The subject of my comment is, "Why are we given mean and variance?" If you take, "We are given mean and variance" as a presupposition, then you are having a different conversation.
The big problem with the maximum entropy argument is that if you apply some transformation to your data, you will end up with a different maximum entropy distribution. For example, you may choose to express your data in terms of rate (events / time) or period (time / events). Maximum entropy won't help you here, you have to have some kind of theoretical understanding of the underlying process that justifies your choice.
The same is true for normal distributions and mean / variance, but it's such an "obvious" choice that people forget to justify their models. My experience is that the premise of the CLT is much easier to justify, and you can use that to support your use of the normal distribution.
The subject of my comment is, "Why are we given mean and variance?" If you take, "We are given mean and variance" as a presupposition, then you are having a different conversation.
The big problem with the maximum entropy argument is that if you apply some transformation to your data, you will end up with a different maximum entropy distribution. For example, you may choose to express your data in terms of rate (events / time) or period (time / events). Maximum entropy won't help you here, you have to have some kind of theoretical understanding of the underlying process that justifies your choice.
The same is true for normal distributions and mean / variance, but it's such an "obvious" choice that people forget to justify their models. My experience is that the premise of the CLT is much easier to justify, and you can use that to support your use of the normal distribution.