I am reading Statistical Rethinking (Section 4.3).

When talking about the i.i.d. assumption used to build a linear regression model - without knowing if distribution values are correlated, the author says:

A moment's reflection tells us that this is hardly ever true, in a physical sense. Whether measuring the same distance repeatedly or studying a population of heights, it is hard to argue that every measurement is independent of the others. For example, heights within families are correlated because of alleles shared through recent shared ancestry.

The i.i.d. assumption doesn't have to seem awkward, however, as long as you remember that probability is inside the golem [the model], not outside in the world. The i.i.d. assumption is about how the golem represents its uncertainty. It is an epistemological assumption. [...] The point isn't to say epistemology trumps reality, but rather that in ignorance of such correlations the most conservative distribution to use is i.i.d. [...]

Even furthermore, there are many types of correlation that do little or nothing to the overall shape of a distribution, but only affect the precise sequence in which values appear. For example, pairs of sisters have highly correlated heights. But the overall distribution of female height remains almost perfectly normal. In such cases, i.i.d. remains perfectly useful, despite ignoring the correlations.

Why is i.i.d. the most conservative distribution? Because it does not introduce additional assumptions in the model?

I am reading Statistical Rethinking (Section 4.3).

When talking about the i.i.d. assumption used to build a linear regression model - without knowing if distribution values are correlated, the author says:

A moment's reflection tells us that this is hardly ever true, in a physical sense. Whether measuring the same distance repeatedly or studying a population of heights, it is hard to argue that every measurement is independent of the others. For example, heights within families are correlated because of alleles shared through recent shared ancestry.

The i.i.d. assumption doesn't have to seem awkward, however, as long as you remember that probability is inside the golem [the model], not outside in the world. The i.i.d. assumption is about how the golem represents its uncertainty. It is an epistemological assumption. [...] The point isn't to say epistemology trumps reality, but rather that in ignorance of such correlations the most conservative distribution to use is i.i.d. [...]

Even furthermore, there are many types of correlation that do little or nothing to the overall shape of a distribution, but only affect the precise sequence in which values appear. For example, pairs of sisters have highly correlated heights. But the overall distribution of female height remains almost perfectly normal. In such cases, i.i.d. remains perfectly useful, despite ignoring the correlations.

Why is i.i.d. the most conservative distribution assumption? Because it does not introduce additional assumptions in the model?

I am reading Statistical Rethinking (Section 4.3).

When talking about the i.i.d. assumption, the author says:

The i.i.d. assumption doesn't have to seem awkward, however, as long as you remember that probability is inside the golem [the model], not outside in the world. The i.i.d. assumption is about how the golem represents its uncertainty. It is an epistemological assumption. [...] The point isn't to say epistemology trumps reality, but rather that in ignorance of [...] correlations the most conservative distribution to use is i.i.d.

Why is i.i.d. the most conservative distribution? Because it does not introduce additional assumptions in the model?

I am reading Statistical Rethinking (Section 4.3).

When talking about the i.i.d. assumption used to build a linear regression model - without knowing if distribution values are correlated, the author says:

A moment's reflection tells us that this is hardly ever true, in a physical sense. Whether measuring the same distance repeatedly or studying a population of heights, it is hard to argue that every measurement is independent of the others. For example, heights within families are correlated because of alleles shared through recent shared ancestry.

The i.i.d. assumption doesn't have to seem awkward, however, as long as you remember that probability is inside the golem [the model], not outside in the world. The i.i.d. assumption is about how the golem represents its uncertainty. It is an epistemological assumption. [...] The point isn't to say epistemology trumps reality, but rather that in ignorance of such correlations the most conservative distribution to use is i.i.d. [...]

Even furthermore, there are many types of correlation that do little or nothing to the overall shape of a distribution, but only affect the precise sequence in which values appear. For example, pairs of sisters have highly correlated heights. But the overall distribution of female height remains almost perfectly normal. In such cases, i.i.d. remains perfectly useful, despite ignoring the correlations.

Why is i.i.d. the most conservative distribution? Because it does not introduce additional assumptions in the model?