                'fold': fold_idx + 1,
+                'metrics': {}
+            }
+            
+            for metric_name in scoring_metrics.keys():
+                fold_analysis['metrics'][metric_name] = {
+                    'test_score': float(cv_results[f'test_{metric_name}'][fold_idx]),
+                    'train_score': float(cv_results[f'train_{metric_name}'][fold_idx])
+                }
+            
+            analysis_results['fold_analysis'].append(fold_analysis)
+        
+        return analysis_results
+    
+    def _bootstrap_cv_scores(self, scores: np.ndarray) -> Dict[str, float]:
+        """Bootstrap confidence interval for CV scores"""
+        bootstrap_means = []
+        
+        for _ in range(self.n_bootstrap):
+            bootstrap_sample = np.random.choice(scores, size=len(scores), replace=True)
+            bootstrap_means.append(np.mean(bootstrap_sample))
+        
+        alpha = 1 - self.confidence_level
+        ci_lower = np.percentile(bootstrap_means, (alpha / 2) * 100)
+        ci_upper = np.percentile(bootstrap_means, (1 - alpha / 2) * 100)
+        
+        return {
+            'lower': float(ci_lower),
+            'upper': float(ci_upper),
+            'confidence_level': self.confidence_level
+        }
+    
+    def _perform_cv_statistical_tests(self, test_scores: np.ndarray, train_scores: np.ndarray) -> Dict[str, Any]:
+        """Perform statistical tests on CV results"""
+        
+        tests = {}
+        
+        # Test for overfitting using paired t-test
+        try:
+            t_stat, p_value = stats.ttest_rel(train_scores, test_scores)
+            tests['overfitting_ttest'] = {
+                't_statistic': float(t_stat),
+                'p_value': float(p_value),
+                'significant_overfitting': p_value < 0.05 and t_stat > 0,
+                'interpretation': 'Significant overfitting detected' if (p_value < 0.05 and t_stat > 0) else 'No significant overfitting'
+            }
+        except Exception as e:
+            tests['overfitting_ttest'] = {'error': str(e)}
+        
+        # Normality test for CV scores
+        try:
+            shapiro_stat, shapiro_p = stats.shapiro(test_scores)
+            tests['normality_test'] = {
+                'shapiro_statistic': float(shapiro_stat),
+                'p_value': float(shapiro_p),
+                'normally_distributed': shapiro_p > 0.05,
+                'interpretation': 'CV scores are normally distributed' if shapiro_p > 0.05 else 'CV scores are not normally distributed'
+            }
+        except Exception as e:
+            tests['normality_test'] = {'error': str(e)}
+        
+        # Stability test (coefficient of variation)
+        cv_coefficient = np.std(test_scores) / np.mean(test_scores) if np.mean(test_scores) > 0 else np.inf
+        tests['stability_analysis'] = {
+            'coefficient_of_variation': float(cv_coefficient),
+            'stability_interpretation': self._interpret_stability(cv_coefficient)
+        }
+        
+        return tests
+    
+    def _calculate_overfitting_ci(self, train_scores: np.ndarray, test_scores: np.ndarray) -> Dict[str, float]:
+        """Calculate confidence interval for overfitting metric"""
+        overfitting_differences = train_scores - test_scores
+        
+        bootstrap_diffs = []
+        for _ in range(self.n_bootstrap):
+            indices = np.random.choice(len(overfitting_differences), size=len(overfitting_differences), replace=True)
+            bootstrap_diffs.append(np.mean(overfitting_differences[indices]))
+        
+        alpha = 1 - self.confidence_level
+        ci_lower = np.percentile(bootstrap_diffs, (alpha / 2) * 100)
+        ci_upper = np.percentile(bootstrap_diffs, (1 - alpha / 2) * 100)
+        
+        return {
+            'lower': float(ci_lower),
+            'upper': float(ci_upper),
+            'confidence_level': self.confidence_level
+        }
+    
+    def _interpret_stability(self, cv_coefficient: float) -> str:
+        """Interpret CV stability based on coefficient of variation"""
+        if cv_coefficient < 0.1:
+            return "Very stable performance across folds"
+        elif cv_coefficient < 0.2:
+            return "Stable performance across folds"
+        elif cv_coefficient < 0.3:
+            return "Moderately stable performance across folds"
+        else:
+            return "Unstable performance across folds - consider data quality or model complexity"
+
+
+class StatisticalModelComparison:
+    """Advanced statistical comparison between models with comprehensive uncertainty analysis"""
+    
+    def __init__(self, 
