b is not deterministic; it is the intensity of the background in the source area. Therefore, the area correction factor is unity, and there is no need to resort to extra variables t.

You are correct that an assumption is made that the background at an off-source location also describes the background under the source. But if you do not make this assumption, you will have 3 variables (s and b in the source region and say b’ in the background region) and 2 equations, so you will have to have another relation saying what b’ is as a function of b. As long as b’ is proportional to b, the proportionality constant can be subsumed into r and it will reduce without loss of generality to the same form as given above. If b’ is a non-linear function of b, well, you shouldn’t be using this formula then.

]]>My question is, what is random and what is fixed? C and B are random variables following the Poisson distribution with given rates, that I don’t doubt. Yet, how come r and b are deterministic? How sure b is fixed and same for both equations in the first line? I bet checking S/N is to ensure gs is zero (or ignorable), though.

All I wish to get is any historic account that b is homogeneous and two b’s in the first line are the same (according to the account, r is a fixed value, independent of s, and I introduced t in tb to indicate that b is not necessarily homogeneous. The model would be written in different fashions).

]]>say again?

]]>*“…old habits die hard, and old codes die harder…*

Ouch! I think you should copyright that!

]]>