# Sampling Functions¶

Listed below are the sampling methods for which functions are provided to simulating draws from distributions that can be specified up to constants of proportionalities. Model-based Sampler constructors are available for use with the `mcmc()`

engine as well as stand-alone functions that can be used independently.

- Approximate Bayesian Computation (ABC)
- Adaptive Mixture Metropolis (AMM)
- Adaptive Metropolis within Gibbs (AMWG)
- Binary Hamiltonian Monte Carlo (BHMC)
- Binary Individual Adaptation (BIA)
- Binary MCMC Model Composition (BMC3)
- Binary Metropolised Gibbs (BMG)
- Discrete Gibbs Sampler (DGS)
- Hamiltonian Monte Carlo (HMC)
- Metropolis-Adjusted Langevin Algorithm (MALA)
- Missing Values Sampler (MISS)
- No-U-Turn Sampler (NUTS)
- Random Walk Metropolis (RWM)
- Shrinkage Slice (Slice)
- Slice Simplex (SliceSimplex)

The following table summarizes the (*d*-dimensional) sample spaces over which each method simulates draws, whether draws are generated univariately or multivariately, and whether transformations are applied to map parameters to the sample spaces.

Model-Based Constructors | Stand-Alone Functions | |||||
---|---|---|---|---|---|---|

Method | Sample Space | Univariate | Multivariate | Transformations | Univariate | Multivariate |

ABC | No | Yes | Yes | No | No | |

AMM | No | Yes | Yes | No | Yes | |

AMWG | Yes | No | Yes | Yes | No | |

BHMC | No | Yes | No | No | Yes | |

BIA | No | Yes | No | No | Yes | |

BMC3 | Yes | Yes | No | Yes | Yes | |

BMG | Yes | Yes | No | Yes | Yes | |

DGS | Finite | Yes | No | No | No | Yes |

HMC | No | Yes | Yes | No | Yes | |

MALA | No | Yes | Yes | No | Yes | |

MISS | Parameter-defined | Yes | Yes | No | No | No |

NUTS | No | Yes | Yes | No | Yes | |

RWM | No | Yes | Yes | No | Yes | |

Slice | Yes | Yes | Optional | Yes | Yes | |

SliceSimplex | d-simplex |
No | Yes | No | No | Yes |