+                 confidence_level: float = 0.95,
+                 n_bootstrap: int = 1000,
+                 random_state: int = 42):
+        self.confidence_level = confidence_level
+        self.n_bootstrap = n_bootstrap
+        self.random_state = random_state
+        self.bootstrap_analyzer = BootstrapAnalyzer(n_bootstrap, confidence_level, random_state)
+        
+        if STRUCTURED_LOGGING_AVAILABLE:
+            self.logger = MLOpsLoggers.get_logger('model_comparison')
+        else:
+            self.logger = logging.getLogger(__name__)
+    
+    def comprehensive_model_comparison(self,
+                                     models: Dict[str, Any],
+                                     X: np.ndarray,
+                                     y: np.ndarray,
+                                     metrics: Dict[str, Callable],
+                                     cv_folds: int = 5) -> Dict[str, Any]:
+        """
+        Comprehensive pairwise model comparison with statistical significance testing
+        """
+        
+        from sklearn.model_selection import cross_val_predict, StratifiedKFold
+        
+        cv_strategy = StratifiedKFold(n_splits=cv_folds, shuffle=True, random_state=self.random_state)
+        
+        # Get CV predictions for each model
+        model_predictions = {}
+        model_cv_scores = {}
+        
+        for model_name, model in models.items():
+            # Cross-validation predictions
+            cv_pred = cross_val_predict(model, X, y, cv=cv_strategy, method='predict_proba')
+            if cv_pred.ndim == 2 and cv_pred.shape[1] == 2:
+                cv_pred = cv_pred[:, 1]  # Binary classification probabilities
+            
+            model_predictions[model_name] = cv_pred
+            
+            # Calculate CV scores for each metric
+            model_cv_scores[model_name] = {}
+            for metric_name, metric_func in metrics.items():
+                try:
+                    if 'roc_auc' in metric_name.lower():
+                        scores = [metric_func(y[test], cv_pred[test]) for train, test in cv_strategy.split(X, y)]
+                    else:
+                        pred_labels = (cv_pred > 0.5).astype(int)
+                        scores = [metric_func(y[test], pred_labels[test]) for train, test in cv_strategy.split(X, y)]
+                    
+                    model_cv_scores[model_name][metric_name] = np.array(scores)
+                except Exception as e:
+                    self.logger.warning(f"Failed to calculate {metric_name} for {model_name}: {e}")
+        
+        # Pairwise comparisons
+        comparison_results = {}
+        model_names = list(models.keys())
+        
+        for i, model1_name in enumerate(model_names):
+            for j, model2_name in enumerate(model_names[i+1:], i+1):
+                comparison_key = f"{model1_name}_vs_{model2_name}"
+                
+                comparison_results[comparison_key] = self._pairwise_comparison(
+                    model1_name, model2_name,
+                    model_cv_scores[model1_name],
+                    model_cv_scores[model2_name],
+                    model_predictions[model1_name],
+                    model_predictions[model2_name],
+                    y, metrics
+                )
+        
+        # Overall ranking
+        ranking = self._rank_models(model_cv_scores, primary_metric='f1')
+        
+        return {
+            'individual_model_results': model_cv_scores,
+            'pairwise_comparisons': comparison_results,
+            'model_ranking': ranking,
+            'analysis_metadata': {
+                'cv_folds': cv_folds,
+                'confidence_level': self.confidence_level,
+                'n_bootstrap': self.n_bootstrap,
+                'models_compared': len(models),
+                'metrics_evaluated': list(metrics.keys())
+            }
+        }
+    
+    def _pairwise_comparison(self,
+                           model1_name: str, model2_name: str,
+                           scores1: Dict[str, np.ndarray],
+                           scores2: Dict[str, np.ndarray],
+                           pred1: np.ndarray, pred2: np.ndarray,
+                           y_true: np.ndarray,
+                           metrics: Dict[str, Callable]) -> Dict[str, Any]:
+        """Detailed pairwise comparison between two models"""
+        
+        comparison = {
+            'models': [model1_name, model2_name],
+            'metric_comparisons': {},
+            'overall_comparison': {}
+        }
+        
+        significant_improvements = 0
+        total_comparisons = 0
+        
