riddle@emory.UUCP (Larry Riddle) (01/22/86)
Thanks to all who responded to my request for references of "real-world"
applications of markov chains. Here is a summary:
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from bonnie!wjh
Markov chain analysis of a tennis game in Finite Markov Chains by
Kemeny & Snell
for continuous time Markov models in reliability theory,
"Probabilistic Reliability: An Engineering Approach" - Shooman, McGraw
Hill
"The Theory and Practice of Reliable System Design" - Siewiorek and Swarz,
Digital
"Reliability Analysis of some Fault Tolerant Computer Architectures" -
Osaki and Nishio, Springer Verlag
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from ulysses!unc!duke!jk
"Probability and Statistics with Computer Science Applications" -
Trivedi
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from bach.berkeley.edu!permutt
"Statistics of Extreme Values..." in Atmospheric Environment, v.19
no.7 (1985) for applications to air pollution
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from bellcore!dph
Harary, Frank and Lipstein, Benjamin, The Dynamics of Brand Loyalty: A
Markovian Approach, Operations Research, vol 10, pp.19-40
Longman, "Use of Markov chains in forecasting store choice", Mgt Sci,
v.16, p281-285
Maffei "Brand preferences and markov processes" Operations research,
v.8, p210-218
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from ucla-cs!trainor
I think you'll find the following book excellent for providing examples.
Lin, Cunshan, and Harbaugh, John W., Graphic Display of Two-and
Three-Dimensional Markov Computer Models in Geology, Van Nostrand
Reinhold, 1984.
They start in 1-d with markov chains to generate geological statifications
in the earth, then to 2-d to simulate patterns in sliced rock (like granite),
and then in 3-d for the shape of objects.
I knew little of Markov properties or probability before seeing the
book this summer. I should have a little paper and software within
a few months based on their stuff, but pushed to state-of-the-art in
computer graphics. The pictures in their book aren't that great.
The pictures generated with my software (in the context of ray tracing)
should be hot...
-Douglas
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Generation of Surface and Internal Texture from Two-and Three-Dimensional
Markov Processes
The mapping of two-dimensional texture onto the surfaces of geometric
objects is widely used in computer graphics to increase realism and
complexity of synthesized images, but these texture maps are often
difficult to generate and manipulate. In addition to the traditional
techniques of scanning-in and painting texture, we propose to generate
texture stochastically from the statistical properties derived from
small sample textures using Markov Processes. This framework seems
promising for the interactive design of texture by artists. This
technique may be extended to three dimensions for the generation of
internal texture or structure, where objects appear to be sculpted from
heterogeneous substances.
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some additional sources
Kalberg, Jarl and Saunders, Anthony, Markov Chains Approaches to the
Analysis of Payment Behavior of Retail Credit Customers, Financial
Management, summer 1983, pp5-14
Cyert, R.M. and Thompson, G.L., Selecting a Portfolio of Credit Risks
by Markov Chains, J. of Business 41(1968), pp39-46
Halina Frydman, Jarl Kallberg and Duen-Li Kao, Test the Adequacy of Markov
Chains and Mover-Stayer Models as Representations of Credit Behavior,
Operations Research 33,no.6 (Nov-Dec 1985) pp1203-1214
Andrew Marshall and Herbert Goldhamer, An Application of Markov Processes
to the Study of the Epidemiology of Mental Disease, J. Am. Stat. Assoc.
50 (1955), pp99-129.
Frank Harary, "A criterion for unanimity in French's Theory of Social
Power" in Studies in Social Power, Dorwin Cartwright (ed.)
Holgate, P. "The size of elephant herds", Math. Gaz. 51(1967) pp302-304
Karlin and McGregor, "On some stochastic models in genetics", in Stochastic
Models in Medicine and Biology, J. Gurland (ed.), Uni.of Wisc Press
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--
Larry Riddle
Emory University
Dept of Math and CS
Atlanta, Ga 30322
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