# Gibbs sampling for d-inverse-gamma model

### Description

The function implements a Gibbs sampler for a univariate DLM having one or more unknown variances in its specification.

### Usage

1 2 3 4 | ```
dlmGibbsDIG(y, mod, a.y, b.y, a.theta, b.theta, shape.y, rate.y,
shape.theta, rate.theta, n.sample = 1,
thin = 0, ind, save.states = TRUE,
progressBar = interactive())
``` |

### Arguments

`y` |
data vector or univariate time series |

`mod` |
a dlm for univariate observations |

`a.y` |
prior mean of observation precision |

`b.y` |
prior variance of observation precision |

`a.theta` |
prior mean of system precisions (recycled, if needed) |

`b.theta` |
prior variance of system precisions (recycled, if needed) |

`shape.y` |
shape parameter of the prior of observation precision |

`rate.y` |
rate parameter of the prior of observation precision |

`shape.theta` |
shape parameter of the prior of system precisions (recycled, if needed) |

`rate.theta` |
rate parameter of the prior of system precisions (recycled, if needed) |

`n.sample` |
requested number of Gibbs iterations |

`thin` |
discard |

`ind` |
indicator of the system variances that need to be estimated |

`save.states` |
should the simulated states be included in the output? |

`progressBar` |
should a text progress bar be displayed during execution? |

### Details

The *d-inverse-gamma* model is a constant univariate DLM with unknown
observation variance, diagonal system variance with unknown diagonal
entries. Some of these entries may be known, in which case they are
typically zero. Independent inverse gamma priors are assumed for the
unknown variances. These can be specified be mean and variance or,
alternatively, by shape and rate. Recycling is applied for the prior
parameters of unknown system variances. The argument `ind`

can
be used to specify the index of the unknown system variances, in case
some of the diagonal elements of `W`

are known. The unobservable
states are generated in the Gibbs sampler and are returned if
`save.states = TRUE`

. For more details on the model and usage
examples, see the package vignette.

### Value

The function returns a list of simulated values.

`dV` |
simulated values of the observation variance. |

`dW` |
simulated values of the unknown diagonal elements of the system variance. |

`theta` |
simulated values of the state vectors. |

### Author(s)

Giovanni Petris GPetris@uark.edu

### References

Giovanni Petris (2010), An R Package for Dynamic Linear
Models. Journal of Statistical Software, 36(12), 1-16.
http://www.jstatsoft.org/v36/i12/.

Petris, Petrone, and Campagnoli, Dynamic Linear Models with
R, Springer (2009).

### Examples

1 | ```
## See the package vignette for an example
``` |