#bayes-estimator

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

Your posterior over a 1-D position is a symmetric mixture of two narrow Gaussians with equal weights, centred at $-2$ and $+2$ . You must report a single estimate. Which loss function leads to an estimate near one of the peaks rather than at $0$ , between them, where the posterior is almost zero?

The 0–1 loss (only an exactly correct estimate counts), whose optimum is a mode1
The squared-error loss, whose optimum is the posterior mean2
The absolute-error loss, whose optimum is the posterior median3
Any of the three, since they agree for every symmetric posterior4

Timed test