The expected squared-error of prediction

$$\begin{split} E_{(Y,\hat{\underline{\theta}})|\underline{x_*}} \{ Y-\hat{Y} \}^2 & = \underbrace{E_{Y|\underline{x} _*} \{ Y - f(\theta; \underline{x}_*) \}^2}_\text{Variability of Y around its conditional expected value} + \\ \\ & \underbrace{[f(\theta;\underline{x}_*) - E_{\hat{\theta}|\underline{x}_*} \{ f(\underline{\hat{\theta}}; \underline{x}_*) \}]^2}_\text{Difference between the expected value and its estimate, Squared Bias} + \\ \\ & \underbrace{E_{\underline{\hat{\theta}}|\underline{x}_*}[f(\underline{\hat{\theta}};\underline{x}_*) - E_{\underline{\hat{\theta}}|\underline{x}_*} \{ f(\underline{\hat{\theta}}; \underline{x}_*) \}]^2}_\text{Change in the model due to the training data used, Variance} \end{split}$$