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Conjugate Bayesian analysis of the Gaussian distribution

Conjugate Bayesian analysis of the Gaussian distributionKevin P. Murphy updated October 3, 20071 IntroductionThe Gaussian or normal distribution is one of the most widelyused in statistics. Estimating its parameters usingBayesian inference and Conjugate priors is also widely used. The use of Conjugate priors allows all the results to bederived in closed form. Unfortunately, different books usedifferent conventions on how to parameterize the variousdistributions ( , put the prior on the precision or the variance, use an inverse gamma or inverse chi-squared, etc),which can be very confusing for the student.

The Gaussian or normal distribution is one of the most widely used in statistics. Estimating its parameters using Bayesian inference and conjugate priors is also widely used. The use of conjugate priors allows all the results to be derived in closed form. Unfortunately, different books use different conventions on how to parameterize the various

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