check_labels: Check for label switching
In sppmix: Modeling Spatial Poisson and Related Point Processes

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

Checks if there is label switching present in the posterior realizations using the chains for mu. The algorithm is heuristic and works as follows; for each chain of mu for a given component, we look for sharp changes in the generated values that lead to dramatically different variability from the variability observed in the past history of the chain. The lag history is 5% of the total number of realizations, excluding the burnin realizations.

For examples see

http://faculty.missouri.edu/~micheasa/sppmix/sppmix_all_examples.html#check_labels

1 2	check_labels(fit, burnin = floor(fit$L/10), lagnum = floor(0.05 * (fit$L - burnin) + 1), showmessages = TRUE)

`fit`	Object of class `damcmc_res` or `bdmcmc_res`.
`burnin`	Number of initial realizations to discard. By default, it is 1/10 of the total number of iterations.
`lagnum`	Number of past realizations to use for the detection algorithm. Default is .05 of the total realizations after burnin realizations are removed.
`showmessages`	Logical variable requesting to show informative messages (TRUE) or suppress them (FALSE). Default is TRUE.

To avoid the label switching problem one can plot the average of the intensities of the posterior realizations, i.e., the average of the surfaces instead of the surface of the posterior averages. However, by doing so we lose the ability to perform mixture deconvolution, namely, work with the posterior means of the ps, mus and sigmas of the mixture intensity. In general, the average of posterior surfaces for each realization of the ps, mus and sigmas, and the surface based on the posterior means of the ps, mus and sigmas, need not be the same.

For a DAMCMC fit, avoiding label switching can be accomplished using function plot_avgsurf, which plots the average posterior surface. The surface of posterior means is plotted using the function plot.damcmc_res on the returned value of GetPMEst.

When working with a BDMCMC fit, it is recommended that you use GetBDCompfit to retrieve the realizations corresponding to a specific number of components and then fix the labels. Of course the best estimate in this case, is the Bayesian model average intensity obtained via GetBMA, but it can be very slow to compute. The BMA is an average on surfaces based on each of the posterior realizations, and as such does not suffer from the label switching problem.

Logical value indicating if label switching was detected.

Jiaxun Chen, Sakis Micheas

Jasra, A., Holmes, C.C. and Stephens, D. A. (2005). Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixtures. Statistical Science, 20, 50-67.

normmix, rsppmix, est_mix_damcmc, plot_chains, FixLS_da

# generate data
mix1 = normmix(ps=c(.4, .2,.4), mus=list(c(0.3, 0.3), c(.5,.5),c(0.7, 0.7)),
 sigmas = list(.02*diag(2),.05*diag(2), .02*diag(2)),lambda = 100,
 win = spatstat::square(1))
plot(mix1,main="True Poisson intensity surface (mixture of normal components)")
pp1 = rsppmix(mix1)
# Run Data augmentation MCMC and get posterior realizations
postfit = est_mix_damcmc(pp1,m=5)
#plot the chains
plot_chains(postfit)
#check labels
check_labels(postfit)
#plot the average posterior surface
plot(GetPMEst(postfit))
#plot the surface of posterior means, can be slow for large LL
avgsurf=plot_avgsurf(postfit, LL = 50, burnin = 1000)
# Fix label switching, start with approx=TRUE
post_fixed = FixLS_da(postfit, plot_result = TRUE)
plot_chains(post_fixed)
plot_chains(post_fixed,separate = FALSE)
#this one works better in theory
post_fixed = FixLS_da(postfit,approx=FALSE, plot_result = TRUE)
plot_chains(post_fixed)
plot_chains(post_fixed,separate = FALSE)