Monte Carlo Convergence and Statistical Drift Test Suite Generator

Role: Lead Quantitative Research Systems Engineer specializing in statistical validation and stochastic model quality assurance.

Context

• Stochastic Algorithm / Estimator Definition: {{stochastic_model_definition}}
• Theoretical Null Hypothesis and Properties: {{null_hypothesis_formulation}}
• Sample Size Progression Schedule: {{sample_size_schedule}}
• Significance Level Alpha: {{significance_alpha}}
• Statistical Test Methodology: {{statistical_test_type}}
• Convergence Metric and Error Bound: {{convergence_metric}}

Task

Develop an automated Python statistical testing script that executes Monte Carlo trials of {{stochastic_model_definition}}, applies {{statistical_test_type}} to test {{null_hypothesis_formulation}} at alpha {{significance_alpha}}, and verifies asymptotic behavior against {{convergence_metric}}.

Method

1. Define reproducible multi-seed execution harness with vectorized pseudo-random and quasi-random sequence generators.
2. Encapsulate {{stochastic_model_definition}} into a vectorized simulator capable of batch sampling across {{sample_size_schedule}}.
3. Construct iterative estimators tracking running empirical means, higher-order moments (skewness, kurtosis), and standard error rates.
4. Implement the exact test statistic computation for {{statistical_test_type}} (e.g., Kolmogorov-Smirnov, Anderson-Darling, permutation test, or t-test).
5. Compute critical values and empirical p-values against the significance threshold {{significance_alpha}} to evaluate {{null_hypothesis_formulation}}.
6. Evaluate convergence decay rates across {{sample_size_schedule}} to confirm empirical convergence matches {{convergence_metric}} (e.g., O(1/sqrt(N)) error decay).
7. Build a failure diagnostic logger detailing distribution shifts, p-value trends, and bootstrap confidence intervals upon test failure.

Constraints

• MUST provide runnable Python script utilizing standard statistical libraries (e.g., SciPy, NumPy, Statsmodels).
• MUST enforce deterministic seed management with options to run permutation multi-seed sweeps.
• MUST NOT hardcode p-value outcomes; all metrics must be dynamically calculated from simulation outputs.
• Implement explicit assertion guards raising descriptive AssertionError messages with computed p-values.

Output format

Return a clean, self-contained Python script organized into the following explicit blocks:

1. Imports, Seed Initialization, and Global Test Constants
2. Monte Carlo Execution Engine for {{stochastic_model_definition}}
3. Statistical Test Function Implementing {{statistical_test_type}}
4. Asymptotic Convergence Verification Suite for {{convergence_metric}}
5. Main CLI Runner with Structured Diagnostic Summary Output

Self-review

• Confirm that the script tests {{null_hypothesis_formulation}} using {{significance_alpha}} correctly.
• Verify that the sample iteration dynamically processes all values in {{sample_size_schedule}}.
• Check that convergence assertions explicitly validate the error bound defined in {{convergence_metric}}.