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Supppose I have a sequence as so (which we can really think of as a sequence of smaller sequences):

[[1 1 1 1 1 1], [2 2 2 2 2 2], [3 3 3 3 3 3], [4 4 4 4 4 4]]

Is it exchangeable? Is it not? Why? It is a fairly loose question I know, but I am trying to understand how to answer this question.

Astrid
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    Without some reference to a probability distribution this question doesn't make sense. – klumbard Dec 13 '18 at 17:31
  • Ok that's a good start; what does one need to know how to answer this? I'm new to exchangeability. – Astrid Dec 13 '18 at 17:34
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    You need to have information, if only partial, about the joint probability of the entire sequence. Exchangeability is a property of that joint distribution (or of the vector random variable used to model the data), after all. It's not a property of any particular sequence. If some textbook or professor is asking to you determine, merely by inspection, whether this sequence of vectors is "exchangeable," then they are using a non-standard definition of the term, so any answer must begin with that definition. – whuber Dec 13 '18 at 17:40
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    Is the grouping in your data an aspect of the data, or have you just grouped it this way to highlight the repeated values. In other words, is your data a vector of 24 scalar values, or is it a vector of 4 vector values, each consisting of 6 elements? – Ben Dec 14 '18 at 04:24
  • Hi! The data is an index type array where each entry has a N repetitions (6 above). The grouping above is artificial and it is really 24 scalar values but which have this ordinal and repetitive structure. – Astrid Dec 14 '18 at 08:24
  • @whuber but if all that I know is that these are counting values (repeated) then can I actually say anything about exchangeability? I.e. These number are used to index things, where the first batch of 1s eg index six other objects – Astrid Dec 14 '18 at 08:26

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