SM.MAP.MixReparametrized: summary of the output produced by K.MixReparametrized
In Ultimixt: Bayesian Analysis of Location-Scale Mixture Models using a Weakly Informative Prior

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Label switching in a simulated Markov chain produced by K.MixReparametrized is removed by the technique of Marin et al. (2004). Namely, component labels are reorded by the shortest Euclidian distance between a posterior sample and the maximum a posteriori (MAP) estimate. Let θ_i be the i-th vector of computed component means, standard deviations and weights. The MAP estimate is derived from the MCMC sequence and denoted by θ_{MAP}. For a permutation τ \in \Im_k the labelling of θ_i is reordered by

\tilde{θ}_i=τ_i(θ_i)

where τ_i=\arg \min_{τ \in \Im_k} \mid \mid τ(θ_i)-θ_{MAP}\mid \mid.

Angular parameters ξ_1^{(i)}, …, ξ_{k-1}^{(i)} and \varpi_1^{(i)}, …, \varpi_{k-2}^{(i)}s are derived from \tilde{θ}_i. There exists an unique solution in \varpi_1^{(i)}, …, \varpi_{k-2}^{(i)} while there are multiple solutions in ξ^{(i)} due to the symmetry of \mid\cos(ξ) \mid and \mid\sin(ξ) \mid. The output of ξ_1^{(i)}, …, ξ_{k-1}^{(i)} only includes angles on [-π, π].

The label of components of θ_i (before the above transform) is defined by

τ_i^*=\arg \min_{τ \in \Im_k}\mid \mid θ_i-τ(θ_{MAP}) \mid \mid.

The number of label switching occurrences is defined by the number of changes in τ^*.

1	SM.MAP.MixReparametrized(estimate, xobs, alpha0, alpha)

`estimate`	Output of K.MixReparametrized
`xobs`	Data set
`alpha0`	Hyperparameter of Dirichlet prior distribution of the mixture model weights
`alpha`	Hyperparameter of beta prior distribution of the radial coordinate

Details.

`MU`	Matrix of MCMC samples of the component means of the mixture model
`SIGMA`	Matrix of MCMC samples of the component standard deviations of the mixture model
`P`	Matrix of MCMC samples of the component weights of the mixture model
`Ang_SIGMA`	Matrix of computed ξ's corresponding to SIGMA
`Ang_MU`	Matrix of computed \varpi's corresponding to MU. This output only appears when k > 2.
`Global_Mean`	Mean, median and 95\% credible interval for the global mean parameter
`Global_Std`	Mean, median and 95\% credible interval for the global standard deviation parameter
`Phi`	Mean, median and 95\% credible interval for the radius parameter
`component_mu`	Mean, median and 95\% credible interval of MU
`component_sigma`	Mean, median and 95\% credible interval of SIGMA
`component_p`	Mean, median and 95\% credible interval of P
`l_stay`	Number of MCMC iterations between changes in labelling
`n_switch`	Number of label switching occurrences

Note.

Kate Lee

Marin, J.-M., Mengersen, K. and Robert, C. P. (2004) Bayesian Modelling and Inference on Mixtures of Distributions, Handbook of Statistics, Elsevier, Volume 25, Pages 459–507.

K.MixReparametrized

#data(faithful)
#xobs=faithful[,1]
#estimate=K.MixReparametrized(xobs,k=2,alpha0=0.5,alpha=0.5,Nsim=1e4)
#result=SM.MAP.MixReparametrized(estimate,xobs,alpha0=0.5,alpha=0.5)

Ultimixt documentation built on May 1, 2019, 10:56 p.m.