This tutorial confuses me a lot…basically I understand most of the formulas, but for some steps, I would do it in a different way. Can someone point out where I am wrong? Thanks!
In exercise 1, we generated the p(\tilde x | x) matrix by going through the values of \tilde x and setting x as a normal distribution centered at \tilde x. To me, it makes more sense to go through x and setting \tilde x as a normal distribution, as the logic is “the perceived location is around the real location”, rather than “the real location is around the perceived location”. I know both cases will result in the same 2D normal distribution, but this is more logical to me.
In exercise 7, for each sound location x_0, the code generates an x-independent input matrix p(\tilde x | x=x_0) to calculate the response function p(\hat x | x=x_0). But why can’t we just directly generate the input matrix p(\tilde x | x) as the function of both x and \tilde x, which will be x-dependent, and directly calculate p(\hat x | x)? This way we don’t have to loop though the possible values of x.
Thanks in advance!