Normal distributions

Outline

Topics

• Quick review of the normal distribution.
• Different parameterizations.

Rationale

The normal distribution is often used in Bayesian analysis when one needs a prior over an unknown \(x\) such that \(x \in (-\infty, \infty) = \mathbb{R}\).

Examples of normal densities

Parameterizations

• There are different conventions to measure the spread.
  • Standard deviation \(\sigma\).
  • Variance, \(\sigma^2\).
  • Precision, \(\tau = 1/\sigma^2\).
• Keep that in mind as different languages will use different conventions!
• Standard deviation is the most intuitive:
  • it is the width of the bell,
  • the only one that has the same units as \(x\) (e.g. if \(x\) is in meters, so is \(\sigma\)).