One thousand posterior draws

Topic: Bayesian foundations · more questions on this topic
‹ What makes a hypothesis test? Prediction is not estimation ›

Suppose \theta^{(1)},\ldots,\theta^{(1000)} are posterior draws. State how you would estimate the posterior mean, median, variance, \mathbb{P}(\theta<0.5\mid x), and an equal-tailed 95\% interval. Which requested summary cannot be recovered merely by selecting an order statistic, and what calculation should replace that attempt?

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