possible 2 typos found in basics of monte carlo methods lecture notes
File in which the problem appears
lectures/src/proj2-monte-carlo.md lines 166-168
Problematic sentence
Metropolis \emph{et al.} solved this as:
A_{RR^\prime}=\begin{cases}&1 &\text{if} \ p(R^\prime) > p(R)\\ \\ &\frac{p(R)}{p(R^\prime)} &\text{if} \ p(R^\prime) < p(R)\end{cases}.\tag{5}
The key to understanding why Eq. (5) solves (4) is by observing that A_{RR'}
and A{R'R}
will necessarily be given by different cases in the Eq. (5).
Correct version
Metropolis \emph{et al.} solved this as:
A_{RR^\prime}=\begin{cases}&1 &\text{if} \ p(R^\prime) > p(R)\\ \\ &\frac{p(R^\prime)}{p(R)} &\text{if} \ p(R^\prime) < p(R)\end{cases}.\tag{5}
The key to understanding why Eq. (5) solves (4) is by observing that A_{RR'}
and A_{R'R}
will necessarily be given by different cases in the Eq. (5).