Menu
Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations.
Install with Codex or Claude Copy this prompt, paste it into Codex, Claude, or another assistant, and let it review the skill page and install it for you.
Based on SOC occupation classification
Bayesian meta-analysis models including fixed effects, random effects, and network meta-analysis with Stan and JAGS implementations.
Foundational knowledge for writing current PyMC models including syntax, distributions, sampling, and ArviZ diagnostics. Use when creating or reviewing PyMC models.
Foundational knowledge for writing modern Stan models including program structure, type system, distributions, and best practices. Use when creating or reviewing Stan models.
Group sequential design methods for interim analyses, alpha spending, and futility stopping. Use when designing trials with interim looks or implementing spending functions.
Core Mediana package functions for Clinical Scenario Evaluation (CSE). Use when designing data models, analysis models, evaluation models, and running comprehensive trial simulations.
Core simtrial package functions for time-to-event clinical trial simulation. Use when generating survival data, performing weighted logrank tests, or running TTE simulations.
| name | regression-models |
| description | Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations. |
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);
}
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)
}
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);
}
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) }
}
model {
alpha ~ normal(0, 5);
beta ~ normal(0, 2.5);
y ~ poisson_log(alpha + X * beta);
}
model {
for (i in 1:N) {
y[i] ~ dpois(lambda[i])
log(lambda[i]) <- alpha + inprod(X[i,], beta[])
}
}
parameters {
real alpha;
vector[K] beta;
real<lower=0> phi; // Overdispersion
}
model {
phi ~ exponential(1);
y ~ neg_binomial_2_log(alpha + X * beta, phi);
}
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);
}
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;
}
| 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 |