stan-fundamentals

Stan Fundamentals

When to Use This Skill

• Writing new Stan models from scratch
• Understanding Stan program structure
• Learning Stan syntax and conventions
• Translating models from other languages to Stan
• Optimizing existing Stan code

Program Structure

Stan models have up to 7 blocks in this exact order:

functions { }           // User-defined functions
data { }                // Input data declarations
transformed data { }    // Data preprocessing
parameters { }          // Model parameters
transformed parameters { } // Derived parameters
model { }               // Log probability
generated quantities { }  // Posterior predictions

All blocks are optional. Empty string is valid (but useless) Stan program.

Type System Quick Reference

Scalars

int n;                    // Integer
real x;                   // Real number
complex z;                // Complex number

Vectors and Matrices

vector[N] v;              // Column vector
row_vector[N] r;          // Row vector
matrix[M, N] A;           // Matrix

Arrays (Modern Syntax)

array[N] real x;          // 1D array of reals
array[M, N] int y;        // 2D array of integers
array[J] vector[K] theta; // Array of vectors

Constrained Types

real<lower=0> sigma;              // Non-negative
real<lower=0, upper=1> p;         // Probability
simplex[K] theta;                 // Sums to 1
ordered[K] c;                     // Ascending
corr_matrix[K] Omega;             // Correlation
cov_matrix[K] Sigma;              // Covariance
cholesky_factor_corr[K] L_Omega;  // Cholesky correlation

Key Distributions

Continuous (SD parameterization!)

y ~ normal(mu, sigma);      // sigma is SD
y ~ student_t(nu, mu, sigma);
y ~ cauchy(mu, sigma);
y ~ exponential(lambda);
y ~ gamma(alpha, beta);
y ~ beta(a, b);
y ~ lognormal(mu, sigma);

Discrete

y ~ bernoulli(theta);
y ~ binomial(n, theta);
y ~ poisson(lambda);
y ~ neg_binomial_2(mu, phi);
y ~ categorical(theta);