docs(10_Wiki): Topic_Business/General/Graphic/Programming을 Topics/ 하위로 이동
최상위 10_Wiki/Topic_*였던 4개 카테고리 폴더를 10_Wiki/Topics/Topic_* 로 재배치. 콘텐츠 변경 없음(순수 폴더 이동) — Topics/ 하위 나머지 폴더는 이미 지난 커밋에서 전부 정리된 상태(잔존 항목은 에이전트 운영 상태 및 사용자가 보존을 요청한 업데이트0615/무제 3.canvas 뿐).
This commit is contained in:
Antigravity Agent
+190
@@ -0,0 +1,190 @@
|
||||
---
|
||||
id: wiki-2026-0508-시뮬레이션과-예측-모델링-simulation-and-pre
|
||||
title: 시뮬레이션과 예측 모델링(Simulation and Predictive Modeling)
|
||||
category: 10_Wiki/Topics
|
||||
status: verified
|
||||
canonical_id: self
|
||||
aliases: [Monte Carlo Simulation, Predictive Modeling, What-if Analysis]
|
||||
duplicate_of: none
|
||||
source_trust_level: A
|
||||
confidence_score: 0.88
|
||||
verification_status: applied
|
||||
tags: [simulation, monte-carlo, forecasting, modeling, statistics]
|
||||
raw_sources: []
|
||||
last_reinforced: 2026-05-10
|
||||
github_commit: pending
|
||||
tech_stack:
|
||||
language: python
|
||||
framework: numpy-scipy
|
||||
---
|
||||
|
||||
# 시뮬레이션과 예측 모델링(Simulation and Predictive Modeling)
|
||||
|
||||
## 매 한 줄
|
||||
> **"매 closed-form 의 unattainable 의 distribution 의 sampling 의 estimate"**. 매 Monte Carlo / discrete-event / agent-based 의 3 family — 매 risk pricing, capacity planning, A/B effect 의 forecast 의 backbone. 매 2026 의 PyMC 5, NumPyro, SimPy 4, Mesa 3 의 standard.
|
||||
|
||||
## 매 핵심
|
||||
|
||||
### 매 simulation 3 family
|
||||
1. **Monte Carlo**: 매 random sampling → integral/expectation 의 estimate. (option pricing, risk VaR.)
|
||||
2. **Discrete-event (DES)**: 매 event timeline 의 advance — queue, server, arrival. (call center, factory.)
|
||||
3. **Agent-based (ABM)**: 매 individual agent + rule + interaction → emergent behavior. (epidemic, market.)
|
||||
|
||||
### 매 predictive modeling vs simulation
|
||||
- **predictive (regression/ML)**: 매 historical → future point estimate.
|
||||
- **simulation**: 매 process model + uncertainty → distribution.
|
||||
- **hybrid**: 매 ML predict mean, 매 simulation propagate variance.
|
||||
|
||||
### 매 validation
|
||||
- 매 backtesting (walk-forward).
|
||||
- 매 calibration (Brier / reliability diagram).
|
||||
- 매 sensitivity analysis (Sobol indices).
|
||||
- 매 convergence check (running mean ± CI).
|
||||
|
||||
## 💻 패턴
|
||||
|
||||
### Monte Carlo — π estimate
|
||||
```python
|
||||
import numpy as np
|
||||
N = 1_000_000
|
||||
xy = np.random.uniform(-1, 1, size=(N, 2))
|
||||
inside = (xy[:,0]**2 + xy[:,1]**2 <= 1).mean()
|
||||
pi_est = 4 * inside # ~3.1416
|
||||
```
|
||||
|
||||
### European call (Black-Scholes MC)
|
||||
```python
|
||||
import numpy as np
|
||||
S0, K, r, sigma, T, N = 100, 105, 0.05, 0.2, 1.0, 200_000
|
||||
Z = np.random.standard_normal(N)
|
||||
ST = S0 * np.exp((r - 0.5*sigma**2)*T + sigma*np.sqrt(T)*Z)
|
||||
payoff = np.maximum(ST - K, 0)
|
||||
price = np.exp(-r*T) * payoff.mean()
|
||||
se = np.exp(-r*T) * payoff.std() / np.sqrt(N) # standard error
|
||||
```
|
||||
|
||||
### Variance reduction — antithetic
|
||||
```python
|
||||
half = N // 2
|
||||
Z = np.random.standard_normal(half)
|
||||
Z_anti = np.concatenate([Z, -Z])
|
||||
ST = S0 * np.exp((r - 0.5*sigma**2)*T + sigma*np.sqrt(T)*Z_anti)
|
||||
# 매 same N, lower variance
|
||||
```
|
||||
|
||||
### Discrete-event (SimPy)
|
||||
```python
|
||||
import simpy, random
|
||||
def customer(env, server):
|
||||
arrive = env.now
|
||||
with server.request() as req:
|
||||
yield req
|
||||
wait = env.now - arrive
|
||||
yield env.timeout(random.expovariate(1/3)) # service ~Exp(mean=3)
|
||||
results.append(wait)
|
||||
|
||||
env = simpy.Environment()
|
||||
server = simpy.Resource(env, capacity=2)
|
||||
results = []
|
||||
def arrivals(env):
|
||||
while True:
|
||||
yield env.timeout(random.expovariate(1/2)) # arrival ~Exp(mean=2)
|
||||
env.process(customer(env, server))
|
||||
env.process(arrivals(env))
|
||||
env.run(until=1000)
|
||||
print('avg wait', sum(results)/len(results))
|
||||
```
|
||||
|
||||
### Agent-based (Mesa 3, sketch)
|
||||
```python
|
||||
from mesa import Agent, Model
|
||||
from mesa.time import RandomActivation
|
||||
|
||||
class Trader(Agent):
|
||||
def step(self):
|
||||
# simple momentum rule
|
||||
if self.model.price > self.last_price: self.buy()
|
||||
else: self.sell()
|
||||
self.last_price = self.model.price
|
||||
|
||||
class Market(Model):
|
||||
def __init__(self, n):
|
||||
self.schedule = RandomActivation(self)
|
||||
self.price = 100
|
||||
for i in range(n): self.schedule.add(Trader(i, self))
|
||||
def step(self):
|
||||
self.schedule.step()
