MCMC

Question 1

What happens when you have many parameters?

Answer 1

You end up having to look at bigger parameter spaces, making good guesses become rare

Question 2

What is the prior?

Answer 2

It represents what we believe about the parameter before seeing the data

Question 3

What is the likelihood?

Answer 3

The probability of observing the data given a particular parameter value

Question 4

What is the posterior?

Answer 4

The updated belief about the parameter after seeing the data.

Question 5

What is MCMC?

Answer 5

An algorithm that steps through the parameter space and moves towards areas of higher likelihood

Question 6

What is a chain in MCMC?

Answer 6

A series of guesses. The rest of the guesses is used to estimate the posterior.

Question 7

What is a “hairy caterpillar” chain?

Answer 7

A well-mixed, stable chain with no trends - indicates good exploration of the parameter space

Question 8

What are signs of a bad MCMC chain?

Answer 8

Not reaching high-likelihood zones
Not mixed well (auto correlated)
Trendy or stuck patterns

Question 9

What are the steps to an MCMC?

Answer 9

1. Starts at a random guess
2. Proposes a small move
3. Keeps or rejects it based on likelihood comparison
4. Repeats steps to form chain of guesses
5. Uses the chain to build the posterior dstribution

Question 10

What are Monte Carlo methods used for?

Answer 10

Estimating numerical results that are difficult to calculate directly.
Simulating random provesses
Approximate probability distributions
Explore parameters spaces

Question 11

What are Monet Carlo methods used for?

Answer 11

To approximate the posterior distribution when it’s too hard to compute directly. You draw thousands of random parameter values and simulate the data and keep the guesses that fit the observed data.