In Section 3.2, Jaynes talks a little about propensities, causality, and mixing forward and backward inference. Then, in a paragraph beginning with the words “More generally, consider …” he introduces the concept of “exchangeability”. I realize that he will discuss this idea in more depth later, but I have three questions that seem appropriate here.
Why does he bring this up here? I missed the connection to the paragraphs which precede this one. [Edit: Oh, I see. Previous paragraphs discussed sampling twice without replacement from a two ball urn—the simplest and most extreme case of exchangeability.]
I think I understand that exchangeability is a generalization of “independence”. That is, in sampling with replacement, all trials are both independent and exchangeable. But when you sample without replacement, trials are no longer independent, though they are still exchangeable. The question is, is there a simple example of a series of trials which is neither independent nor exchangeable?
Am I correct that there is no example of a sequence which is independent but not exchangeable?
In Section 3.2, Jaynes talks a little about propensities, causality, and mixing forward and backward inference. Then, in a paragraph beginning with the words “More generally, consider …” he introduces the concept of “exchangeability”. I realize that he will discuss this idea in more depth later, but I have three questions that seem appropriate here.
Why does he bring this up here? I missed the connection to the paragraphs which precede this one. [Edit: Oh, I see. Previous paragraphs discussed sampling twice without replacement from a two ball urn—the simplest and most extreme case of exchangeability.]
I think I understand that exchangeability is a generalization of “independence”. That is, in sampling with replacement, all trials are both independent and exchangeable. But when you sample without replacement, trials are no longer independent, though they are still exchangeable. The question is, is there a simple example of a series of trials which is neither independent nor exchangeable?
Am I correct that there is no example of a sequence which is independent but not exchangeable?