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What is observed and what is observable? I found this two word frequently in the context of random variable and realization of random variable.

What is the difference between observed and observable?

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I think it is as simple as the grammatical form implies.

Observable is something that can in principle be observed (a variable or a process that is generating outcomes).
Observed is something that has been observed on a particular occasion (a realization of a variable, an outcome of a process).

For example, if Ann and Tom are rolling dice in another room (you do not see them) and they only report to you the sum of the two scores after each roll, there are two unobservable variables (the individual scores) and one observable variable (the sum); you have a number of observed outcomes (the ones Ann and Tom reported to you). If Ann and Tom are rolling dice right in front of you, all of these variables are observable, and all the outcomes are observed. If you have observed 10 rolls and then closed your eyes and missed one, this last one was unobserved.

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  • $\begingroup$ Is unobservable and nonobservable same ? $\endgroup$ – time Feb 21 '15 at 2:32
  • $\begingroup$ I guess so. Unobservable is the one I encounter much more frequently. $\endgroup$ – Richard Hardy Feb 21 '15 at 7:41
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For example rolling a dice result in an observable experiment and each outcome is an observed event.

Please refer to page 2 of Foundations of Probability in line 15-18. here is the link in google books: https://books.google.co.uk/books?id=U427dN6QLxwC&pg=PA2&dq=observable+experiment&hl=en&sa=X&ei=R2TnVK_8OpLW7Ab56oDYDA&ved=0CCsQ6AEwAg#v=onepage&q=observable%20and%20observed&f=false

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  • $\begingroup$ This is rather sparse & hard to interpret. Can you add more description to flesh it out a little? $\endgroup$ – gung Feb 20 '15 at 16:40
  • $\begingroup$ Contrary to the usage here, many texts and papers--including the one you use as a reference!--reserve the term "event" for measurable sets of outcomes. Phrases like "observable experiment" appear redundant: what would a "nonobservable experiment" be? $\endgroup$ – whuber Feb 20 '15 at 19:55

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