Update README.md

README.md

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----
-license: apache-2.0
----
+---
+language: en
+license: apache-2.0
+tags:
+- bayesian
+- risk-scoring
+- ai-reliability
+- governance
+- sre
+---
+
+# ARF Risk Scoring Model
+
+A Bayesian risk scoring model for AI system reliability and failure prediction.  
+This model implements the core risk assessment logic from the [Agentic Reliability Framework (ARF)](https://huggingface.co/spaces/A-R-F/Agentic-Reliability-Framework-API).
+
+## 📌 Problem
+
+AI‑driven systems fail silently in production. Without a calibrated measure of failure probability, operations teams cannot decide whether to approve, deny, or escalate infrastructure changes.
+
+## 🔍 Mathematical Formulation
+
+Given a set of signals (telemetry, context), the risk score is defined as:
+
+\[
+\text{Risk}(x) = P(\text{Failure} \mid \text{Signals}, \text{Context})
+\]
+
+Internally, ARF combines:
+- **Conjugate Beta priors** for per‑category online updates.
+- **Hyperpriors** that share statistical strength across categories.
+- **Hamiltonian Monte Carlo (HMC)** to capture complex patterns (time‑of‑day, user role, environment).
+
+The final risk score is a weighted average of these three components, with weights determined by data availability.
+
+## 🚀 Usage
+
+You can use this model directly via the ARF API, or integrate the underlying Python library.
+
+### Example with ARF API (Python)
+
+```python
+import requests
+
+response = requests.post(
+    "https://a-r-f-agentic-reliability-framework-api.hf.space/api/v1/incidents/evaluate",
+    json={
+        "service_name": "payment-gateway",
+        "event_type": "latency_spike",
+        "severity": "high",
+        "metrics": {"latency_p99": 350, "error_rate": 0.12}
+    }
+)
+result = response.json()
+print(f"Risk score: {result['risk_score']:.3f}")
+print(f"Risk factors: {result['risk_factors']}")
+print(f"Recommended action: {result['recommended_action']}")
+```
+
+### Example using the ARF Python package
+
+```python
+from agentic_reliability_framework.core.governance.risk_engine import RiskEngine
+
+engine = RiskEngine()
+risk, explanation, contributions = engine.calculate_risk(
+    intent=some_intent,
+    cost_estimate=100.0,
+    policy_violations=[]
+)
+print(f"Risk: {risk}")
+```
+
+📚 Links
+--------
+
+*   **ARF Space**: [Agentic Reliability Framework (ARF) v4 API](https://huggingface.co/spaces/A-R-F/Agentic-Reliability-Framework-API)
+    
+*   **GitHub Repository**: [arf-foundation/agentic-reliability-framework](https://github.com/arf-foundation/agentic-reliability-framework)
+    
+*   **Documentation**: [API Docs](https://a-r-f-agentic-reliability-framework-api.hf.space/api/docs)
+    
+
+📊 Input / Output
+-----------------
+
+InputTypeDescriptionservice\_namestringName of the service being evaluatedevent\_typestringType of incident (e.g., latency\_spike)severitystringlow / medium / high / criticalmetricsdictTelemetry values (latency, error rate, CPU, etc.)OutputTypeDescriptionrisk\_scorefloatCalibrated failure probability (0–1)risk\_factorsdictAdditive contributions from conjugate, hyperprior, HMCrecommended\_actionstringapprove / deny / escalatedecision\_traceobjectExpected losses and variance
+
+📄 License
+----------
+
+Apache 2.0 – See [LICENSE](https://github.com/arf-foundation/agentic-reliability-framework/blob/main/LICENSE) for details.
+
+🤝 Contributing
+---------------
+
+Contributions are welcome! Please refer to the [contribution guidelines](https://github.com/arf-foundation/agentic-reliability-framework/blob/main/CONTRIBUTING.md) in the main repository.