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I have been reading about autoregressive models. Based on what I've read, it seems to me that all autoregressive models use ancestral sampling. For instance, this paper says the following in Abstract:

We introduce a deep, generative autoencoder capable of learning hierarchies of distributed representations from data. Successive deep stochastic hidden layers are equipped with autoregressive connections, which enable the model to be sampled from quickly and exactly via ancestral sampling.

However, what I don't understand is why (as I understand it) all autoregressive models use ancestral sampling. Why is ancestral sampling used in autoregressive models?

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My understanding is that the answer to this question is basically 'ancestral sampling is used in autoregressive models because it fits well the structure/dynamics of autoregressive models (the ancestor-descendent relationship, etc.)'. It's not a very satisfying answer, but my understanding is that it's correct.

If anyone has a better answer, feel free to post.

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