# statistics

The biasvariance decomposition allows one to decompose the contributions to the meansquared error of an estimator into two parts, the variance stemming from the fluctuations of the prediction and the bias measuring the deviation of the expected value of the prediction from the true value. While being a very straightforward relation, it allows fundamental insight into necessary tradeoffs when constructing estimators. In this post I show how to derive the biasvariance decomposition in the multivariate setting motivated by a use case in quantum metrology and talk a bit about Stein’s paradox.