Does additional data always reduce posterior variance?

🫧 Open on Bubbles A discussion over lunch today brought up the fact that additional data does not always decrease the size of a confidence interval. This post will look at this from a Bayesian perspective. In general, new information reduces your uncertainty regarding whatever you’re estimating. The posterior distribution becomes more concentrated as more data are collected. That’s what happens “in general” but does it necessarily happen every time you get new data? Conceivably if you get surprising data, d