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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Schiffel, Jeffrey A" <jeffrey.a.schiffel@xxxxxxxxxx>
Date: Tue, 12 Feb 2008 13:41:14 -0600
Message-id: <ECF42862FCA16D41BFA98F8C45F0955402E27253@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
There are a number of tests, depending on the data you have and what you want to do.

For example you may wish to compare a sample to a hypothetical value, compare two unpaired sampled groups, compare two paired groups, or quantify whether two variables move together. There are a great number of possible tests, of which, for example, the t-test, Wilcoxon or Mann-Whitney tests, and chi square are common, since most data tends toward one of a relatively few possible distributions. Each has its use depending on what you suspect an underlying distribution may be, what data you have, and what degree of confidence you need.


Monte-Carlo analysis generates data thatg is expected to be similar to available experimental data. The artificially created data (or sets of generated data) should match the experimental data’s distribution, but with varying amounts of (usually normal, I think) white noise injected. This allows for measurement of the noise versus the information.


I don’t know much about Latin hypercubes, but I suspect the method is an experimental design like Latin squares, but for multi-dimensional data.

-- Jeff

From: Sharma, Ravi [mailto:Ravi.Sharma@xxxxxxxxxxx]
Sent: Tuesday, February 12, 2008 12:18 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Axiomatic ontology


How do we test for randomness, you described white noise, what are the techniques in Statistics (stochastic or indeterminate sense) and mathematics?

How does Monte Carlo or Latin Hypercube enter this determination, i.e. number of trials and distributions for them?




(Dr. Ravi Sharma) Senior Enterprise Architect

Vangent, Inc. Technology Excellence Center (TEC)

8618 Westwood Center Drive, Suite 310, Vienna VA 22182
(o) 703-827-0638, (c) 313-204-1740 www.vangent.com

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Schiffel, Jeffrey A
Sent: Tuesday, February 12, 2008 1:08 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Axiomatic ontology


A series of unfair coin tosses can easily be random. The distribution of the random variable will not be uniform (as is the case of a fair coin), but it may still be random. It is just that the probabilities must be described by a different distribution. Pink noise is a simple example, since the randomness compared to white noise is red-shifted.


-- Jeffrey Schiffel 


From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: Tuesday, February 12, 2008 11:28 AM
To: Barker, Sean (UK)
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Axiomatic ontology

At 10:14 AM +0000 2/12/08, Barker, Sean (UK) wrote:

Pat's claim "The definition of a random sequence is that no matter how
much of it you have, there is no way even in principle to compute any
information about the next item." is true only where you exclude
probabilistic estimates (which you might do depending on how you
interpret "information"). For example, if you encode the tosses of a
coin as a bit stream, as you continue to observe the bit stream, you
will be able to make increasing accurate estimates of the probability
that the next bit will be a 1. Given the additional knowledge that this
is the encoding of coin flips, you will also be able to estimate the

probability that it is a fair coin.


No, wait. A series of tosses of an unfair coin is not a random sequence. One gets randomness just when the actual probability of each toss being a head is 0.5 precisely.


What you say above is correct, of course, but it can be translated as: if a series of bits is not random, this can be detected with increasing accuracy as the series gets longer. Also, of course, if it is random, this can also be detected (if it were previously unknown), but that does not mean that any particular toss can be predicted.







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