bayesian with stan

bayesian 이론 정리 및 stan을 통한 분석

stan 사용 환경 설정

r에서 stan을 활용하기 위해서는 rtools 설치가 필요하다. windows 환경에서 rtools4.2부터는 별도의 환경변수 설정 없이 설치만 하면 이용이 가능하다고 했지만 stan은 다른 설정이 필요한 듯하다.

해결방법을 찾을 때까지는 wsl ubuntu에서 stan을 사용

단순회귀모형

data {
  int N;
  real X[N];
  real Y[N];
}

parameters {
  real a;
  real b;
  real mu;
  real<lower=0> sigma;
}

model {
  for (n in 1:N) {
    Y[n] ~ normal(a + b * X[n], sigma);
  }
}

library(rstan)
data <- list(N=nrow(cars), X=cars$dist, Y=cars$speed)
fit <- stan(file = "lm.stan", data = data, seed=1234)

fit

> fit
Inference for Stan model: lm.
4 chains, each with iter=2000; warmup=1000; thin=1; 
post-warmup draws per chain=1000, total post-warmup draws=4000.

               mean      se_mean           sd          2.5%           25%           50%         75%         97.5% n_eff Rhat
a      8.290000e+00 2.000000e-02 9.300000e-01  6.490000e+00  7.650000e+00  8.280000e+00  8.9100e+00  1.008000e+01  2785 1.00
b      1.700000e-01 0.000000e+00 2.000000e-02  1.300000e-01  1.500000e-01  1.700000e-01  1.8000e-01  2.000000e-01  2754 1.00
mu    -1.028316e+15 4.466057e+15 8.995785e+15 -1.499126e+16 -6.540879e+15 -8.474066e+14  5.6003e+14  2.555615e+16     4 2.08
sigma  3.240000e+00 1.000000e-02 3.400000e-01  2.650000e+00  3.000000e+00  3.210000e+00  3.4500e+00  4.000000e+00  3346 1.00
lp__  -8.189000e+01 3.000000e-02 1.250000e+00 -8.511000e+01 -8.250000e+01 -8.157000e+01 -8.0950e+01 -8.043000e+01  1616 1.00

Samples were drawn using NUTS(diag_e) at Wed Jun 14 23:46:43 2023.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at 
convergence, Rhat=1).