Hi,
I am currently working my way through Peter Green's 1995 reversible jump
MCMC paper and am trying to figure out how to calculate the prior
distribution on the step positions s_1,...,s_k. The paper states that
conditional on the number of steps k, the priors on the positions are the
even-numbered order statistics of 2k+1 uniform variables distributed
on [0,L].
One possible move is to update one point s_j, chosen randomly from
s_1,...,s_k.
The acceptance probability is given as:
min{1,(likelihood ratio) x
{(s_{j+1}-s'_j)(s'_j-s_{j-1})}/{(s_{j+1}-s_j)(s_j-s_{j-1})}}
This derivation is probably straightforward but has stumped me.
If anyone could tell me how it is derived or has a copy of a tutorial
paper or something that uses this specific example then that would be
most appreciated.
Many thanks,
TJ McKinley
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