Let’s take the very first scatter plot. Consider the following alternative way of labeling the x and y axes. The y-axis is now the quality of a health intervention, and it consists of two components: short-term effects and long-term effects. You do a really thorough study that perfectly measures the short-term effects, while the long-term effects remain unknown to you. The x-value is what you measured (the short-term effects); the actual quality of the intervention is the x-value plus some unknown, mean zero variance 1 number.
So whereas previously (i.e. in the setting I actually talk about), we have E[measurement | quality] = quality (I’m calling this the frequentist sense of “unbiased”), now we have E[quality | measurement] = measurement (what I call the Bayesian sense of “unbiased”).
Let’s take the very first scatter plot. Consider the following alternative way of labeling the x and y axes. The y-axis is now the quality of a health intervention, and it consists of two components: short-term effects and long-term effects. You do a really thorough study that perfectly measures the short-term effects, while the long-term effects remain unknown to you. The x-value is what you measured (the short-term effects); the actual quality of the intervention is the x-value plus some unknown, mean zero variance 1 number.
So whereas previously (i.e. in the setting I actually talk about), we have E[measurement | quality] = quality (I’m calling this the frequentist sense of “unbiased”), now we have E[quality | measurement] = measurement (what I call the Bayesian sense of “unbiased”).
Yes—though I think this is just an elaboration of what Abram wrote here.