Description:
In the introduction to the Linear Regression chapter the model is given by $y_n = f(x_n) + \epsilon$, with the note that $\epsilon$ is an iid random variable. Usually, we use the term iid for several r.v.s. Of course, one needs to understand that for any $n$, $\epsilon$ will be different, will be another independent copy of the corresponding r.v., but this can be misleading and unclear for a person who is not mathematically mature.
Location:
version 2022-01-11
Chapter 9
page 289 (lines 5,6), page 291 (line 10)
line 5
Proposed solution:
One of the possible solutions can be to add an index to $\epsilon$, i.e. to write $\epsilon_n$. Another solution is to write the model in the form $y = f(x)+\epsilon$, where $\epsilon$ is a r.v. that describes the measurement/observation noise ... (without mentioning the iid part).
Description: In the introduction to the Linear Regression chapter the model is given by $y_n = f(x_n) + \epsilon$, with the note that $\epsilon$ is an iid random variable. Usually, we use the term iid for several r.v.s. Of course, one needs to understand that for any $n$, $\epsilon$ will be different, will be another independent copy of the corresponding r.v., but this can be misleading and unclear for a person who is not mathematically mature.
Location:
Proposed solution: One of the possible solutions can be to add an index to $\epsilon$, i.e. to write $\epsilon_n$. Another solution is to write the model in the form $y = f(x)+\epsilon$, where $\epsilon$ is a r.v. that describes the measurement/observation noise ... (without mentioning the iid part).