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:
yamltopic_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.

