Sentence 1: True, fair point.
Sentence 2: This isn’t obvious to me. Selecting random values from a truncated normal distribution is (slightly) more complex than, say, a uniform distribution over the same range, but it is demonstrably (slightly) less complex than selecting random values from an unbounded normal distribution. Without finite boundaries, you’d need infinite precision arithmetic just to draw a value.
The problem is not with value selection, the problem is with model manipulation. The normal distribution is very well-studied, it has a number of appealing properties which make working with it rather convenient, there is a lot of code written to work with it, etc. Replace it with a truncated normal and suddenly a lot of things break.
Sentence 1: True, fair point. Sentence 2: This isn’t obvious to me. Selecting random values from a truncated normal distribution is (slightly) more complex than, say, a uniform distribution over the same range, but it is demonstrably (slightly) less complex than selecting random values from an unbounded normal distribution. Without finite boundaries, you’d need infinite precision arithmetic just to draw a value.
The problem is not with value selection, the problem is with model manipulation. The normal distribution is very well-studied, it has a number of appealing properties which make working with it rather convenient, there is a lot of code written to work with it, etc. Replace it with a truncated normal and suddenly a lot of things break.
Oh! I see what you’re saying. Definitely can’t argue with that.