Frequently Asked Questions

## a log-pdf to sample from
p.log <- function(x) {
  B <- 0.03 # controls 'bananacity'
  -x[1]^2 / 200 - 1 / 2 * (x[2] + B * x[1]^2 - 100 * B)^2
}

set.seed(20201209)

res1 <- MCMCEnsemble(
  p.log,
  lower.inits = c(a = -10, b = -10), upper.inits = c(a = -5, b = -5),
  max.iter = 3000, n.walkers = 10,
  method = "stretch",
  coda = TRUE
)
#> Using stretch move with 10 walkers.

summary(res1$samples)
#> 
#> Iterations = 1:300
#> Thinning interval = 1 
#> Number of chains = 10 
#> Sample size per chain = 300 
#> 
#> 1. Empirical mean and standard deviation for each variable,
#>    plus standard error of the mean:
#> 
#>      Mean    SD Naive SE Time-series SE
#> a -3.4972 9.084  0.16584         1.4141
#> b -0.1255 4.116  0.07515         0.5463
#> 
#> 2. Quantiles for each variable:
#> 
#>      2.5%     25%    50%   75%  97.5%
#> a -20.642 -10.134 -2.887 3.098 12.403
#> b  -9.974  -1.766  1.148 2.675  4.401

plot(res1$samples)

res2 <- MCMCEnsemble(
  p.log,
  lower.inits = c(a = -10, b = -10), upper.inits = c(a = -5, b = -5),
  max.iter = 3000, n.walkers = 10,
  method = "differential.evolution",
  coda = TRUE
)
#> Using differential.evolution move with 10 walkers.

summary(res2$samples)
#> 
#> Iterations = 1:300
#> Thinning interval = 1 
#> Number of chains = 10 
#> Sample size per chain = 300 
#> 
#> 1. Empirical mean and standard deviation for each variable,
#>    plus standard error of the mean:
#> 
#>       Mean    SD Naive SE Time-series SE
#> a  0.14194 9.874  0.18028         0.9203
#> b -0.01001 3.697  0.06751         0.4142
#> 
#> 2. Quantiles for each variable:
#> 
#>      2.5%    25%     50%   75% 97.5%
#> a -19.189 -6.265 -0.1711 7.735 18.07
#> b  -8.556 -1.963  1.2788 2.687  4.34

plot(res2$samples)