|
||||
# update price by net demand ...
|
||||
```
|
||||
|
||||
### Bayesian forecasting (PyMC 5)
|
||||
```python
|
||||
import pymc as pm
|
||||
with pm.Model() as m:
|
||||
mu = pm.Normal('mu', 0, 10)
|
||||
sigma = pm.HalfNormal('sigma', 5)
|
||||
y = pm.Normal('y', mu=mu, sigma=sigma, observed=data)
|
||||
trace = pm.sample(2000, tune=1000, chains=4)
|
||||
|
||||
with m:
|
||||
ppc = pm.sample_posterior_predictive(trace, var_names=['y'])
|
||||
# 매 forecast distribution + uncertainty
|
||||
```
|
||||
|
||||
### Bootstrap CI
|
||||
```python
|
||||
import numpy as np
|
||||
def bootstrap_ci(data, stat=np.mean, B=10_000, alpha=0.05):
|
||||
boot = [stat(np.random.choice(data, size=len(data), replace=True)) for _ in range(B)]
|
||||
return np.quantile(boot, [alpha/2, 1-alpha/2])
|
||||
```
|
||||
|
||||
### Sensitivity (Sobol)
|
||||
```python
|
||||
from SALib.sample import saltelli
|
||||
from SALib.analyze import sobol
|
||||
problem = {'num_vars': 3, 'names': ['x1','x2','x3'],
|
||||
'bounds': [[0,1]]*3}
|
||||
X = saltelli.sample(problem, 1024)
|
||||
Y = np.array([model(*x) for x in X])
|
||||
Si = sobol.analyze(problem, Y)
|
||||
print(Si['ST']) # total-order indices
|
||||
```
|
||||
|
||||
## 매 결정 기준
|
||||
| 문제 | Approach |
|
||||
|---|---|
|
||||
| Integral / expectation | Monte Carlo |
|
||||
| Queue / capacity | Discrete-event (SimPy) |
|
||||
| Heterogeneous actors + interaction | Agent-based (Mesa) |
|
||||
| Forecasting + uncertainty | Bayesian (PyMC / NumPyro) |
|
||||
| Calibration / quantification | bootstrap / Sobol |
|
||||
| 매 large N + GPU | NumPyro (JAX) |
|
||||
|
||||
**기본값**: 매 simple expectation → MC 의 NumPy, 매 queue → SimPy, 매 forecast w/ uncertainty → PyMC 5.
|
||||
|
||||
## 🔗 Graph
|
||||
- 부모: [[Statistics]] · [[Forecasting]]
|
||||
- 변형: [[Monte Carlo]] · [[MCMC]]
|
||||
- 응용: [[Risk Management]]
|
||||
- Adjacent: [[Bayesian_Inference|Bayesian Inference]]
|
||||
|
||||
## 🤖 LLM 활용
|
||||
**언제**: model assumption 의 review, variance reduction 의 propose, sensitivity result 의 interpret.
|
||||
**언제 X**: large-scale agent simulation 의 direct execution — specialized engine 의 use.
|
||||
|
||||
## ❌ 안티패턴
|
||||
- **N 의 too small**: 매 standard error 의 estimate 의 누락 — running mean check.
|
||||
- **PRNG 의 fixed seed forever**: 매 single-path bias — multiple seeds 의 ensemble.
|
||||
- **Closed-form available 의 simulate**: 매 unnecessary — analytical solution 의 prefer.
|
||||
- **Calibration 누락**: 매 forecast 의 overconfident — Brier/reliability 의 add.
|
||||
|
||||
## 🧪 검증 / 중복
|
||||
- Verified (Glasserman "Monte Carlo Methods in Financial Engineering", Law "Simulation Modeling and Analysis", PyMC 5 / SimPy 4 docs).
|
||||
- 신뢰도 A.
|
||||
|
||||
## 🕓 Changelog
|
||||
| 날짜 | 변경 |
|
||||
|---|---|
|
||||
| 2026-05-08 | Phase 1 |
|
||||
| 2026-05-10 | Manual cleanup — MC/DES/ABM + PyMC + Sobol 의 정리 |
|
||||
Reference in New Issue
Block a user