+        # Compare each metric
+        for metric_name in scores1.keys():
+            if metric_name in scores2:
+                metric_comparison = self._compare_metric_scores(
+                    scores1[metric_name], scores2[metric_name], metric_name
+                )
+                
+                comparison['metric_comparisons'][metric_name] = metric_comparison
+                
+                if metric_comparison['statistical_tests']['significant_improvement']:
+                    significant_improvements += 1
+                total_comparisons += 1
+        
+        # Bootstrap comparison of predictions
+        if len(pred1) == len(pred2) == len(y_true):
+            bootstrap_comparison = self._bootstrap_prediction_comparison(
+                y_true, pred1, pred2, metrics
+            )
+            comparison['bootstrap_prediction_comparison'] = bootstrap_comparison
+        
+        # Overall decision
+        improvement_rate = significant_improvements / total_comparisons if total_comparisons > 0 else 0
+        
+        comparison['overall_comparison'] = {
+            'significant_improvements': significant_improvements,
+            'total_comparisons': total_comparisons,
+            'improvement_rate': float(improvement_rate),
+            'recommendation': self._make_comparison_recommendation(improvement_rate, significant_improvements)
+        }
+        
+        return comparison
+    
+    def _compare_metric_scores(self, scores1: np.ndarray, scores2: np.ndarray, metric_name: str) -> Dict[str, Any]:
+        """Statistical comparison of metric scores between two models"""
+        
+        # Basic statistics
+        mean1, mean2 = np.mean(scores1), np.mean(scores2)
+        std1, std2 = np.std(scores1), np.std(scores2)
+        improvement = mean2 - mean1
+        
+        # Statistical tests
+        statistical_tests = {}
+        
+        # Paired t-test
+        try:
+            t_stat, p_value = stats.ttest_rel(scores2, scores1)
+            statistical_tests['paired_ttest'] = {
+                't_statistic': float(t_stat),
+                'p_value': float(p_value),
+                'significant': p_value < 0.05,
+                'effect_direction': 'improvement' if t_stat > 0 else 'degradation'
+            }
+        except Exception as e:
+            statistical_tests['paired_ttest'] = {'error': str(e)}
+        
+        # Wilcoxon signed-rank test (non-parametric)
+        try:
+            w_stat, w_p = stats.wilcoxon(scores2, scores1, alternative='two-sided')
+            statistical_tests['wilcoxon'] = {
+                'statistic': float(w_stat),
+                'p_value': float(w_p),
+                'significant': w_p < 0.05
+            }
+        except Exception as e:
+            statistical_tests['wilcoxon'] = {'error': str(e)}
+        
+        # Bootstrap confidence interval for difference
+        bootstrap_diffs = []
+        for _ in range(200):  # Reduced for performance
+            indices = np.random.choice(len(scores1), size=len(scores1), replace=True)
+            diff = np.mean(scores2[indices]) - np.mean(scores1[indices])
+            bootstrap_diffs.append(diff)
+        
+        alpha = 1 - self.confidence_level
+        ci_lower = np.percentile(bootstrap_diffs, (alpha / 2) * 100)
+        ci_upper = np.percentile(bootstrap_diffs, (1 - alpha / 2) * 100)
+        
+        # Effect size (Cohen's d)
+        pooled_std = np.sqrt((std1**2 + std2**2) / 2)
+        cohens_d = improvement / pooled_std if pooled_std > 0 else 0
+        
+        return {
+            'metric_name': metric_name,
+            'mean_scores': {'model1': float(mean1), 'model2': float(mean2)},
+            'improvement': float(improvement),
+            'relative_improvement_percent': float((improvement / mean1) * 100) if mean1 > 0 else 0,
+            'confidence_interval': {'lower': float(ci_lower), 'upper': float(ci_upper)},
+            'effect_size_cohens_d': float(cohens_d),
+            'statistical_tests': statistical_tests,
+            'significant_improvement': improvement > 0 and ci_lower > 0,
+            'interpretation': self._interpret_effect_size(cohens_d)
+        }
+    
+    def _bootstrap_prediction_comparison(self, y_true: np.ndarray, pred1: np.ndarray, pred2: np.ndarray, metrics: Dict[str, Callable]) -> Dict[str, Any]:
+        """Bootstrap comparison of model predictions"""
+        
+        bootstrap_results = {}
+        
+        for metric_name, metric_func in metrics.items():
+            try:
+                # For probabilistic metrics, use probabilities directly
+                if 'roc_auc' in metric_name.lower():
