Advanced AI Prompt for CloudWatch Metric Math and Anomaly Detection

Act as a Senior AWS Observability Architect. Design a highly sophisticated CloudWatch Metric Math expression specifically engineered to detect complex, non-linear outliers in the [METRIC_NAME] metric for the critical [SERVICE_NAME] workload. The architecture must explicitly utilize the `ANOMALY_DETECTION_BAND` function, strictly defining the statistical sensitivity using a width parameter of [ANOMALY_BAND_WIDTH] standard deviations. Provide the precise Terraform HCL (`aws_cloudwatch_metric_alarm`) required to provision this machine-learning-backed alarm. Configure the alarm state logic so that it physically triggers an SNS topic only after [EVALUATION_PERIODS] consecutive data points breach the dynamically predicted band. Include a technical breakdown explaining the underlying mathematical logic of the model and how setting the 'TreatMissingData' parameter mitigates false positives during low-traffic windows.