SM.MixReparametrized {Ultimixt}

summary of the output produced by K.MixReparametrized

Description

This is a generic function that summarizes the MCMC samples produced by K.MixReparametrized. The function invokes several estimation methods which choice depends on the unimodality or multimodality of the argument.

Usage

SM.MixReparametrized(xobs, estimate)

Arguments

xobs

vector of observations

estimate

output of K.MixReparametrized

Details

This function outputs posterior point estimates for all parameters of the mixture model. They mostly differ from the generaly useless posterior means. The output summarizes unimodal MCMC samples by computing measures of centrality, including mean and median, while multimodal outputs require a pre-processing, due to the label switching phenomenon (Jasra et al., 2005). The summary measures are then computed after performing a multi-dimensional k-means clustering (Hartigan and Wong, 1979) following the suggestion of Fruhwirth-Schnatter (2006).

Value

Mean

vector of mean and median of simulated draws from the conditional posterior of the mixture model mean

Sd

vector of mean and median of simulated draws from the conditional posterior of the mixture model standard deviation

Phi

vector of mean and median of simulated draws from the conditional posterior of the radial coordinate

Angles. 1.

vector of means of the angular coordinates used for the component means in the mixture distribution

Angles. 2.

vector of means of the angular coordinates used for the component standard deviations in the mixture distribution

weight.i

vector of mean and median of simulated draws from the conditional posterior of the component weights of the mixture distribution; i=1, \ldots, k

mean.i

vector of mean and median of simulated draws from the conditional posterior of the component means of the mixture distribution; i=1, \ldots, k

sd.i

vector of mean and median of simulated draws from the conditional posterior of the component standard deviations of the mixture distribution; i=1, \ldots, k

Acc rat

vector of final acceptance rate of the proposal distributions of the algorithm with no calibration stage for the proposal scales

Opt scale

vector of optimal proposal scales obtained the by calibration stage

Note

For multimodal outputs such as the mixture model weights, component means, and component variances, for each MCMC draw, first the labels of the weights p_i, i=1, \ldots, k and corresponding component means and standard deviations are permuted in such a way that p_1\le \ldots \le p_k. Then the component means and standard deviations are jointly partitioned into k clusters by applying a standard k-means algorithm with k clusters, following Fruhwirth-Schnatter (2006) method. The obtained classification sequence was then used to reorder and identify the other component-specific parameters, namely component mean hyperparameters and weights. For each group, cluster centers are considered as parameter estimates.

Author(s)

Kaniav Kamary

References

Jasra, A., Holmes, C. and Stephens, D. (2005). Markov Chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science, 20, 50–67.

Hartigan, J. A. and Wong, M. A. (1979). A K-means clustering algorithm. Applied Statistics 28, 100–108.

Fruhwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. Springer-Verlag.

See Also

K.MixReparametrized

Examples

#data(faithful)
#xobs=faithful[,1]
#estimate=K.MixReparametrized(xobs, k=2, alpha0=.5, alpha=.5, Nsim=20000)
#summari=SM.MixReparametrized(xobs,estimate)