Jumping distribution

1. What is a jumping distribution?
2. What is a good acceptance rate for MCMC?
3. What is proposal density?
4. What is Metropolis-Hastings used for?

What is a jumping distribution?

A usual choice is to let be a Gaussian distribution centered at , so that points closer to are more likely to be visited next, making the sequence of samples into a random walk. The function. is referred to as the proposal density or jumping distribution.

What is a good acceptance rate for MCMC?

Lastly, the acceptance rate depends on the problem but typically for 1-d problems, the acceptance rate should be around 44% (around 23% for more than 5 parameters).

What is proposal density?

Proposal density is the function we use to sample from the proposal distribution to generate a candidate value for the target density in the MH algorithm. Transition kernel is a conditional density that relates how we move to xt+1 from xt.

What is Metropolis-Hastings used for?

The Metropolis-Hastings algorithm is one of the most popular Markov Chain Monte Carlo (MCMC) algorithms. Like other MCMC methods, the Metropolis-Hastings algorithm is used to generate serially correlated draws from a sequence of probability distributions. The sequence converges to a given target distribution.