Metropolis–Hastings algorithm in R

Steps

for \(i=1,2,\dots,n\)

1. Sample candidate value \(x^i\) from a proposal distribution \(q(x^i|x^{i-1})\)

2. 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 \(r=min(1,\alpha)\)

4. Sample \(U\sim Unif(0,1)\)

5. \[ x^i=\begin{cases} x^{i-1}, &u<r \\x^i, &u\geq r\end{cases} \]

An example