Interview Question: From Prior to Posterior

Sample Question #223 (statistics – Bayesian inference)

Suppose that x is normally distributed with mean μ and variance 4. Assume that the prior distribution of μ is also normal with mean 0 and variance 25. What is the posterior distribution of μ given the data point x?

[Taken from exercise 12.1 in Tsay’s Analysis of Financial Time Series, 2nd ed.]

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One Response to Interview Question: From Prior to Posterior

  1. Brett says:

    ANSWER
     
    If you say on your resume that you know statistics, you should have at least some passing knowledge of Bayesian analysis.
     
    The posterior mean of μ is [4*0+1*25*x]/(4+1*25), where 1 is the number of observations we have, which is just one data point. The sample mean of one data point is just the data point itself, x. The posterior variance of μ is 4*25/(4+1*25).
     

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