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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.

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    $\begingroup$ Without some reference to a probability distribution this question doesn't make sense. $\endgroup$ – klumbard Dec 13 '18 at 17:31
  • $\begingroup$ Ok that's a good start; what does one need to know how to answer this? I'm new to exchangeability. $\endgroup$ – Astrid Dec 13 '18 at 17:34
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    $\begingroup$ 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. $\endgroup$ – whuber Dec 13 '18 at 17:40
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    $\begingroup$ 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? $\endgroup$ – Ben - Reinstate Monica Dec 14 '18 at 4:24
  • $\begingroup$ 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. $\endgroup$ – Astrid Dec 14 '18 at 8:24

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