Statistical Modeling Experiment Design Causal Inference

---
name: statistical-modeling-experiment-design-causal-inference
description: "World-class senior data scientist skill specialising in statistical modeling, experiment design, causal inference, and predictive analytics. Covers A/B testing (sample sizing, two-proportion z-tests, Bonferroni correction), difference-in-differences, feature engineering pipeline…"
category: "AI & Agents"
author: community
version: "2.1.1"
icon: bot
---

# Senior Data Scientist

World-class senior data scientist skill for production-grade AI/ML/Data systems.

## Core Workflows

### 1. Design an A/B Test

```python
import numpy as np
from scipy import stats

def calculate_sample_size(baseline_rate, mde, alpha=0.05, power=0.8):
    """
    Calculate required sample size per variant.
    baseline_rate: current conversion rate (e.g. 0.10)
    mde: minimum detectable effect (relative, e.g. 0.05 = 5% lift)
    """
    p1 = baseline_rate
    p2 = baseline_rate * (1 + mde)
    effect_size = abs(p2 - p1) / np.sqrt((p1 * (1 - p1) + p2 * (1 - p2)) / 2)
    z_alpha = stats.norm.ppf(1 - alpha / 2)
    z_beta = stats.norm.ppf(power)
    n = ((z_alpha + z_beta) / effect_size) ** 2
    return int(np.ceil(n))

def analyze_experiment(control, treatment, alpha=0.05):
    """
    Run two-proportion z-test and return structured results.
    control/treatment: dicts with 'conversions' and 'visitors'.
    """
    p_c = control["conversions"] / control["visitors"]
    p_t = treatment["conversions"] / treatment["visitors"]
    pooled = (control["conversions"] + treatment["conversions"]) / (control["visitors"] + treatment["visitors"])
    se = np.sqrt(pooled * (1 - pooled) * (1 / control["visitors"] + 1 / treatment["visitors"]))
    z = (p_t - p_c) / se
    p_value = 2 * (1 - stats.norm.cdf(abs(z)))
    ci_low = (p_t - p_c) - stats.norm.ppf(1 - alpha / 2) * se
    ci_high = (p_t - p_c) + stats.norm.ppf(1 - alpha / 2) * se
    return {
        "lift": (p_t - p_c) / p_c,
        "p_value": p_value,
        "significant": p_value < alpha,
        "ci_95": (ci_low, ci_high),
    }

# --- Experiment checklist ---
# 1. Define ONE primary metric and pre-register secondary metrics.
# 2. Calculate sample size BEFORE starting: calculate_sample_size(0.10, 0.05)
# 3. Randomise at the user (not session) level to avoid leakage.
# 4. Run for at least 1 full business cycle (typically 2 weeks).
# 5. Check for sample ratio mismatch: abs(n_control - n_treatment) / expected < 0.01
# 6. Analyze with analyze_experiment() and report lift + CI, not just p-value.
# 7. Apply Bonferroni correction if testing multiple metrics: alpha / n_metrics
```

### 2. Build a Feature Engineering Pipeline

```python
import pandas as pd
import numpy as np
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.impute import SimpleImputer
from sklearn.compose import ColumnTransformer

def build_feature_pipeline(numeric_cols, categorical_cols, date_cols=None):
    """
    Returns a fitted-ready ColumnTransformer for structured tabular data.
    """
    numeric_pipeline = Pipeline([
        ("impute", SimpleImputer(strategy="median")),
        ("scale",  StandardScaler()),
    ])
    categorical_pipeline = Pipeline([
        ("impute", SimpleImputer(strategy="most_frequent")),
        ("encode", OneHotEncoder(handle_unknown="ignore", sparse_output=False)),
    ])
    transformers = [
        ("num", numeric_pipeline, numeric_cols),
        ("cat", categorical_pipeline, categorical_cols),
    ]
    return ColumnTransformer(transformers, remainder="drop")

def add_time_features(df, date_col):
    """Extract cyclical and lag features from a datetime column."""
    df = df.copy()
    df[date_col] = pd.to_datetime(df[date_col])
    df["dow_sin"] = np.sin(2 * np.pi * df[date_col].dt.dayofweek / 7)
    df["dow_cos"] = np.cos(2 * np.pi * df[date_col].dt.dayofweek / 7)
    df["month_sin"] = np.sin(2 * np.pi * df[date_col].dt.month / 12)
    df["month_cos"] = np.cos(2 * np.pi * df[date_col].dt.month / 12)
    df["is_weekend"] = (df[date_col].dt.dayofweek >= 5).astype(int)
    return df

# --- Feature engineering checklist ---
# 1. Never fit transformers on the full dataset — fit on train, transform test.
# 2. Log-transform right-skewed numeric features before scaling.
# 3. For high-cardinality categoricals (>50 levels), use target encoding or embeddings.
# 4. Generate lag/rolling features BEFORE the train/test split to avoid leakage.
# 5. Document each feature's business meaning alongside its code.
```

