高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (894ﾚｽ)
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866: １３２人目の素数さん [sage] 2025/06/05(木) 13:25:27.68 ID:tGlaBVfa

> stancode(fit)
// generated with brms 2.22.0
functions {
/* compute monotonic effects
* Args:
*   scale: a simplex parameter
*   i: index to sum over the simplex
* Returns:
*   a scalar between 0 and rows(scale)
*/
real mo(vector scale, int i) {
if (i == 0) {
return 0;
} else {
return rows(scale) * sum(scale[1:i]);
}
}
}
data {
int<lower=1> N;  // total number of observations
array[N] int Y;  // response variable
int<lower=1> K;  // number of population-level effects
matrix[N, K] X;  // population-level design matrix
int<lower=1> Kc;  // number of population-level effects after centering
int<lower=1> Ksp;  // number of special effects terms
int<lower=1> Imo;  // number of monotonic variables
array[Imo] int<lower=1> Jmo;  // length of simplexes
array[N] int Xmo_1;  // monotonic variable
vector[Jmo[1]] con_simo_1;  // prior concentration of monotonic simplex
int prior_only;  // should the likelihood be ignored?
}
transformed data {
matrix[N, Kc] Xc;  // centered version of X without an intercept
vector[Kc] means_X;  // column means of X before centering
for (i in 2:K) {
means_X[i - 1] = mean(X[, i]);
Xc[, i - 1] = X[, i] - means_X[i - 1];
}
}
parameters {
vector[Kc] b;  // regression coefficients
real Intercept;  // temporary intercept for centered predictors
simplex[Jmo[1]] simo_1;  // monotonic simplex
vector[Ksp] bsp;  // special effects coefficients
}
transformed parameters {
real lprior = 0;  // prior contributions to the log posterior
lprior += normal_lpdf(b[1] | 0.15, 0.3);
lprior += normal_lpdf(b[2] | 0.08, 0.3);
lprior += normal_lpdf(b[3] | 0.8, 0.3);
lprior += normal_lpdf(b[4] | 0.5, 0.3);
lprior += normal_lpdf(Intercept | -4, 2);
lprior += dirichlet_lpdf(simo_1 | con_simo_1);
lprior += normal_lpdf(bsp[1] | -0.5, 0.3);
}
model {
// likelihood including constants
if (!prior_only) {
// initialize linear predictor term
vector[N] mu = rep_vector(0.0, N);
mu += Intercept;
for (n in 1:N) {
// add more terms to the linear predictor
mu[n] += (bsp[1]) * mo(simo_1, Xmo_1[n]);
}
target += bernoulli_logit_glm_lpmf(Y | Xc, mu, b);
}
// priors including constants
target += lprior;
}
generated quantities {
// actual population-level intercept
real b_Intercept = Intercept - dot_product(means_X, b);
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/866

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