Metropolis-Hastings

MH is one way of doing MCMC.

Output: $p(\theta)$ - inferred posterior distribution

Given:

• $g(\theta)$ -
• $q(\theta)$ -

Algo:

• start with initial guess $\theta_0$
• Repeat the below maxSteps times
  • sample $\theta^*$ from $q(\theta^*\|\theta_{i-1})$
  • $$\alpha = \frac{g(\theta^*) q(\theta_{i-1}|\theta^*)}{g(\theta_{i-1}) q(\theta^*|\theta_{i-1})}$$
  • if $\alpha >= 1$ set $\theta_i = \theta^*$
  • if $\alpha$ is between 0 and 1 set $\theta_i = \theta^*$ with probability $\alpha$