# sdPrior v1.0-0

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## Scale-Dependent Hyperpriors in Structured Additive Distributional Regression

Utility functions for scale-dependent and alternative hyperpriors. The distribution parameters may capture location, scale, shape, etc. and every parameter may depend
on complex additive terms (fixed, random, smooth, spatial, etc.) similar to a generalized additive model. Hyperpriors for all effects can be elicitated within the package. Including complex tensor product interaction terms and variable selection priors. The basic model is explained in in Klein and Kneib (2016) <doi:10.1214/15-BA983>.

## Functions in sdPrior

Name | Description | |

mdf_sd | Marginal Density for Given Scale Parameter and Scale-Dependent Prior for \(\tau^2\) | |

get_theta_linear | Find Scale Parameter for Inverse Gamma Hyperprior of Linear Effects with Spike and Slab Prior | |

mdf_gbp | Marginal Density for Given Scale Parameter and Half-Cauchy Prior for \(\tau\) | |

mdf_ga | Marginal Density for Given Scale Parameter and Half-Normal Prior for \(\tau\) | |

mdf_ig | Marginal Density for Given Scale Parameter and Inverse Gamma Prior for \(\tau^2\) | |

mdf_aunif | Marginal Density for Given Scale Parameter and Approximated Uniform Prior for \(\tau\) | |

hyperparlin | Find Scale Parameter for Inverse Gamma Hyperprior of Linear Effects with Spike and Slab Prior | |

mdbeta | Marginal Density of \(\beta\) | |

zambia_height92 | Malnutrition in Zambia | |

papprox_unif | Compute Cumulative Distribution Function of Approximated (Differentiably) Uniform Distribution. | |

rapprox_unif | Draw Random Numbers from Approximated (Differentiably) Uniform Distribution. | |

zambia_graph | Prior precision matrix for spatial variable in Zambia data set | |

get_theta | Find Scale Parameter for (Scale Dependent) Hyperprior | |

get_theta_aunif | Find Scale Parameter for Hyperprior for Variances Where the Standard Deviations have an Approximated (Differentiably) Uniform Distribution. | |

hyperpar | Find Scale Parameters for Inverse Gamma Hyperprior of Nonlinear Effects with Spike and Slab Prior (Simulation-based) | |

hyperpar_mod | Find Scale Parameter for modular regression | |

get_theta_ga | Find Scale Parameter for Gamma (Half-Normal) Hyperprior | |

get_theta_gbp | Find Scale Parameter for Generalised Beta Prime (Half-Cauchy) Hyperprior | |

get_theta_ig | Find Scale Parameter for Inverse Gamma Hyperprior | |

DesignM | Computing Designmatrix for Splines | |

dapprox_unif | Compute Density Function of Approximated (Differentiably) Uniform Distribution. | |

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