An intuition for physicists: information gain from experiments

Johannes Buchner

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arXiv · 2205.00009

An intuition for physicists: information gain from experiments

Johannes Buchner

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Abstract

How much one has learned from an experiment is quantifiable by the information gain, also known as the Kullback-Leibler divergence. The narrowing of the posterior parameter distribution $P(\theta|D)$ compared with the prior parameter distribution $\pi(\theta)$, is quantified in units of bits, as: $ D_{\mathrm{KL}}(P|\pi)=\int\log_{2}\left(\frac{P(\theta|D)}{\pi(\theta)}\right)\,P(\theta|D)\,d\theta $. This research note gives an intuition what one bit of information gain means. It corresponds to a Gaussian shrinking its standard deviation by a factor of three.

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Johannes Buchner. 2022-04-29. An intuition for physicists: information gain from experiments. https://arxiv.org/abs/2205.00009

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