Let’s think about that we’re measuring the approval ranking of an unpopular politician. Suppose we pattern ten polls and get the values
How can we assemble a posterior distribution for our perception within the politician’s imply approval ranking?
Let’s assume that the polls are impartial and identically distributed random variables, X_1, …, X_n. The central restrict theorem tells us that the pattern imply will asymptotically strategy a traditional distribution with variance σ²/n
the place μ and σ² are the imply and variance of X_i.
Motivated by this asymptotic restrict, let’s approximate the chance of noticed knowledge y with
Utilizing the target prior
(extra on this later) and integrating out σ² provides us a t distribution for the posterior, π(µ|y)
the place
Let’s have a look at the posterior distribution for the info in Desk 1.
