Important note: Choosing a point estimate to describe the posterior distribution is hardly ever necessary and is often harmful as it discards information

Point estimates: is a single-value summary of the posterior distribution

• mean
• median
• mode

Which point estimate to use?

• Loss function - a rule that tells you the cost associated with using any particular point estimate.

• Different loss functions nominate different point estimates

• Goal: find the parameter value (or a decision) that will minimize our expected loss; do this by using the posterior to average over our uncertainty in the true value