### 3. Train, Evaluate, and Select a Prediction Model

```python
from sklearn.model_selection import StratifiedKFold, cross_validate
from sklearn.metrics import make_scorer, roc_auc_score, average_precision_score
import xgboost as xgb
import mlflow

SCORERS = {
    "roc_auc":  make_scorer(roc_auc_score, needs_proba=True),
    "avg_prec": make_scorer(average_precision_score, needs_proba=True),
}

def evaluate_model(model, X, y, cv=5):
    """
    Cross-validate and return mean ± std for each scorer.
    Use StratifiedKFold for classification to preserve class balance.
    """
    cv_results = cross_validate(
        model, X, y,
        cv=StratifiedKFold(n_splits=cv, shuffle=True, random_state=42),
        scoring=SCORERS,
        return_train_score=True,
    )
    summary = {}
    for metric in SCORERS:
        test_scores = cv_results[f"test_{metric}"]
        summary[metric] = {"mean": test_scores.mean(), "std": test_scores.std()}
        # Flag overfitting: large gap between train and test score
        train_mean = cv_results[f"train_{metric}"].mean()
        summary[metric]["overfit_gap"] = train_mean - test_scores.mean()
    return summary

def train_and_log(model, X_train, y_train, X_test, y_test, run_name):
    """Train model and log all artefacts to MLflow."""
    with mlflow.start_run(run_name=run_name):
        model.fit(X_train, y_train)
        proba = model.predict_proba(X_test)[:, 1]
        metrics = {
            "roc_auc":  roc_auc_score(y_test, proba),
            "avg_prec": average_precision_score(y_test, proba),
        }
        mlflow.log_params(model.get_params())
        mlflow.log_metrics(metrics)
        mlflow.sklearn.log_model(model, "model")
        return metrics

# --- Model evaluation checklist ---
# 1. Always report AUC-PR alongside AUC-ROC for imbalanced datasets.
# 2. Check overfit_gap > 0.05 as a warning sign of overfitting.
# 3. Calibrate probabilities (Platt scaling / isotonic) before production use.
# 4. Compute SHAP values to validate feature importance makes business sense.
# 5. Run a baseline (e.g. DummyClassifier) and verify the model beats it.
# 6. Log every run to MLflow — never rely on notebook output for comparison.
```

### 4. Causal Inference: Difference-in-Differences

```python
import statsmodels.formula.api as smf

def diff_in_diff(df, outcome, treatment_col, post_col, controls=None):
    """
    Estimate ATT via OLS DiD with optional covariates.
    df must have: outcome, treatment_col (0/1), post_col (0/1).
    Returns the interaction coefficient (treatment × post) and its p-value.
    """
    covariates = " + ".join(controls) if controls else ""
    formula = (
        f"{outcome} ~ {treatment_col} * {post_col}"
        + (f" + {covariates}" if covariates else "")
    )
    result = smf.ols(formula, data=df).fit(cov_type="HC3")
    interaction = f"{treatment_col}:{post_col}"
    return {
        "att":     result.params[interaction],
        "p_value": result.pvalues[interaction],
        "ci_95":   result.conf_int().loc[interaction].tolist(),
        "summary": result.summary(),
    }

# --- Causal inference checklist ---
# 1. Validate parallel trends in pre-period before trusting DiD estimates.
# 2. Use HC3 robust standard errors to handle heteroskedasticity.
# 3. For panel data, cluster SEs at the unit level (add groups= param to fit).
# 4. Consider propensity score matching if groups differ at baseline.
# 5. Report the ATT with confidence interval, not just statistical significance.
```

## Reference Documentation

- **Statistical Methods:** `references/statistical_methods_advanced.md`
- **Experiment Design Frameworks:** `references/experiment_design_frameworks.md`
- **Feature Engineering Patterns:** `references/feature_engineering_patterns.md`

## Common Commands

```bash
# Testing & linting
python -m pytest tests/ -v --cov=src/
python -m black src/ && python -m pylint src/

# Training & evaluation
python scripts/train.py --config prod.yaml
python scripts/evaluate.py --model best.pth

# Deployment
docker build -t service:v1 .
kubectl apply -f k8s/
helm upgrade service ./charts/

# Monitoring & health
kubectl logs -f deployment/service
python scripts/health_check.py
```