BSPBSS-vignette

library(BSPBSS)

A toy example

This is a basic example which shows you how to solve a common problem.

First we load the package and generate simulated images with a probabilistic ICA model:

library(BSPBSS)
set.seed(612)
sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)

The true source signals are three 2D geometric patterns (set smooth=0 to generate patterns with sharp edges).

levelplot2D(sim$S,lim = c(-0.04,0.04), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).

which generate observed images such as

levelplot2D(sim$X[1:3,], lim = c(-0.12,0.12), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).

Then we generate initial values for mcmc,

ini = init_bspbss(sim$X, sim$coords, q = 3, ker_par = c(0.1,50), num_eigen = 50)

and run!

res = mcmc_bspbss(ini$X,ini$init,ini$prior,ini$kernel,n.iter=2000,n.burn_in=1000,thin=10,show_step=100)
#> iter 100 Wed Jun 17 09:13:27 2026
#> 
#> zeta0.122581 stepsize_zeta 0.00712258 accp_rate_zeta 0.37
#> iter 200 Wed Jun 17 09:13:27 2026
#> 
#> zeta0.169392 stepsize_zeta 0.00783484 accp_rate_zeta 0.34
#> iter 300 Wed Jun 17 09:13:28 2026
#> 
#> zeta0.183347 stepsize_zeta 0.00861832 accp_rate_zeta 0.35
#> iter 400 Wed Jun 17 09:13:28 2026
#> 
#> zeta0.184539 stepsize_zeta 0.00948015 accp_rate_zeta 0.43
#> iter 500 Wed Jun 17 09:13:28 2026
#> 
#> zeta0.244617 stepsize_zeta 0.0104282 accp_rate_zeta 0.34
#> iter 600 Wed Jun 17 09:13:28 2026
#> 
#> zeta0.213486 stepsize_zeta 0.011471 accp_rate_zeta 0.33
#> iter 700 Wed Jun 17 09:13:29 2026
#> 
#> zeta0.212432 stepsize_zeta 0.0126181 accp_rate_zeta 0.5
#> iter 800 Wed Jun 17 09:13:29 2026
#> 
#> zeta0.196011 stepsize_zeta 0.0138799 accp_rate_zeta 0.36
#> iter 900 Wed Jun 17 09:13:29 2026
#> 
#> zeta0.215478 stepsize_zeta 0.0152679 accp_rate_zeta 0.26
#> iter 1000 Wed Jun 17 09:13:29 2026
#> 
#> zeta0.179026 stepsize_zeta 0.0152679 accp_rate_zeta 0.26
#> iter 1100 Wed Jun 17 09:13:30 2026
#> 
#> zeta0.223209 stepsize_zeta 0.0152679 accp_rate_zeta 0.42
#> iter 1200 Wed Jun 17 09:13:30 2026
#> 
#> zeta0.210055 stepsize_zeta 0.0152679 accp_rate_zeta 0.25
#> iter 1300 Wed Jun 17 09:13:30 2026
#> 
#> zeta0.189362 stepsize_zeta 0.0152679 accp_rate_zeta 0.43
#> iter 1400 Wed Jun 17 09:13:30 2026
#> 
#> zeta0.187921 stepsize_zeta 0.0152679 accp_rate_zeta 0.27
#> iter 1500 Wed Jun 17 09:13:31 2026
#> 
#> zeta0.21858 stepsize_zeta 0.0152679 accp_rate_zeta 0.32
#> iter 1600 Wed Jun 17 09:13:31 2026
#> 
#> zeta0.197298 stepsize_zeta 0.0152679 accp_rate_zeta 0.27
#> iter 1700 Wed Jun 17 09:13:31 2026
#> 
#> zeta0.172833 stepsize_zeta 0.0152679 accp_rate_zeta 0.28
#> iter 1800 Wed Jun 17 09:13:31 2026
#> 
#> zeta0.175111 stepsize_zeta 0.0152679 accp_rate_zeta 0.3
#> iter 1900 Wed Jun 17 09:13:32 2026
#> 
#> zeta0.197636 stepsize_zeta 0.0152679 accp_rate_zeta 0.29
#> iter 2000 Wed Jun 17 09:13:32 2026
#> 
#> zeta0.210071 stepsize_zeta 0.0152679 accp_rate_zeta 0.3

Then the results can be summarized by

res_sum = sum_mcmc_bspbss(res, ini$X, ini$kernel, start = 101, end = 200, select_p = 0.5)

and shown by

levelplot2D(res_sum$S, lim = c(-1.3,1.3), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).

For comparison, we show the estimated sources provided by informax ICA here.

levelplot2D(ini$init$ICA_S, lim = c(-1.7,1.7), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).

- A toy example