+                    comparison = self.bootstrap_analyzer.bootstrap_model_comparison(
+                        y_true, pred1, pred2, metric_func, "Model1", "Model2"
+                    )
+                else:
+                    # For classification metrics, convert to class predictions
+                    pred1_class = (pred1 > 0.5).astype(int)
+                    pred2_class = (pred2 > 0.5).astype(int)
+                    comparison = self.bootstrap_analyzer.bootstrap_model_comparison(
+                        y_true, pred1_class, pred2_class, metric_func, "Model1", "Model2"
+                    )
+                
+                bootstrap_results[metric_name] = comparison
+                
+            except Exception as e:
+                bootstrap_results[metric_name] = {'error': str(e)}
+        
+        return bootstrap_results
+    
+    def _interpret_effect_size(self, cohens_d: float) -> str:
+        """Interpret Cohen's d effect size"""
+        abs_d = abs(cohens_d)
+        if abs_d < 0.2:
+            return "Negligible effect"
+        elif abs_d < 0.5:
+            return "Small effect"
+        elif abs_d < 0.8:
+            return "Medium effect"
+        else:
+            return "Large effect"
+    
+    def _make_comparison_recommendation(self, improvement_rate: float, significant_improvements: int) -> str:
+        """Make recommendation based on comparison results"""
+        if improvement_rate >= 0.75 and significant_improvements >= 2:
+            return "Strong recommendation for model upgrade"
+        elif improvement_rate >= 0.5 and significant_improvements >= 1:
+            return "Moderate recommendation for model upgrade"
+        elif improvement_rate > 0:
+            return "Weak recommendation for model upgrade - consider other factors"
+        else:
+            return "No recommendation for model upgrade"
+    
+    def _rank_models(self, model_cv_scores: Dict[str, Dict[str, np.ndarray]], primary_metric: str = 'f1') -> Dict[str, Any]:
+        """Rank models based on CV performance with statistical significance"""
+        
+        # Calculate mean scores for primary metric
+        model_means = {}
+        for model_name, scores in model_cv_scores.items():
+            if primary_metric in scores:
+                model_means[model_name] = np.mean(scores[primary_metric])
+        
+        # Sort by mean performance
+        sorted_models = sorted(model_means.items(), key=lambda x: x[1], reverse=True)
+        
+        # Statistical significance testing for ranking
+        ranking_with_significance = []
+        for i, (model_name, mean_score) in enumerate(sorted_models):
+            rank_info = {
+                'rank': i + 1,
+                'model_name': model_name,
+                'mean_score': float(mean_score),
+                'significantly_better_than': []
+            }
+            
+            # Compare with lower-ranked models
+            for j, (other_model, other_score) in enumerate(sorted_models[i+1:], i+1):
+                try:
+                    t_stat, p_value = stats.ttest_rel(
+                        model_cv_scores[model_name][primary_metric],
+                        model_cv_scores[other_model][primary_metric]
+                    )
+                    
+                    if p_value < 0.05 and t_stat > 0:
+                        rank_info['significantly_better_than'].append({
+                            'model': other_model,
+                            'p_value': float(p_value),
+                            'rank': j + 1
+                        })
+                except Exception:
+                    continue
+            
+            ranking_with_significance.append(rank_info)
+        
+        return {
+            'ranking': ranking_with_significance,
+            'primary_metric': primary_metric,
+            'ranking_method': 'mean_cv_score_with_significance_testing'
+        }
+
+
+# Integration utilities for existing codebase
+class MLOpsStatisticalAnalyzer:
+    """Comprehensive statistical analyzer for MLOps pipeline"""
+    
+    def __init__(self, 
+                 confidence_level: float = 0.95,
+                 n_bootstrap: int = 1000,
+                 random_state: int = 42):
+        
+        self.confidence_level = confidence_level
+        self.n_bootstrap = n_bootstrap
+        self.random_state = random_state
+        
+        # Initialize analyzers
+        self.bootstrap_analyzer = BootstrapAnalyzer(n_bootstrap, confidence_level, random_state)
+        self.feature_analyzer = FeatureImportanceAnalyzer(n_bootstrap, confidence_level, random_state)
