Statistics and R

If you have written many functions, it would be more convenient to build up a package. It is also wonderful to share the tools you created by developing a R package. I will introduce some easy steps to achieve this goal. Preparation We need to creat a project for the new package. Creat a new project Click these butthons in your Rstudio. File > New project > New Dictionary > R package

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