dlmGibbsDIG function

Gibbs sampling for d-inverse-gamma model

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

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 thin iterations for every saved iteration
• 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.

Returns

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.

References

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

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

Author(s)

Giovanni Petris GPetris@uark.edu

Examples

## See the package vignette for an example