Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
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Monte Carlo approach<br />
• Basic goal lin Bayesian inference: describe posterior distribution<br />
ib i<br />
over the parameters.<br />
• Monte Carlo approach:<br />
– Sample large number of representative points from posterior.<br />
– From points, calculate descriptive statistics.<br />
• E.g., consider beta(θ | a, b) distribution:<br />
ib ti<br />
– Mean and standard deviation can be analytically derived.<br />
• Expressed exactly in terms of parameters a and b.<br />
– Cumulative probability distribution (cdf, qbeta in R) can be<br />
computed.<br />
• Used to determine credible intervals.<br />
• But: suppose didn’t know analytical formulas or cdf.
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