Stan implementation

Stan is a powerful probabilistic programming language and high-performance probabilistic computation library, with support for:

• Robust and mature probabilistic programming language constructs.
• High-performance mathematical computation libraries.
• Markov chain Monte Carlo (MCMC) optimisation methods.
• Bayesian inference.
• Variational inference.
• Interfaces to data and analysis languages (R, Python, shell, MATLAB, Julia, Stata).

Stan supported probability distributions

• Binary probability distributions
  • Bernoulli
  • Bernoulli, logit parameterisation
• Bounded discrete probability distributions
  • Binomial
  • Binomial, logit parameterisation
  • Beta-binomial
  • Categorical
  • Discrete range
  • Hypergeometric
  • Multinomial
  • Multinomial, logit parameterisation
  • Ordered logistic
  • Ordered probit
• Unbounded discrete probability distributions
  • Negative binomial
  • Negative binomial, alternative parameterisation
  • Negative binomial, log alternative parameterisation
  • Poisson
  • Poisson, log parameterisation
• Unbounded continuous probability distributions
  • Cauchy
  • Double exponential (Laplace)
  • Double exponential (Laplace), skew
  • Gaussian process
  • Gaussian process, Cholesky parameterisation
  • Gumbel
  • Logistic
  • Multivariate normal
  • Multivariate normal, Cholesky parameterisation
  • Multivariate normal, precision parameterisation
  • Multivariate Student’s t
  • Normal
  • Normal, exponentially modified
  • Normal, skew
  • Student’s t
• Bounded continuous probability distributions
  • Uniform
• Positive continuous probability distributions
  • Chi-square
  • Exponential
  • Frechet
  • Gamma
  • Inverse chi-square
  • Inverse chi-square, scaled
  • Inverse gamma
  • Log-normal
  • Rayleigh
  • Weibull
• [0, 1]-bounded continuous probability distributions
  • Beta
  • Beta, proportion parameterisation
  • Dirichlet
• Correlation probability distributions
  • LKJ correlation
  • LKJ correlation, Cholesky parameterisation
• Covariance probability distributions
  • Inverse Wishart
  • Wishart

Stan supported probabilistic models

• Binary probabilistic models
  • Bernoulli-logit generalised linear model (logistic regression)
• Bounded discrete probabilisitc models
  • Categorical-logit generalised linear model (softmax regression)
• Unbounded discrete probabilisitc models
  • Negative-binomial-log generalised linear model (negative binomial regression)
  • Poisson-log generalized linear model (Poisson regression)
• Continuous models
  • Normal-identity generalised linear model (linear regression)