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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
Jeffrey
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?
Thanks.
Ravi
(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.
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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