This is the first example from ?bamlss:

set.seed(1337)

d <- GAMart()
f <- num ~ s(x1) + s(x2) + s(x3) + te(lon, lat)
b <- bamlss(f, data = d, sampler = FALSE, verbose = FALSE)

b <- apify(b, propose = "iwlsC_gp")

nsamp <- 500

samples <- matrix(
  data     = NA_real_,
  nrow     = nsamp,
  ncol     = length(parameters(b, "mu", "s(x1)")),
  dimnames = list(NULL, names(parameters(b, "mu", "s(x1)")))
)

for (i in 1:nsamp) {
  prop <- propose(b, "mu", "s(x1)")
  if (log(runif(1)) <= prop$alpha) b <- accept(b, "mu", "s(x1)", prop)
  samples[i,] <- parameters(b, "mu", "s(x1)")
}

par(mfrow = c(ncol(samples), 2))
plot(as.mcmc(samples), auto.layout = FALSE)

par(mfrow = c(1, 1))

Some more API examples:

predictors(b)
#> [1] "mu"    "sigma"
smooths(b, predictor = "mu")
#> [1] "s(x1)"       "s(x2)"       "s(x3)"       "te(lon,lat)" "p"
parameters(b, "mu", "s(x1)")
#>            b1            b2            b3            b4            b5 
#> -0.0067264089 -0.0029561932 -0.0003810828  0.0079394603  0.0017411598 
#>            b6            b7            b8            b9         tau21 
#>  0.0090295349  0.0001365967 -0.0175519081 -0.1597753593  0.0022726896
b <- update_logpost(b)
logpost(b)
#> [1] 229.6844
#> attr(,"outdated")
#> [1] FALSE
b <- set_parameters(b, "mu", "s(x1)", parameters(b, "mu", "s(x1)") + 0.01)
outdated(fx(b, "mu", "s(x1)"))
#> [1] TRUE
outdated(eta(b, "mu"))
#> [1] TRUE
outdated(logpost(b))
#> [1] TRUE
b <- update_logpost(b)
logpost(b)
#> [1] 190.7844
#> attr(,"outdated")
#> [1] FALSE
grad_logpost(b, "mu", "s(x1)")
#>  [1]  -994.198941   153.131874  -947.441555  -141.396974 -1190.468594
#>  [6]  -423.074531 -1271.468653    -1.201107 -1061.496652   -45.103787
hess_logpost(b, "mu", "s(x1)")
#>            [,1]       [,2]       [,3]        [,4]      [,5]        [,6]
#>  [1,] 20101.928 -1995.9642 16496.3887  1025.81638 18225.440  3140.46362
#>  [2,] -1995.964  3835.7844 -1799.5426 -1269.69972 -2439.421  -613.94683
#>  [3,] 16496.389 -1799.5426 20808.6831   946.72821 17385.198  3132.54623
#>  [4,]  1025.816 -1269.6997   946.7282  5850.55190  1392.192   -17.89478
#>  [5,] 18225.440 -2439.4214 17385.1982  1392.19192 30965.252  3575.27065
#>  [6,]  3140.464  -613.9468  3132.5462   -17.89478  3575.271 13291.09983
#>  [7,] 18739.899 -2709.6234 17859.9605  1585.12122 19880.860  3724.11362
#>  [8,] -2324.002 -2737.7247 -2873.3659  2905.59741 -2601.433  3894.92587
#>  [9,] 20136.782 -2178.5037 18648.3658   961.32257 20561.405  3048.84505
#>            [,7]      [,8]       [,9]
#>  [1,] 18739.899 -2324.002 20136.7817
#>  [2,] -2709.623 -2737.725 -2178.5037
#>  [3,] 17859.961 -2873.366 18648.3658
#>  [4,]  1585.121  2905.597   961.3226
#>  [5,] 19880.860 -2601.433 20561.4052
#>  [6,]  3724.114  3894.926  3048.8451
#>  [7,] 45004.966 -2421.137 21132.2253
#>  [8,] -2421.137  5268.296 -2787.2009
#>  [9,] 21132.225 -2787.201 21750.8277