Does additional data always reduce posterior variance?
Additional data does not always decrease the size of a confidence interval. From a Bayesian perspective, new information generally reduces uncertainty and makes the posterior distribution more concentrated, but the effect on posterior variance can depend on the specific circumstances.
Background
John D. Cook is a mathematician and blogger who writes about statistics, Bayesian inference, and numerical computing for a technically literate audience. Bayesian statistics treats unknown parameters as random variables with a "prior" distribution (your initial belief), which is updated with data to produce a "posterior" distribution (your updated belief). The "posterior variance" measures how much uncertainty remains after seeing the data — smaller variance means more certainty. This post challenges the intuitive assumption that more data always makes you more certain; it gives a concrete example where adding data actually increases posterior variance, because the new data conflicts with the prior in a way that spreads the posterior out. This matters for anyone doing statistical modeling, machine learning, or scientific inference: it shows that the relationship between data quantity and uncertainty is more subtle than commonly assumed.