regression-models
Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations.
Quellinformationen
- Repository
- choxos/BiostatAgent
- Letzte Quellaktivität
- 10. Januar 2026 um 18:48
- Erkannte Sprache von SKILL.md
- Englisch
- Sterne
- 11
- Forks
- 1
Installationsoptionen
Standardmäßig ist der Prompt ausgewählt, der zuerst die Quelle prüft. Sie können zu einem direkten Befehl wechseln oder eine lokale Kopie herunterladen.
Quelldateien prüfen
Lesen Sie SKILL.md und alle von SkillsMP angezeigten Begleitdateien, bevor Sie sich für eine Installation entscheiden.
SKILL.md wird angezeigt
SKILL.md
Quellanweisungen · Schreibgeschützte Vorschau- name
- regression-models
- description
- Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations.
# Regression Models
## Linear Regression
### Stan
```stan
data {
int<lower=0> N;
int<lower=0> K;
matrix[N, K] X;
vector[N] y;
}
parameters {
real alpha;
vector[K] beta;
real<lower=0> sigma;
}
model {
alpha ~ normal(0, 10);
beta ~ normal(0, 5);
sigma ~ exponential(1);
y ~ normal(alpha + X * beta, sigma);
}
generated quantities {
array[N] real y_rep;
for (n in 1:N)
y_rep[n] = normal_rng(alpha + X[n] * beta, sigma);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dnorm(mu[i], tau)
mu[i] <- alpha + inprod(X[i,], beta[])
}
alpha ~ dnorm(0, 0.001)
for (k in 1:K) { beta[k] ~ dnorm(0, 0.001) }
tau ~ dgamma(0.001, 0.001)
sigma <- 1/sqrt(tau)
}
```
## Logistic Regression
### Stan
```stan
data {
int<lower=0> N;
int<lower=0> K;
matrix[N, K] X;
array[N] int<lower=0,upper=1> y;
}
parameters {
real alpha;
vector[K] beta;
}
model {
alpha ~ normal(0, 2.5);
beta ~ normal(0, 2.5);
y ~ bernoulli_logit(alpha + X * beta);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dbern(p[i])
logit(p[i]) <- alpha + inprod(X[i,], beta[])
}
alpha ~ dnorm(0, 0.4) # SD ≈ 1.58
for (k in 1:K) { beta[k] ~ dnorm(0, 0.4) }
}
```
## Poisson Regression
### Stan
```stan
model {
alpha ~ normal(0, 5);
beta ~ normal(0, 2.5);
y ~ poisson_log(alpha + X * beta);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dpois(lambda[i])
log(lambda[i]) <- alpha + inprod(X[i,], beta[])
}
}
```
## Negative Binomial (Overdispersed Counts)
### Stan
```stan
parameters {
real alpha;
vector[K] beta;
real<lower=0> phi; // Overdispersion
}
model {
phi ~ exponential(1);
y ~ neg_binomial_2_log(alpha + X * beta, phi);
}
```
## Robust Regression (Student-t Errors)
### Stan
```stan
parameters {
real alpha;
vector[K] beta;
real<lower=0> sigma;
real<lower=1> nu; // Degrees of freedom
}
model {
nu ~ gamma(2, 0.1); // Prior on df
y ~ student_t(nu, alpha + X * beta, sigma);
}
```
## QR Decomposition (For Correlated Predictors)
```stan
transformed data {
matrix[N, K] Q = qr_thin_Q(X) * sqrt(N - 1.0);
matrix[K, K] R = qr_thin_R(X) / sqrt(N - 1.0);
matrix[K, K] R_inv = inverse(R);
}
parameters {
vector[K] theta;
real<lower=0> sigma;
}
model {
y ~ normal(Q * theta, sigma);
}
generated quantities {
vector[K] beta = R_inv * theta;
}
```
## Prior Recommendations
| Parameter | Weakly Informative | Reference |
|-----------|-------------------|-----------|
| Intercept | `normal(0, 10)` | Scale of outcome |
| Coefficients | `normal(0, 2.5)` | Gelman et al. |
| SD (sigma) | `exponential(1)` | Half-normal alternative |
| Logistic coef | `normal(0, 2.5)` | ~4 logit units = extreme |
Auf GitHub ansehen