Here is a simulation of a one-dimensional "Metropolis algorithm" Markov
chain, started in stationarity. The target (stationary) distribution is
Exp(1), with density exp(-x). The
proposal distribution is Q(x,.) = Unif[x-k,x+k], with density
1/2k. Each proposal value y>0 is accepted with probability =
min(1, exp(-(y-x))).
Try restarting this page several times to see different simulation
runs. Note that the mean sample value "should" be 1.0, but
in fact it isn't very accurate! (Indeed,
it's possible the entire graph will lie above the screen, so you won't
see a thing!)
To see why I care about these issues, check out my
research papers (e.g. this one).
See the chain run!
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