There is a package Parallel
detectCores(): return how many cores exist on your PC.
cl <- makeCluster(np): initialize a cluster mc with np processes.
Apply Operations using Clusters:
clusterCall, clusterEvalQ, clusterApply, clusterExport, clusterMap,
parLapply, parSapply, parApply, parRapply, parCapply
stopCluster(cl): release the occupied cores.
An example Check how many cores exist on my PC.
library(parallel) detectCores() ## [1] 12 Define a function.
sim <- function(x){ rnorm(1, mean = x) } Use parallel to speed up the calculation.
Steps for \(i=1,2,\dots,n\)
Sample candidate value \(x^i\) from a proposal distribution \(q(x^i|x^{i-1})\)
Compute acceptance probability:
\[\alpha=\frac{p(x^i)q(x^{i-1}|x^i)}{p(x^{i-1})q(x^i|x^{i-1})}\] 3. Compute \(r=min(1,\alpha)\)
Sample \(U\sim Unif(0,1)\)
\[ x^i=\begin{cases} x^{i-1}, &u<r \\x^i, &u\geq r\end{cases} \]
An example
R code for bootstrap and permutation test.