Description Usage Arguments Value References Examples

The Zellner-Siow cauchy g-prior utilizes the inverse crossproduct is to determine the proper scale of the coefficient priors
by treating the inverse crossproduct of the model matrix as a covariance matrix for a multivariate normal prior distribution
for the coefficients, which is scaled by the parameter "g". The logic is that variables which carry the most information will
consequently have a more dispersed prior, while variables that carry less information will have priors more concentrated about
zero. While the joint prior is multivariate normal, the implied independent marginal priors are Cauchy distributions.
The approach here is to let g be a random variable estimated as part of the model, rather than fixed values of g=N.
This avoids several problems associated with fixed-g priors. For more information, see Liang et al. (2008).

The model specification is given below. Note that the model formulae have been adjusted to reflect the fact that JAGS
parameterizes the normal and multivariate normal distributions by their precision, rater than (co)variance.
For generalized linear models plug-in pseudovariances are used.

Plugin Pseudo-Variances:

1 2 3 |

`formula` |
the model formula |

`data` |
a data frame |

`family` |
one of "gaussian", "st" (Student-t with nu = 3), "binomial", or "poisson". |

`log_lik` |
Should the log likelihood be monitored? The default is FALSE. |

`iter` |
How many post-warmup samples? Defaults to 10000. |

`warmup` |
How many warmup samples? Defaults to 1000. |

`adapt` |
How many adaptation steps? Defaults to 2000. |

`chains` |
How many chains? Defaults to 4. |

`thin` |
Thinning interval. Defaults to 1. |

`method` |
Defaults to "parallel". For an alternative parallel option, choose "rjparallel". Otherwise, "rjags" (single core run). |

`cl` |
Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores. |

`...` |
Other arguments to run.jags. |

A run.jags object.

Zellner, A. & Siow S. (1980). Posterior odds ratio for selected regression hypotheses. In Bayesian statistics. Proc. 1st int. meeting (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 585–603. University Press, Valencia.

Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel and A. Zellner, editors, Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, 233–243.

Liang, Paulo, Molina, Clyde, & Berger (2008) Mixtures of g Priors for Bayesian Variable Selection, Journal of the American Statistical Association, 103:481, 410-423, DOI: 10.1198/016214507000001337

1 | ```
zsGlm()
``` |

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