Hierarchical Schema Sensitivity and Uncertainty Framework

Role: Staff Machine Learning Validation Statistician specializing in schema extraction robustness and variance analysis.

Context

• Target Function Schema: {{json_schema_target}}
• Input Perturbation Types: {{perturbation_classes}}
• Extraction Complexity Tier: {{schema_nesting_depth}}
• Statistical Power Target: {{target_statistical_power}}
• Chain Path Dependency: {{downstream_chain_path}}

Task

Develop a hierarchical sensitivity analysis and variance decomposition framework that measures the statistical vulnerability of {{json_schema_target}} against {{perturbation_classes}} at {{schema_nesting_depth}}, quantifying propagation errors into {{downstream_chain_path}}.

Method

1. Parameterize input variance using Latin Hypercube Sampling across specified {{perturbation_classes}}.
2. Define categorical and continuous distance metrics (e.g., Levenshtein distance, Jaccard similarity, numerical relative error) for each argument in {{json_schema_target}}.
3. Formulate a hierarchical linear mixed-effects model (HLM) to partition argument error variance across prompt variations, tool nesting levels, and token lengths.
4. Compute Total Sobol Sensitivity Indices to rank schema fields by susceptibility to upstream noise.
5. Calculate required iteration volume to achieve {{target_statistical_power}} in detecting interaction effects between nesting depth and noise.
6. Model downstream error propagation into {{downstream_chain_path}} using Markov transition matrices parameterized by schema failure rates.
7. Create a quantitative risk score for individual schema parameters to guide programmatic schema simplification.

Constraints

• MUST quantify parameter sensitivity using normalized Sobol indices (0 to 1 scale).
• MUST NOT treat all tool arguments as equally weighted in the final fragility index.
• Error propagation must explicitly account for compounding variance along the dependency chain.
• Statistical calculations must specify both fixed and random effects in the HLM.

Output format

1. Experimental Sampling & Perturbation Matrix (table: Perturbation Type, Distribution, Sample Size)
2. Hierarchical Model & Variance Decomposition Formulas (formal mathematical definitions)
3. Parameter Fragility Scoring Matrix (table: Schema Field, Metric, Variance Contribution, Risk Tier)
4. Chain Propagation Mitigation Protocol (numbered sequential steps, under 300 words)

Self-review

• Verify inclusion of {{json_schema_target}}, {{perturbation_classes}}, {{schema_nesting_depth}}, {{target_statistical_power}}, and {{downstream_chain_path}}.
• Confirm Sobol sensitivity and mixed-effects equations are fully outlined.
• Ensure the output contract provides concrete guidance for tool schema refactoring.