Convenience in Mathematical Statistics
Definition
A bias $\text{Bias}$ is defined as follows for an estimator $\widehat{\theta}$ of a parameter $\theta$. $$ \text{Bias} ( \theta ) = E(\widehat{\theta}) - \theta $$
Description
While the term Bias can be purified into bias or tendency, the most commonly used term is Bias, pronounced as it is. In Korean, “편의(Convenience)” overwhelmingly means convenience, and it seems appropriate to purify it into ‘bias’ both mathematically and in actual usage. However, in the context of statistical analysis or machine learning, the case where ‘편의’ means convenience is significantly rare, and because the term ‘bias’ is so useful, using ‘편의’ is less confusing. Nonetheless, as mentioned, it is usually just called bias. Bias represents the difference between the expected value of the estimator and the true value, and it often has a trade-off relationship with variance which is frequently expressed in the form of squares. $$ \text{MSE} \left( \widehat{\theta} \right) = \operatorname{Var} \left( \widehat{\theta} \right) + \text{Bias} \left( \widehat{\theta} \right)^{2} $$ Having a large square of bias means that the estimate fails to accurately hit the parameter. Therefore, if the bias is not properly adjusted, any precision in prediction can result in a skewed prediction. In statistics, especially mathematical statistics, since probability is mainly dealt with, the variance is often precisely known, and bias is something they prefer not to deal with if possible. Therefore, they try to control the bias to be completely $0$, and such estimators without bias are called unbiased estimators.