Suppose we have two sensors with known (and different) variances v and vy, but unknown (and the same) mean µ. Suppose we

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Suppose We Have Two Sensors With Known And Different Variances V And Vy But Unknown And The Same Mean U Suppose We 1 (81.79 KiB) Viewed 26 times

Suppose we have two sensors with known (and different) variances v and vy, but unknown (and the same) mean µ. Suppose we observe n, observations from the first sensor and ny observations from the second sensor. Call these Da and Dy. Assume all distributions are Gaussian. - 1. What is the posterior p(μ Dx, Dy), assuming a non-informative prior for u? Give an explicit expression for the posterior mean and variance. Hint: use Bayesian updating twice, once to get from p(u) → p(µ\D₂) (starting from a non-informative prior, which we can simulate using a precision of 0), and then again to get from p(μ Dx) → p(µ Dx, Dy). 2. Suppose the y sensor is very unreliable. What will happen to the posterior mean estimate? Give a simplified approximate expression.