GIBBS_update: Gibbs Update
In Newmi1988/seeds: Estimate Hidden Inputs using the Dynamic Elastic Net

Description Usage Arguments Details Value

Algorithm implemented according to Engelhardt et al. 2017. The BDEN defines a conditional Gaussian prior over each hidden input. The scale of the variance of the Gaussian prior is a strongly decaying and smooth distribution peaking at zero, which depends on parameters Lambda2, Tau and Sigma. The parameter Tau is itself given by an exponential distribution (one for each component of the hidden influence vector) with parameters Lambda1. In consequence, sparsity is dependent on the parameter vector Lambda1, whereas smoothness is mainly controlled by Lambda2. These parameters are drawn from hyper-priors, which can be set in a non-informative manner or with respect to prior knowledge about the degree of shrinkage and smoothness of the hidden influences (Engelhardt et al. 2017).

1	GIBBS_update(D, EPS_inner, R, ROH, SIGMA_0, n, SIGMA, LAMBDA2, LAMBDA1, TAU)

`D`	diagonal weight matrix of the current Gibbs step
`EPS_inner`	row-wise vector of current hidden influences [tn,tn+1]
`R`	parameter for needed for the Gibbs update (for details see Engelhardt et al. 2017)
`ROH`	parameter for needed for the Gibbs update (for details see Engelhardt et al. 2017)
`SIGMA_0`	prior variance of the prior for the hidden influences
`n`	number of system states
`SIGMA`	current variance of the prior for the hidden influences (calculated during the Gibbs update)
`LAMBDA2`	current parameter (smoothness) needed for the Gibbs update (for details see Engelhardt et al. 2017)
`LAMBDA1`	current parameter (sparsity) needed for the Gibbs update (for details see Engelhardt et al. 2017)
`TAU`	current parameter (smoothness) needed for the Gibbs update (for details see Engelhardt et al. 2017)