aiming-lab/autoresearchclaw/statistical-problem-formulation

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Formulate statistical research problems with formal notation, target parameters, assumptions, hypotheses, evaluation criteria, and theory targets.

Install

npx vskill@latest install aiming-lab/autoresearchclaw/statistical-problem-formulation

SKILL.md

Statistical Problem Formulation

Overview

Use this skill before any method design, theory, experiment, or report writing. The goal is to transform a broad topic into a precise statistical problem.

Required Formulation Elements

ElementQuestions
Observed dataWhat is observed? What is the sample size? Are samples iid, dependent, clustered, censored, or selected?
Data modelWhat family of distributions or data-generating processes is considered?
TargetWhat parameter, decision, prediction, or risk is the object of study?
AssumptionsWhat must hold for the target to be identifiable or the method to work?
HypothesesWhat claims should be supported, refuted, or made inconclusive?
CriteriaWhat metrics define success or failure?
Theory targetWhat property should be derived: bias, variance, consistency, rate, coverage, error bound, robustness, or impossibility?

Handoff Schema

The problem formulation should be precise enough to support this structured handoff:

yaml
topic_id: TXX
title: ""
research_question: ""
observed_data:
  notation: ""
  sampling: iid | dependent | clustered | time_series | selected | unknown
data_model:
  notation: ""
  family: ""
target:
  name: ""
  notation: ""
  type: estimand | decision | prediction | risk | descriptive_quantity
  truth_source: analytic | simulation | oracle | empirical_reference | not_applicable
assumptions:
  structural: []
  sampling: []
  regularity: []
  identifiability: []
claims:
  - id: C1
    statement: ""
    formal_statement: ""
evaluation_criteria:
  - name: ""
    direction: ""
theory_targets:
  - identifiability
  - bias
  - consistency
blocking_ambiguities: []

Template

markdown
# Problem Formulation
 
## Research Question
...
 
## Observed Data
Let ...
 
## Data-Generating Model
Assume ...
 
## Target / Estimand
Define ...
 
## Candidate Procedure Class
We consider procedures ...
 
## Assumptions
1....
 
## Claims / Hypotheses
-...
 
## Evaluation Criteria
-...
 
## Theoretical Questions
-...
 
## Experimental Questions
-...

Quality Bar

A formulation passes only if another researcher could implement or analyze the problem without guessing the target, assumptions, or success criteria.

Security

  • Security scanPassed, 90 of 100Pattern checks on the skill's files.
  • Model reviewPassed

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Quality evaluation

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Source

Popularity

Repository stars
13,869
Repository forks
1,628
7-day trend score
48

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