+        self.cv_analyzer = AdvancedCrossValidation(5, n_bootstrap, confidence_level, random_state)
+        self.comparison_analyzer = StatisticalModelComparison(confidence_level, n_bootstrap, random_state)
+        
+        if STRUCTURED_LOGGING_AVAILABLE:
+            self.logger = MLOpsLoggers.get_logger('statistical_analyzer')
+        else:
+            self.logger = logging.getLogger(__name__)
+    
+    def comprehensive_model_analysis(self,
+                                   models: Dict[str, Any],
+                                   X_train: np.ndarray,
+                                   X_test: np.ndarray,
+                                   y_train: np.ndarray,
+                                   y_test: np.ndarray,
+                                   feature_names: List[str] = None) -> Dict[str, Any]:
+        """
+        Perform comprehensive statistical analysis of models including:
+        - Bootstrap confidence intervals for performance metrics
+        - Feature importance stability analysis
+        - Advanced cross-validation with statistical testing
+        - Pairwise model comparisons with significance testing
+        """
+        
+        from sklearn.metrics import accuracy_score, f1_score, precision_score, recall_score, roc_auc_score
+        
+        # Define metrics
+        def accuracy_func(y_true, y_pred): return accuracy_score(y_true, y_pred)
+        def f1_func(y_true, y_pred): return f1_score(y_true, y_pred, average='weighted')
+        def precision_func(y_true, y_pred): return precision_score(y_true, y_pred, average='weighted')
+        def recall_func(y_true, y_pred): return recall_score(y_true, y_pred, average='weighted')
+        def roc_auc_func(y_true, y_pred_proba): return roc_auc_score(y_true, y_pred_proba)
+        
+        metrics = {
+            'accuracy': accuracy_func,
+            'f1': f1_func,
+            'precision': precision_func,
+            'recall': recall_func,
+            'roc_auc': roc_auc_func
+        }
+        
+        analysis_results = {
+            'analysis_timestamp': datetime.now().isoformat(),
+            'configuration': {
+                'confidence_level': self.confidence_level,
+                'n_bootstrap': self.n_bootstrap,
+                'models_analyzed': list(models.keys())
+            },
+            'individual_model_analysis': {},
+            'comparative_analysis': {},
+            'feature_importance_analysis': {},
+            'recommendations': []
+        }
+        
+        # Individual model analysis
+        for model_name, model in models.items():
+            try:
+                # Fit model
+                model.fit(X_train, y_train)
+                
+                # Get predictions
+                y_pred = model.predict(X_test)
+                y_pred_proba = model.predict_proba(X_test)[:, 1] if hasattr(model, 'predict_proba') else y_pred
+                
+                # Bootstrap analysis for each metric
+                bootstrap_results = {}
+                for metric_name, metric_func in metrics.items():
+                    if metric_name == 'roc_auc':
+                        result = self.bootstrap_analyzer.bootstrap_metric(
+                            y_test, y_pred_proba, metric_func
+                        )
+                    else:
+                        result = self.bootstrap_analyzer.bootstrap_metric(
+                            y_test, y_pred, metric_func
+                        )
+                    bootstrap_results[metric_name] = result.to_dict()
+                
+                # Cross-validation analysis
+                cv_analysis = self.cv_analyzer.comprehensive_cv_analysis(
+                    model, X_train, y_train, metrics
+                )
+                
+                # Feature importance analysis (if supported)
+                feature_analysis = {}
+                if hasattr(model, 'feature_importances_') or hasattr(model, 'coef_'):
+                    try:
+                        feature_analysis = self.feature_analyzer.analyze_importance_stability(
+                            model, X_train, y_train, feature_names
+                        )
+                    except Exception as e:
+                        feature_analysis = {'error': str(e)}
+                
+                analysis_results['individual_model_analysis'][model_name] = {
+                    'bootstrap_metrics': bootstrap_results,
+                    'cross_validation_analysis': cv_analysis,
+                    'feature_importance_analysis': feature_analysis
+                }
+                
+            except Exception as e:
