2nd/10_Wiki/Topic_Programming/DevOps_and_Security/Statistics & Data Analysis.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-statistics-data-analysis	Statistics & Data Analysis	10_Wiki/Topics	verified	self	stats data analysis applied statistics	none	A	0.9	applied	statistics data-analysis ab-testing ml observability		2026-05-10	pending	language framework python numpy-scipy-statsmodels-pymc

Statistics & Data Analysis

매 한 줄

"매 data 의 lying 의 — 매 stats 의 catching". Statistics 의 uncertainty 의 quantify 의, 매 patterns 의 noise 의 separate 의 의 discipline. 2026 의 production 의 standard 의: Bayesian methods (PyMC, Stan), causal inference (DoWhy, EconML), CUPED 의 A/B test variance reduction.

매 핵심

매 핵심 dichotomy

• Frequentist: p-values, confidence intervals — 매 long-run frequency 의.
• Bayesian: posteriors, credible intervals — 매 belief update 의.
• 2026 trend: Bayesian 의 production analytics 의 dominant (interpretable, sequential-safe).

매 must-know toolkit

• Hypothesis tests: t-test, Mann-Whitney, χ², Fisher exact.
• Regression: OLS, GLM (logistic, Poisson), mixed-effects.
• Causal: difference-in-differences, IV, RDD, synthetic control.
• A/B: CUPED, sequential testing (mSPRT), multi-armed bandits.

매 응용

1. Product A/B testing (CUPED + sequential).
2. SRE — anomaly detection on metrics.
3. SAST/SCA findings 의 risk scoring (Bayesian prior).

💻 패턴

Welch t-test (A/B)

import numpy as np
from scipy import stats
control = np.array([...])
treatment = np.array([...])
t, p = stats.ttest_ind(control, treatment, equal_var=False)
ci = stats.t.interval(0.95, len(control)+len(treatment)-2,
                      loc=treatment.mean()-control.mean(),
                      scale=stats.sem(np.concatenate([control, treatment])))
print(f"Δ={treatment.mean()-control.mean():.4f}, p={p:.4f}, 95%CI={ci}")

CUPED variance reduction

import numpy as np
def cuped_adjust(y_pre, y_post):
    theta = np.cov(y_pre, y_post)[0,1] / np.var(y_pre)
    return y_post - theta * (y_pre - y_pre.mean())
y_adj_c = cuped_adjust(pre_c, post_c)
y_adj_t = cuped_adjust(pre_t, post_t)

Bayesian A/B (PyMC)

import pymc as pm
with pm.Model() as m:
    p_a = pm.Beta('p_a', 1, 1)
    p_b = pm.Beta('p_b', 1, 1)
    pm.Binomial('obs_a', n=n_a, p=p_a, observed=k_a)
    pm.Binomial('obs_b', n=n_b, p=p_b, observed=k_b)
    pm.Deterministic('lift', (p_b - p_a) / p_a)
    idata = pm.sample(2000, tune=1000)
print(f"P(B>A) = {(idata.posterior['lift']>0).mean().item():.3f}")

Sequential testing (mSPRT)

import numpy as np
def msprt(x, y, sigma2_tau=0.01, alpha=0.05):
    n = min(len(x), len(y))
    delta = y[:n] - x[:n]
    s2 = delta.var(ddof=1)
    t = delta.mean() * np.sqrt(n)
    lr = np.sqrt(s2/(s2+n*sigma2_tau)) * np.exp(
        n*sigma2_tau*t**2 / (2*s2*(s2+n*sigma2_tau)))
    return lr > 1/alpha

Causal — difference-in-differences (statsmodels)

import statsmodels.formula.api as smf
m = smf.ols('y ~ treated * post + C(unit) + C(time)', data=df).fit(
    cov_type='cluster', cov_kwds={'groups': df['unit']})
print(m.params['treated:post'])

Anomaly — robust z (MAD)

import numpy as np
def mad_z(x):
    med = np.median(x)
    mad = np.median(np.abs(x - med))
    return 0.6745 * (x - med) / (mad + 1e-9)
anomalies = np.abs(mad_z(latency_p99)) > 3.5

매 결정 기준

상황	Method
2-arm online experiment, fixed N	Welch t-test + CUPED
sequential / peeking 위험	mSPRT or Bayesian
many arms, exploration value	Thompson sampling bandit
observational, treatment effect	DiD / IV / synthetic control
heavy-tailed (revenue)	Mann-Whitney + bootstrap CI

기본값: Welch + CUPED for online A/B; Bayesian for small-N or peeking; bootstrap for non-Gaussian.

🔗 Graph

• 부모: Probability Theory
• 변형: Bayesian Statistics · Causal Inference
• 응용: Anomaly Detection · ML Evaluation
• Adjacent: PyMC

🤖 LLM 활용

언제: experiment design review, p-value 해석, choosing test for distribution shape, generating PyMC models from descriptions. 언제 X: trusting LLM-computed p-values 없이 의 verification — 매 arithmetic mistakes.

❌ 안티패턴

• Peeking: 매 fixed-N test 의 daily check 의 stop — 매 false positive rate 의 5% → 30%+.
• HARKing: 매 hypothesis after results known.
• p<0.05 worship: 매 effect size 무시.
• Ignoring multiple testing: 매 20 metrics 의 →약 1 의 false positive 의 expected.
• CUPED 의 covariate 의 post-treatment 의: 매 invalidates.

🧪 검증 / 중복

• Verified (Microsoft CUPED paper 2013, Optimizely Stats Engine, Gelman BDA3, Wasserman All of Stats).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — A/B + Bayesian + causal patterns