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Statistical Theory Analysis

Research
statistical-theory-analysis

Statistical Theory Analysis is an Agent Skill for research published in the aiming-lab/AutoResearchClaw repository on GitHub: a SKILL.md instruction file an AI agent can load to do this task.

Analyze theoretical properties of statistical methods under the formal formulation: identifiability, bias, variance, consistency, asymptotics, coverage, error bounds, robustness, and limitations.

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How to use this skill

Bring this guide into your coding agent with a prompt tailored to the tool you use.

  1. Open your project in Codex.
  2. Copy and paste the prompt below.
  3. Review files and risks before approving any action.
Prompt to paste
Inspect the Agent Skill at https://github.com/aiming-lab/AutoResearchClaw/blob/HEAD/external/agents/stat_research_agent/skills/statistical-theory-analysis/SKILL.md and all supporting files. Report provenance, permissions, scripts, dependencies, and security risks. Propose an exact installation into .agents/skills/statistical-theory-analysis, but wait for my approval before writing files or running scripts.

Copying this prompt does not install or run the skill. Review third-party files before use.

Statistical Theory Analysis

Overview

Use this skill after method proposal and before final experimental comparison. Theory is required as a stage even if the final output is a simulation paper.

Theory Outputs

Depending on the topic, provide:

  • Identifiability argument
  • Bias or variance calculation
  • Consistency statement
  • Asymptotic distribution
  • Coverage or calibration argument
  • Risk or error bound
  • Robustness analysis
  • Sensitivity or impossibility result
  • Counterexample showing failure outside assumptions

Theorem Template

## Proposition
Under assumptions A1-Ak, method M satisfies ...

## Proof Sketch
1. ...
2. ...
3. ...

## Interpretation
This predicts that ...

## Limitations
The result does not cover ...

Experimental Predictions

Every theoretical claim should produce an empirical prediction when possible:

  • Direction of metric change
  • Condition under which the method should improve
  • Stress condition under which it should fail
  • Baseline it should outperform