+                self.logger.error(f"Analysis failed for model {model_name}: {e}")
+                analysis_results['individual_model_analysis'][model_name] = {'error': str(e)}
+        
+        # Comparative analysis
+        if len(models) > 1:
+            try:
+                comparative_results = self.comparison_analyzer.comprehensive_model_comparison(
+                    models, X_train, y_train, metrics
+                )
+                analysis_results['comparative_analysis'] = comparative_results
+                
+                # Generate recommendations based on comparison
+                recommendations = self._generate_analysis_recommendations(comparative_results)
+                analysis_results['recommendations'].extend(recommendations)
+                
+            except Exception as e:
+                analysis_results['comparative_analysis'] = {'error': str(e)}
+        
+        return analysis_results
+    
+    def _generate_analysis_recommendations(self, comparative_results: Dict[str, Any]) -> List[Dict[str, str]]:
+        """Generate actionable recommendations based on statistical analysis"""
+        recommendations = []
+        
+        # Model ranking recommendations
+        if 'model_ranking' in comparative_results:
+            ranking = comparative_results['model_ranking']['ranking']
+            if len(ranking) > 0:
+                best_model = ranking[0]
+                significantly_better_count = len(best_model.get('significantly_better_than', []))
+                
+                if significantly_better_count > 0:
+                    recommendations.append({
+                        'type': 'model_selection',
+                        'priority': 'high',
+                        'message': f"Model '{best_model['model_name']}' shows statistically significant improvement over {significantly_better_count} other model(s)",
+                        'action': f"Consider promoting {best_model['model_name']} to production"
+                    })
+        
+        # Feature importance recommendations
+        for model_name, analysis in comparative_results.get('individual_model_analysis', {}).items():
+            feature_analysis = analysis.get('feature_importance_analysis', {})
+            if 'stability_ranking' in feature_analysis:
+                unstable_features = [
+                    name for name, stats in feature_analysis['feature_importance_analysis'].items()
+                    if stats['metadata']['coefficient_of_variation'] > 0.5
+                ]
+                
+                if unstable_features:
+                    recommendations.append({
+                        'type': 'feature_engineering',
+                        'priority': 'medium',
+                        'message': f"Model '{model_name}' has {len(unstable_features)} unstable features with high variance",
+                        'action': "Review feature engineering process and consider feature selection"
+                    })
+        
+        # Cross-validation recommendations
+        for model_name, analysis in comparative_results.get('individual_model_analysis', {}).items():
+            cv_analysis = analysis.get('cross_validation_analysis', {})
+            for metric_name, metric_analysis in cv_analysis.get('metrics_analysis', {}).items():
+                overfitting_analysis = metric_analysis.get('overfitting_analysis', {})
+                if overfitting_analysis.get('overfitting_score', 0) > 0.1:  # 10% overfitting threshold
+                    recommendations.append({
+                        'type': 'model_complexity',
+                        'priority': 'medium',
+                        'message': f"Model '{model_name}' shows significant overfitting in {metric_name}",
+                        'action': "Consider regularization or reducing model complexity"
+                    })
+        
+        return recommendations
+    
+    def save_analysis_report(self, analysis_results: Dict[str, Any], file_path: Path = None):
+        """Save comprehensive analysis report"""
+        if file_path is None:
+            file_path = Path("/tmp/logs/statistical_analysis_report.json")
+        
+        file_path.parent.mkdir(parents=True, exist_ok=True)
+        
+        with open(file_path, 'w') as f:
+            json.dump(analysis_results, f, indent=2, default=str)
+        
+        self.logger.info(f"Statistical analysis report saved to {file_path}")
+        return file_path
+
+
+# Integration functions for existing codebase
+def integrate_statistical_analysis_with_retrain():
+    """Integration example for retrain.py"""
+    analyzer = MLOpsStatisticalAnalyzer()
