Now we'll move on to discussing Bayesian methods for analyzing the means of quantitative data. This section is similar to the previous one on Bayesian methods for analyzing proportions, but it focuses on the means of quantitative data. Here, we look at constructing credible intervals and performing hypothesis testing.
Suppose that we assume that our data was drawn from a normal distribution with an unknown mean, μ, and an unknown variance, σ2. The conjugate prior, in this case, will be the normal inverse gamma (NIG) distribution. This is a two-dimensional distribution, and gives a posterior distribution for both the unknown mean and the unknown variance.
In this section, we only care about what the unknown mean ...
