MCMC

MCMC

1. Bayes Theorem

   • Prior: the belief without data
   • posterior distribution
     • wacky prior? impossible to solve analytically--what to do
   • likelihood: what the observed data is telling us
   • likelihood: the data we observe, the evidence
   • posterior: combine prior and likelihood -->tells which parameter values maxi the chance of obeseving particular data, by taking into account of the prior distribution
   • what about when prior is wacky(not common distribution shape), and hard to compute analytically the posterior distribution
     • This is when we use MCMC

2. that is when MCMC comes along: Allows us to estimate the shape of posterior distribution

3. Monte Carlo Simulation

4. Markov Chain

5. Explanation of MCMC

6. Monte Carlo: the simulation technique

7. Markov Chain: memoryless

   • Stationary State

8. So, now What is MCMC