Talk:Random sequence

Huh? Major error in first sentence.

A random sequence is an element of a measure space whose elements happen to be called sequences. It is not a usually sequence of random variables. The word random indicates that the sequence lives in some set of measure 1, with the precise measure 1 set often determined by context.

Is Chaitin-Kolmogorov randomness really different from statistical randomness?

I'm not sure about this statement. Really, if you look at the string created by the outcome of ALL coin tosses, and append the results of each new coin toss to this string, you'll find that there is no computer algorithm which significantly compresses this string: in other words, no computer program can predict the outcome of all the worlds coin tosses. Therefore coin tosses are random, in the Chaitin-Kolmogorov sense of randomness. Neptune235 20:03, 8 March 2007 (UTC)[reply]

The difference is that statistical measures don't tell you whether a particular sequence is random; they only tell you that with high probability a certain procedure will generate a random sequence. It is perfectly possible for a fair coin to flip an infinite sequence of zeros. CMummert · talk 03:48, 9 March 2007 (UTC)[reply]

I am confused. What is the difference between random vector and random sequence?

What do you mean by a "Random vector"? — Carl (CBM · talk) 01:22, 24 June 2007 (UTC)[reply]

Is Chaitin-Kolmogorov randomness really different from statistical randomness?

I think this is hard to handle correctly without simply constructing a random sequence. Basically, you do this.

Deduce the existence of a random sequence S using the axiom of choice.
Show that you can use a homomorphism from N -> NxN to produce a countable collection of such random sequences S_i
Each random variable X_i is really a function applied to S_i. It looks like this X_i = f(S_i).
Then you can talk about distributions and such by describing the functions f.

I think Kolmogorov randomness is not different from statistical randomness. If you do the preceeding, then S has Kolmogorov randomness, but each X_i has statistical randomness, which is (it seems) a special case of Kolmogorov randomness.

Randomness is not a thing that can be deduced after the fact with complete certainty. A sequence must be constructed as a random sequence, you can never look at a sequence and be certain that it is random. In the same way, you cannot examine a sequence to see that it is infinite. Any algorithm attempting to do so would never finish. You need to know the difference between finite and infinite sequences from the beginning, and use something like the axiom of infinity to generate the latter. Same with random sequences, but use the axiom of choice to generate them. —Preceding unsigned comment added by 205.228.53.13 (talk) 20:29, 23 January 2009 (UTC)[reply]

I believe a sequence can be Kolmogorov random without being statistically random. That basically says there are sequences that can't be compressed by a Turing machine but can be compressed by a Turing machine with a halting oracle. There is more info at algorithmically random sequence. 69.228.170.24 (talk) 00:12, 25 May 2010 (UTC)[reply]

Merge proposal

There was a merge proposal template (to algorithmically random sequence which I removed, as therre was no response. Looking at the "what links here", it seems that there are many articles for which this other article would not be a good target to link to. Melcombe (talk) 17:54, 12 February 2010 (UTC)[reply]

sequence and its randomness

This has been flagged among other troubled "articles on randomness".

Regarding the lead sentence, someone observes above that "A random sequence is an element of a measure space whose elements happen to be called sequences. It is not a usually sequence of random variables." Here is a related observation. Together with Stochastic process and Sequence, the lead seems to say that random sequence and discrete stochastic process are synonyms.

This article is really about its adjective, however; in noun form it is about randomness of sequences. In other words, it is about what distinguishes random sequences from other sequences and, in part, whether and how we can compute the distinction.

If the lead is a mistake, as our someone says, is it a tactical error or a mathematical blunder? Other "process" articles do waver on whether a process is an indexed collection of rather simple entities, say non-negative real random variables, or a single entity with more complex structure. A simple example of tactics in contrast to mathematics is whether zero is a natural number or N = {1, 2, 3, ...} Sometimes the answer is that some authors or teachers, some readers or students, handle it one way and some the other way. --P64 (talk) 22:21, 13 March 2010 (UTC)[reply]

I, I guess the random someone you mentioned, made fixes to it after this message. It still needs work, now that I have looked at it again, but a is not as bad as before. History2007 (talk) 03:19, 25 May 2010 (UTC)[reply]

Appropriateness of content

This article feels like a discussion on randomness rather than random sequences. Does anybody agree? — Preceding unsigned comment added by 70.91.187.165 (talk) 06:41, 2 June 2018 (UTC)[reply]