Suppose that the prior distribution p(,) for the parameters , and of a Cauchy distribution is
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Suppose that the prior distribution p(µ,σ) for the parameters µ, and σ of a Cauchy distribution
is uniform in µ and σ, and that two observations x1 = 2 and x2 = 6 are available from this distribution. Calculate the value of the posterior density p(µ, σlx) (ignoring the factor 1/π2) to two decimal places for µ, = 0, 2, 4, 6, 8 and σ = 1, 2, 3, 4, 5. Use Simpson's rule to approximate the posterior marginal density of µ, and hence go on to find an approximation to the posterior probability that
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