ENTROPY LIMITED

            Providing Management, Engineering, and Statistical Services since 1973

ENTROPY MINIMAX MULTIVARIATE STATISTICAL ANALYSES    

Entropy Minimax was invented by R. Christensen in 1963.  Originally
conceived as an answer to the age-old philosophical problem of the
justification of inductive reasoning and as an explanation of the
evolution of languages, Entropy Minimax was almost immediately
applied to more "practical" problems such as seeking patterns
in large databases and development of statistical forecasting
models.
    

Examples of some of the problems addressed by entropy minimax include:    

  Estimating five-year survival likelihood for coronary artery disease patients
  Estimating response to chemotherapy in acute myelocytic leukemia
  Estimating response to chemotherapy in non-Hodgkin's lymphoma
  Differential diagnosis of diseases of the cervical spine
  Screening drugs for potential antineoplastic activity
  Differential diagnosis of heart diseases using ECG wave forms
  Assessing symptoms of pelvic surgery patients
  Analyzing out-patient clinic use/overuse
  Developing screens for radiology
  Analyzing protein structure/function patterns in DNA coding of adenyl kinase
  Developing an understanding of molecular evolution    

  Detecting underground storage system leakage
  Modeling irreversible processes with incomplete information via hazard axes
  Modeling fracture of UO2 pellets subjected to large thermal gradients
  Modeling fission gas release in nuclear fuel rods under
    commercial operating conditions
  Modeling failure (rupture) of nuclear fuel rods under commercial
    operating conditions
  Modeling longitudinal distortion (bowing) of rods in nuclear
    fuel assembles during commercial reactor operations
  Modeling radial distortion (swelling) of nuclear fuel rods
    under simulated LOCA (Loss Of Coolant Accident) conditions    

  Forecasting annual precipitation in Northern California at 2 month
    and 6 month lead times
  Forecasting winter precipitation in Western Oregon at 7 month lead time
  Forecasting spring and winter precipitation in Eastern Washington
    at 6 and 7 month lead times
  Forecasting winter precipitation in Central Arizona at 2 month lead time
  Forecasting summer temperature in Central Arizona at 8 month lead time    

  Estimating probabilities using data reported in published literature
  Step sizing in numerical solution of differential equations
  Performing non-linear curve fitting
  Feature selection in complex situations
    

If you wish to learn more about entropy minimax, you may
consult the following references:    

  "Minimax Entropy and Learning by Diffusion,"
  J. Shah, IEEE Conf. on Computer Vision and Pattern Recognition, June 1998.    

  "Entropy Minimax Multivariate Statistical Modeling-II: Applications,"
  R. Christensen, Int. J. General Systems, 1986, Vol. 12, pp. 227-305.    

  "The minimum entropy principle is not the principle of minimum
  cross-entropy," R.A. Christensen, Int. J. General Systems, Vol. 12, 1986,
  pp. 401-404.    

  "Entropy Minimax Multivariate Statistical Modeling-I: Theory,"
  R. Christensen, Int. J. General Systems, 1985, Vol. 11, pp. 231-277.    

  "Entropy Minimax," M. Singh (ed.), Encyclopedia of Systems and Control,
  Pergamon Press, Oxford, 1985, pp. 1473-1479.    

  "Entropy Minimax Expansions for Waveform Analysis," R. Christensen,
  Pattern Recognition, 1979, Vol. 11, pp. 41-49.    

  "Molecular Evolution as a Process of Message Refinement," R. Christensen, T.
  Reichert and J. Yu, Journal of Molecular Evolution, 1976, Vol. 8, pp. 41-49.    

  "Unit Measure Violations in Pattern Recognition: Ambiguity and Irrelevancy,"
  R. Christensen and T. Reichert, Pattern Recognition, 1976, Vol. 8,
  pp. 239-245.    

  "Crossvalidation: Minimizing the Entropy of the Future," R. Christensen,
  Inform. Proc. Letters, 1975, Vol. 4, pp. 73-76.    

  "Entropy Minimax, a Non-Bayesian Approach to Probability Estimation
  from Empirical Data," R. Christensen, Proc. of the 1973 Intl. Conf. on
  Cybernetics and Society, IEEE Systems, Man and Cybernetics Society,
  73 CHO 799-7-SMC, 1973, pp. 321-325.    

  "Entropy minimax processing of incomplete data sets," R.A. Christensen,
  Proc. of the 1973 Intl. Conf. on Cybernetics and Society, IEEE 73 CHO
  799-7-SMC, 1973, pp. 326-327.    

  "A Pattern Discovery Program for Analyzing Qualitative and Quantitative
  Data," R. Christensen, Behavioral Science, 1968, Vol. 13, pp. 423-424.    

  "Induction and the Evolution of Language," R. Christensen, Physics Dept.,
  Univ. of Calif., Berkeley, 1963 [appears in Entropy Minimax Sourcebook,
  Vol. 2: Philosophical Origins, ISBN 0-938876-04-X, 1980, pp. 121-155].
    

If you wish more information on Entropy Limited's multivariate statistical
analysis services, contact:
  
Entropy Limited, South Great Road, Lincoln, MA 01773
Attn: Customer Service
Voice: 781/259-8901
Fax:   781/259-1255
Email: EntropyLimited@worldnet.att.net