Normal-Normal Conjugate Model
With known observation variance, a Gaussian prior on a mean yields a Gaussian posterior whose mean is a precision-weighted average of the prior mean and the sample mean; precisions (inverse variances) add, so more data mechanically pulls the posterior toward the data.
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With known observation variance, a Gaussian prior on a mean yields a Gaussian posterior whose mean is a precision-weighted average of the prior mean and the sample mean; precisions (inverse variances) add, so more data mechanically pulls the posterior toward the data.
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