Write a simple MCMC routine using Python. Please include input and output.

MCMC Assignment 1 (1) Write a simple MCMC routine (in python) to produce N - 10000 draws {xi) from the Gaussian distribution Note that the parameters , are fixed here, and they define the properties of the distribu- tion. As a concrete example, set -1, -1. For the proposal distribution, use where No.a2l is a draw from a gaussian distribution with mean 0 and variance 2-2. You can use numpy. random. normal ( ) to draw random numbers. Google knows all about it. (a) Run your code trying four different jump size scalings, = 0.01, = 0.1, 1.0 and = 10.0. Visually inspect the chains. Which one appears to be exploring the distri- bution most effectively? (b) Have your code compute the acceptance fraction for the proposed jumps (i.e. the frac- tion of the proposed jumps that are accepted). Does a high acceptance rate necessarily mean efficient exploration of the posterior distribution? MCMC Assignment 1 (1) Write a simple MCMC routine (in python) to produce N - 10000 draws {xi) from the Gaussian distribution Note that the parameters , are fixed here, and they define the properties of the distribu- tion. As a concrete example, set -1, -1. For the proposal distribution, use where No.a2l is a draw from a gaussian distribution with mean 0 and variance 2-2. You can use numpy. random. normal ( ) to draw random numbers. Google knows all about it. (a) Run your code trying four different jump size scalings, = 0.01, = 0.1, 1.0 and = 10.0. Visually inspect the chains. Which one appears to be exploring the distri- bution most effectively? (b) Have your code compute the acceptance fraction for the proposed jumps (i.e. the frac- tion of the proposed jumps that are accepted). Does a high acceptance rate necessarily mean efficient exploration of the posterior distribution