2.3.6 Bayesian Inference for the Gaussian - The Variance

In this video we continue our investigation of Bayesian inference for the Gaussian, this time starting with the situation where we know the mean and want to infer the variance. Working instead with the precision, we find that the conjugate prior is the Gamma distribution, whose parameters correspond to an effective number of observations, and an effective variance. We then consider the case where neither the mean nor the variance are known and both must be inferred, and find that the conjugate prior there is the Gaussian-Gamma distribution. We finish the section by touching on high-dimensional versions of these results, and meeting the Wishart, inverse Wishart, and Gaussian-Wishart distributions.