Tutorial

To use waspr the user first needs to load the package as follows:

library(waspr)

The user must provide a 3-dimensional array with posterior samples for all parameters for each subset posterior (rows = subset posteriors, columns = parameters, slices = samples). The amount of parameters and samples must be equal for each subset posterior, these posterior samples may be obtained from any type of MCMC algorithm. waspr provides an example array with posterior samples for 8 parameters for 8 subset posteriors, pois_logistic, that will be used to illustrate the functionality of the package.

The main function wasp() runs the swapping algorithm, combines its output and computes the Wasserstein barycenter. It has four arguments, mcmc, that specifies the 3-dimensional array with samples for each subset posterior, and optional arguments par.names, that can be used to specify parameter names, iter to specify the maximum number of iterations of the swapping algorithm, acc to specify the accuracy of the swapping algorithm and out to indicate whether the results per iteration of the swap algorithm should be printed.

out <- wasp(pois_logistic,
            iter = 10,
            acc = 0.001,
            par.names = c("beta_s", "alpha_l", "beta_l",
                         "baseline_sigma", "baseline_mu",
                         "correlation", "sigma_s", "sigma_l"))

wasp() prints the iteration number and cost function value of the swapping algorithm. The out object is of class wasp and contains several elements. To obtain the Wasserstein barycenter of the subset posteriors a user can specify out$barycenter. This returns a matrix of posterior samples (rows) for all parameters (columns) of the full data posterior. A summary of the approximation of the full data posterior is available through summary(out).

summary(out)
#>                      mean       mode         sd      LB HPD     UB HPD
#> beta_s          0.5527601  0.5518034 0.10988949  0.36598187  0.7896041
#> alpha_l         2.6811079  2.6959176 0.19199304  2.30380675  3.0295802
#> beta_l          0.7508520  0.7339988 0.21631011  0.37281283  1.1740767
#> baseline_sigma  0.3563222  0.3811609 0.06859910  0.21910807  0.4870079
#> baseline_mu    -0.8008872 -0.7516167 0.10867533 -1.01168299 -0.5944583
#> correlation     0.1732170  0.1392670 0.07437737  0.02824474  0.3059979
#> sigma_s         1.7225455  1.7535499 0.17920847  1.40126462  2.0610585
#> sigma_l         1.2190297  1.2612822 0.07558163  1.06768047  1.3569757