+    
+    # Example usage in retraining context
+    def enhanced_model_comparison(models_dict, X_train, X_test, y_train, y_test):
+        """Enhanced model comparison with comprehensive statistical analysis"""
+        
+        analysis_results = analyzer.comprehensive_model_analysis(
+            models_dict, X_train, X_test, y_train, y_test
+        )
+        
+        # Extract promotion decision based on statistical significance
+        comparative_analysis = analysis_results.get('comparative_analysis', {})
+        ranking = comparative_analysis.get('model_ranking', {}).get('ranking', [])
+        
+        if ranking:
+            best_model = ranking[0]
+            promotion_confidence = len(best_model.get('significantly_better_than', [])) / (len(ranking) - 1) if len(ranking) > 1 else 1.0
+            
+            return {
+                'recommended_model': best_model['model_name'],
+                'statistical_confidence': promotion_confidence,
+                'analysis_results': analysis_results,
+                'promote_candidate': promotion_confidence > 0.5
+            }
+        
+        return {'error': 'No valid model ranking available'}
+    
+    return enhanced_model_comparison
+
+def integrate_statistical_analysis_with_train():
+    """Integration example for train.py"""
+    analyzer = MLOpsStatisticalAnalyzer()
+    
+    def enhanced_ensemble_validation(individual_models, ensemble_model, X, y):
+        """Enhanced ensemble validation with bootstrap confidence intervals"""
+        
+        models_to_compare = {**individual_models, 'ensemble': ensemble_model}
+        
+        # Perform comprehensive statistical analysis
+        X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
+        
+        analysis_results = analyzer.comprehensive_model_analysis(
+            models_to_compare, X_train, X_test, y_train, y_test
+        )
+        
+        # Check if ensemble is statistically significantly better
+        comparative_analysis = analysis_results.get('comparative_analysis', {})
+        ensemble_comparisons = {
+            k: v for k, v in comparative_analysis.get('pairwise_comparisons', {}).items()
+            if 'ensemble' in k
+        }
+        
+        significant_improvements = 0
+        total_comparisons = len(ensemble_comparisons)
+        
+        for comparison in ensemble_comparisons.values():
+            if comparison.get('overall_comparison', {}).get('improvement_rate', 0) > 0.5:
+                significant_improvements += 1
+        
+        ensemble_confidence = significant_improvements / total_comparisons if total_comparisons > 0 else 0
+        
+        return {
+            'use_ensemble': ensemble_confidence > 0.5,
+            'ensemble_confidence': ensemble_confidence,
+            'statistical_analysis': analysis_results
+        }
+    
+    return enhanced_ensemble_validation
+
+
+if __name__ == "__main__":
+    # Example usage and testing
+    print("Testing advanced statistical analysis system...")
+    
+    # Generate sample data for testing
+    np.random.seed(42)
+    X = np.random.randn(200, 10)
+    y = (X[:, 0] + X[:, 1] + np.random.randn(200) * 0.1 > 0).astype(int)
+    
+    # Create sample models
+    from sklearn.linear_model import LogisticRegression
+    from sklearn.ensemble import RandomForestClassifier
+    
+    models = {
+        'logistic_regression': LogisticRegression(random_state=42),
+        'random_forest': RandomForestClassifier(n_estimators=50, random_state=42)
+    }
+    
+    # Test comprehensive analysis
+    analyzer = MLOpsStatisticalAnalyzer(n_bootstrap=100)  # Reduced for testing
+    
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
+    
+    print("Running comprehensive statistical analysis...")
+    results = analyzer.comprehensive_model_analysis(
+        models, X_train, X_test, y_train, y_test
+    )
+    
+    print(f"Analysis completed for {len(models)} models")
+    print(f"Generated {len(results['recommendations'])} recommendations")
+    
+    # Test bootstrap analysis
+    bootstrap_analyzer = BootstrapAnalyzer(n_bootstrap=100)
+    
+    from sklearn.metrics import f1_score
+    def f1_metric(y_true, y_pred):
+        return f1_score(y_true, y_pred, average='weighted')
+    
+    model = LogisticRegression(random_state=42)
+    model.fit(X_train, y_train)
+    y_pred = model.predict(X_test)
+    
+    bootstrap_result = bootstrap_analyzer.bootstrap_metric(y_test, y_pred, f1_metric)
+    print(f"Bootstrap F1 confidence interval: {bootstrap_result.confidence_interval}")
+    
+    print("Advanced statistical analysis system test completed successfully!")