Metropolis-Hastings algorithm

General Metropolis-Hastings algorithm
• Specific procedure just described was special case:
– Discrete positions (θ);
– One dimension;
– Moves that proposed one position left or right.
• General algorithm applies to:
– Continuous values;
– Any number of dimensions;
– More general proposed distributions.
• Essentials are same as for special case:
– Have some target distribution, P(θ), over a multidimensional
continuous parameter space.
– Would like to generate representative samples.
– Must be able to find value of P(θ) for any candidate value of θ.
– Distribution P(θ) does not need to be normalized, merely non-negative.
– Typical Bayesian application: P(θ) is product of likelihood and prior.