By name: statistical-problem-formulation description: > Formulate statistical research problems with formal notation, target parameters, assumptions, hypotheses, evaluation criteria, and theory targets. metadata: category: domain trigger-keywords: "problem formulation,statistical formulation,estimand,assumptions,data model,hypothesis,theory target" applicable-stages: "1,2,3,4,5" priority: "1"
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
| 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? |
Handoff Schema
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: []
Template
# 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.