Metropolis-Hastings algorithm

• Initial i assumptions:
Monte Carlo approach
– Prior distribution is specified by function (continuous or discrete) that is
easily evaluated (by computer):
• If specify θ, then p(θ) is easily determined.
– Likelihood function, p(D | θ), can be determined for any specified values of
D and θ.
– (Actually, all that is required is that the product of the prior and the
likelihood be easily determined.)
• Method produces an approximation of the posterior distribution, p(θ | D):
– Provides large number of θ values sampled from the posterior distribution.
– Can be used to estimate:
• Mean, median, standard ddeviation of posterior.
• Credible HDI regions.
• Etc.
• Example of Monte Carlo method.