Formulate statistical research problems with formal notation, target parameters, assumptions, hypotheses, evaluation criteria, and theory targets.
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.
| Element | Questions |
|---|---|
| Observed data | What is observed? What is the sample size? Are samples iid, dependent, clustered, censored, or selected? |
| Data model | What family of distributions or data-generating processes is considered? |
| Target | What parameter, decision, prediction, or risk is the object of study? |
| Assumptions | What must hold for the target to be identifiable or the method to work? |
| Hypotheses | What claims should be supported, refuted, or made inconclusive? |
| Criteria | What metrics define success or failure? |
| Theory target | What property should be derived: bias, variance, consistency, rate, coverage, error bound, robustness, or impossibility? |
The problem formulation should be precise enough to support this structured handoff:
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: []
# 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
- ...
A formulation passes only if another researcher could implement or analyze the problem without guessing the target, assumptions, or success criteria.
AFaffaan-m/ECC278k近 7 天新增 4,046 个 star
GAgarrytan/gstack136k近 7 天新增 883 个 star
ADaddyosmani/agent-skills106k近 7 天新增 3,628 个 star
NEnexu-io/open-design101k近 7 天新增 1,126 个 star
NEnexu-io/open-design101k近 7 天新增 1,126 个 star
THthedotmack/claude-mem100k近 7 天新增 3,024 个 star