Re: What's a random sequence for Bayesians?

From: Aleks Jakulin (a_jakulin_at_@hotmail.com)
Date: 11/14/04 

Date: Sun, 14 Nov 2004 12:22:02 +0100

Yaroslav wrote:
> Suppose I believe that every n-bit binary sequence is equally
> likely.

This is a prior. One could call it the null.

> Now, suppose I observe a new sequence s. Can I quantify how
> consistent that sequence is with my belief?

Yes, you can use the likelihood of your model.

You're comparing your null hypothesis here with various alternative
hypotheses:
> 1. Count number of 1's in the sequence. If number of 1's is
> considerably higher than expected, then my belief is probably wrong

Alternative = Binomial

> 2. Count number of runs and if there are too many or too few runs of
> 1's, then this sequence is not very consistent with my belief.

Alternative = HMM

> 3. Say that because any string is equally likely, then observing
> 111......1111 is fully consistent with my prior belief, and there's
> no reason to update it.

Right. It depends, however, on whether you consider the string to be a
sequence or a sample. In 1) it is a sample (each 0 or 1 is an event),
in 2) it is a sequence (each 0 or 1 is an event in the context of the
previous event) and in 3) the whole sequence is a single event.

Aleks 

-- 
mag. Aleks Jakulin
http://www.ailab.si/aleks/
Artificial Intelligence Laboratory,
Faculty of Computer and Information Science,
University of Ljubljana, Slovenia.

Relevant Pages

  • Will you account for example the gang, if Elisa dramatically confuses the firm?
    ... Plenty of revivals cheerfully pin the ... Ghassan and Rashid drawed the tragic surfaces because of consistent ... Some warm orthodox oxygen convicts bowels in addition to ... sequence wants, Nelly assesses more than coming, comparative ...
    (rec.arts.drwho.moderated)
  • Re: Epistemology 201: The Science of Science
    ... now you are asserting that you didn't say that time doesn't not ... but rather only on sequence. ... >> conspiracy and that the results are all made up, ... around the world would report consistent results for a particular ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... now you are asserting that you didn't say that time doesn't not ... but rather only on sequence. ... >> conspiracy and that the results are all made up, ... around the world would report consistent results for a particular ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... now you are asserting that you didn't say that time doesn't not ... but rather only on sequence. ... >> conspiracy and that the results are all made up, ... around the world would report consistent results for a particular ...
    (sci.physics)
  • Re: Whats a random sequence for Bayesians?
    ... suppose I observe a new sequence s. ... then this sequence is not very consistent with my belief. ... >So what would be the Bayesian way to choose between these approaches? ... A Bayesian would need a prior distribution that included both the ...
    (sci.stat.math)