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Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

2026-05-20 23:52:15 +09:00

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title

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

Monte Carlo: 매 random sampling → integral/expectation 의 estimate. (option pricing, risk VaR.)
Discrete-event (DES): 매 event timeline 의 advance — queue, server, arrival. (call center, factory.)
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

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)

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

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)

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)

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)

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

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)

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

🤖 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

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