Metropolis-Hastings algorithm

General Metropolis-Hastings algorithm
• Sample values from target distribution generated by taking a random
walk through the multidimensional parameter space.
– Begins at arbitrary point, specified by user, where P(θ) is non-zero.
– At each time step:
• Move to new position in parameter space is proposed.
• Decide whether or not to accept move to new position.
– Proposal distributions can be of various forms.
• Goal is to efficiently explore regions of parameter space where P(θ)
has greatest mass.
• Simplest case: proposal distribution is normal, centered on current
position.
• Proposed move will typically ybe near present position, with probability
of more distant positions decreasing with distance:
0.4
0.35
0.3
025 0.25
P()
0.2
0.15
0.1
0.05
0
-3 -2 -1 0 1 2 3