7.2 The big idea 2/2

But we are using MCMC to approximate this pdf (so we can’t sample it).

For we are going to use two tricks:

We do know that \(f(u|y = 6.25) \propto f(\mu)L(u|y = 6.25)\)

For step 1 we can use an other model or distribution to generate proposals

\[ \mu_{proposal}|\mu \sim Unif(\mu - w, \mu, + w) \]

with pdf:

\[ q(\mu'|\mu) = \frac{1}{2 w}\]

This give us a way for doing step1!