Science > Physics > Quantum Gravity 142.6: Nearest Neighbor and Conditional Statistics
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
20 May 2007 01:35:35 AM |
| Object: |
Quantum Gravity 142.6: Nearest Neighbor and Conditional Statistics |
From Osher Doctorow
Physicists who are tempted at first glance to reject the idea of
matrices and tensors as reflecting "nearest neighbors" in terms of
distances from a particular element to other elements of the matrix
(as discussed in previous parts of this Section) may be surprised to
learn that mathematical statisticians and applied statistical pattern
recognition/classification/learning researchers often make
considerable use of "nearest neighbor statistics" and one-step-at-a-
time Conditional Probability-Statistics models including Markov chains
which are in several ways closely related to Nearest Neighbor
Statistics.
I have explained relationships between Probable Influence/Causation
(PI), Conditional Probability, and Independent Probability/Statistics
in this and other sci.physics threads, but readers can learn more
about "Nearest Neighbor Statistics" from Wikipedia's "K-nearest
neigbor algorithm," or Philip M. Dixon's (Iowa State U.) "Nearest
neighbor methods," 20 Dec 2001, www.stat.iastat.edu/preprint/articles/2001-19.pdf,
26 pages.
Markov Chains are discussed in both Wolfram and Wikipedia and various
other places on the internet even without including arXiv and Front
for the Mathematics ArXiv. They are usually fairly well explained
and explored in third year probability courses for undergraduates (or
the third course in a sequence of such courses), and are heavily
studied by the Bayesian School or Bayesian Theory which is a major
branch of Mainsteam Statistics whose main tool is conditional
probability (look that up too on the internet). Their influence has
extended into quite a few sciences, engineering, artificial
intelligence, medicine, etc., including economics and physics.
Osher Doctorow
.
|
|
|
Related Articles |
Quantum Gravity 1427: Retyping: Nearest Neighbor Graphs and Matrices in Computers, Cryptography, Computational Complexity
Quantum Gravity 1427: Nearest Neighbor Graphs and Matrices in Computers, Cryptography, Computational Complexity
Vaccinate Thy Neighbor... a strategy that finds the individuals mostlikely...
The One and Only Quantum of Heat
Books on Quantum Mechanics for the Layperson?
Quantum Conflicts
Quantum Foam?
Quantum cryptography tackles video
| Quantum computing speed limits
believe in quantum pi
Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) Duals 9: Complex-Quaternion-Octonion-PI Coding of 1
Nonrenormalization vs Renormalization 17: Valuations, Adeles, Ideles, Dedekind Zeta Functions, Quantum Statistical Mechanics, Euler Characteristics, Unit Spheres
Understanding quantum mechnanics
Quantum Gravity Via Expansion-Contraction 26.0: Memory Via Volterra Integral, Integrodifferential, Convolution Equations
The Quantum Pyramid
|
|
|
