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Bayesian estimation of means

Peter Ralph

Advanced Biological Statistics

Estimating means, part 2

The problem

We are interested in estimating the average body weight of squirrels in a nearby patch of forest (for the purpose of comparing to other locations). We have only weighed so far five squirrels, whose weights, in grams, are

642, 687, 451, 410, 586

Suppose that the distribution of squirrel weights is Normal with mean \(\mu\) and standard deviation \(\sigma\).

  1. Assuming that \(\sigma=150\), choose a Normal prior for \(\mu\) and find the maximum posterior estimate for \(\mu\), given the data.

  2. Choose Normal prior distributions for \(\mu\) and \(\sigma\), and find the maximum posterior estimates for both.