refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-statistical-analysis
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title: Statistical Analysis
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Statistics, Inferential Statistics, Data Analysis]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [statistics, hypothesis-testing, regression, bayesian]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python / R
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framework: scipy / statsmodels / pymc / R-tidyverse
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---
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# Statistical Analysis
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## 매 한 줄
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> **"매 데이터의 uncertainty 를 정량화"**. Fisher–Neyman frequentist framework 부터 Gelman 2020s Bayesian workflow까지, 2026 현재 표준은 statsmodels + PyMC 5.x + ArviZ pipeline 으로 reproducible inference를 빌드하는 것이다.
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## 매 핵심
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### 매 두 paradigm
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- **Frequentist**: parameter 는 fixed, data 가 random. p-value, confidence interval, MLE.
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- **Bayesian**: parameter 도 random, prior + likelihood → posterior. Credible interval, posterior predictive.
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- **2026 합의**: 매 둘 다 도구 — small n / strong prior 면 Bayesian, large n / regulated 면 frequentist.
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### 매 핵심 절차
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- **EDA**: distribution, missing, outlier, correlation matrix.
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- **Hypothesis test**: t-test, χ², Mann-Whitney, permutation. Effect size + CI 동봉.
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- **Regression**: OLS → GLM → mixed-effects → hierarchical Bayesian.
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- **Model checking**: residual diagnostics, posterior predictive checks, k-fold CV.
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### 매 응용
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1. A/B test 분석 (web, ML model rollout).
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2. Clinical trial efficacy.
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3. Causal inference (DiD, IV, RDD, double ML).
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4. Risk modeling (insurance, finance).
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## 💻 패턴
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### Welch's t-test + effect size + CI (scipy 1.13+)
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```python
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import numpy as np
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from scipy import stats
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def welch_with_effect(a, b):
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t, p = stats.ttest_ind(a, b, equal_var=False)
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n1, n2 = len(a), len(b)
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s1, s2 = a.var(ddof=1), b.var(ddof=1)
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pooled = np.sqrt(((n1-1)*s1 + (n2-1)*s2) / (n1+n2-2))
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cohen_d = (a.mean() - b.mean()) / pooled
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df = (s1/n1 + s2/n2)**2 / ((s1/n1)**2/(n1-1) + (s2/n2)**2/(n2-1))
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se = np.sqrt(s1/n1 + s2/n2)
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crit = stats.t.ppf(0.975, df)
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diff = a.mean() - b.mean()
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return dict(t=t, p=p, d=cohen_d, ci=(diff - crit*se, diff + crit*se))
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```
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### OLS regression with diagnostics (statsmodels)
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```python
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import statsmodels.api as sm
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import statsmodels.formula.api as smf
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model = smf.ols("y ~ x1 + x2 + C(group)", data=df).fit(cov_type="HC3")
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print(model.summary())
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# diagnostics
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from statsmodels.stats.diagnostic import het_breuschpagan
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bp = het_breuschpagan(model.resid, model.model.exog)
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print("Breusch-Pagan p:", bp[1])
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```
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### Hierarchical Bayesian (PyMC 5.x)
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```python
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import pymc as pm
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import arviz as az
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with pm.Model() as hier:
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mu_a = pm.Normal("mu_a", 0, 5)
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sigma_a = pm.HalfNormal("sigma_a", 1)
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a = pm.Normal("a", mu_a, sigma_a, shape=n_groups)
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b = pm.Normal("b", 0, 1)
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sigma = pm.HalfNormal("sigma", 1)
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mu = a[group_idx] + b * x
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pm.Normal("y_obs", mu, sigma, observed=y)
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idata = pm.sample(2000, tune=1000, target_accept=0.95)
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az.plot_trace(idata)
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az.summary(idata, var_names=["mu_a", "sigma_a", "b"])
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```
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### Bootstrap CI
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```python
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import numpy as np
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def bootstrap_ci(data, stat=np.mean, n=10_000, alpha=0.05, rng=None):
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rng = rng or np.random.default_rng(42)
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boots = stat(rng.choice(data, size=(n, len(data)), replace=True), axis=1)
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lo, hi = np.quantile(boots, [alpha/2, 1-alpha/2])
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return stat(data), (lo, hi)
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```
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### Multiple testing correction
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```python
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from statsmodels.stats.multitest import multipletests
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reject, pvals_corr, _, _ = multipletests(pvals, alpha=0.05, method="fdr_bh")
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```
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### Causal inference: doubly robust (EconML / DoubleML)
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```python
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from econml.dml import LinearDML
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from sklearn.ensemble import GradientBoostingRegressor
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dml = LinearDML(
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model_y=GradientBoostingRegressor(),
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model_t=GradientBoostingRegressor(),
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discrete_treatment=False,
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cv=5,
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)
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dml.fit(Y, T, X=X, W=W)
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print(dml.effect(X), dml.effect_interval(X))
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| 2-group mean compare, normal-ish | Welch's t-test |
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| Non-parametric, small n | Mann-Whitney / permutation |
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| Multi-level data | Mixed-effects (lme4 / statsmodels) |
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| Strong prior, small n | Bayesian (PyMC) |
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| Causal effect from observational | DML / IV / RDD |
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| Many comparisons | FDR (BH), not Bonferroni unless ≤10 tests |
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**기본값**: statsmodels for frequentist, PyMC 5 + ArviZ for Bayesian, EconML for causal.
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## 🔗 Graph
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- 부모: [[Probability Theory]]
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- 변형: [[Bayesian_Inference|Bayesian Inference]] · [[Causal Inference]]
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- Adjacent: [[Machine Learning]] · [[Power Analysis]]
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## 🤖 LLM 활용
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**언제**: pipeline scaffolding, EDA narrative, model spec translation, plot 코드 생성.
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**언제 X**: numerical p-value computation 직접 — library 사용. 매 LLM의 hallucinated stat 의 X.
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## ❌ 안티패턴
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- **p-hacking**: 매 multiple test 후 cherry-pick — pre-registration + correction 필수.
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- **CI vs PI 혼동**: confidence interval ≠ prediction interval. 매 명확히 구분.
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- **HARKing**: hypothesis after results — exploratory vs confirmatory 분리.
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- **Naive default prior**: PyMC `Normal(0, 100)` 의 X — domain-informed weakly-informative prior.
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- **n=30 rule**: 매 myth — distribution shape 기반 결정.
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## 🧪 검증 / 중복
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- Verified (Wasserman "All of Statistics", Gelman BDA3, statsmodels docs 0.14+, PyMC 5.x docs).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — frequentist + Bayesian + causal patterns |
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