Statistical mechanical approaches to models with many poorly known parameters

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 2 1, 2003, Pages

  Brown, Kevin S ^a   Sethna, James P ^a  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOCHEMISTRY; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; STATISTICAL METHODS; THERMODYNAMIC PROPERTIES;

BIOCHEMICAL REGULATION; STATISTICAL ENSEMBLE METHOD;

STATISTICAL MECHANICS;

ALGORITHM; ANIMAL; BIOCHEMISTRY; BIOLOGICAL MODEL; ENTROPY; MONTE CARLO METHOD; PROCEDURES; RAT; STATISTICAL MODEL; THEORETICAL MODEL; THERMODYNAMICS; TIME; TUMOR CELL LINE;

ALGORITHMS; ANIMALS; BIOCHEMISTRY; CELL LINE, TUMOR; ENTROPY; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; MONTE CARLO METHOD; RATS; THERMODYNAMICS; TIME FACTORS;

EID: 42749109054     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. K.C. Chen, A. Csikasz-Nagy, B. Gyorffy, J. Val, B. Novak, and J.J. Tyson, Mol. Biol. Cell 11, 369 (2000).
2. G. von Dassow, E. Meir, E. M. Munro, and G.M. Odell, Nature (London) 406, 188 (2000).
3. A.E. Smith, B.M. Slepchenko, J.C. Schaff, L.M. Loew, and I.G. Macara, Science 295, 488 (2002).
4. A. Hoffmann, A. Levchenko, M.L. Scott, and D. Baltimore, Science 298, 241 (2002).
5. We have tried to find the appropriate attribution for this quote but have been unsuccessful. Variants of the statement (differing in the number of parameters) have been attributed to C.F. Gauss, Niels Bohr, Lord Kelvin, Enrico Fermi, and Richard Feyman.
6. B. Novak, A. Csikasz-Nagy, B. Gyorffy, K. Chen, and J.J. Tyson, Biophys. Chem. 72, 185 (1998).
7. B. Schoeberl, C. Eichler-Jonsson, E.D. Gilles, and G. Müller, Nat. Biotechnol. 20, 370 (2002).
8. D. Battogtokh, D.K. Asch, M.E. Case, J. Arnold, and H.-B. Schüttler, Proc. Natl. Acad. Sci. U.S.A. 99, 16 904 (2002).
9. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
10. W.K. Hastings, Biometrika 57, 97, (1970).
11. K.S. Brown, C.C. Hill, G.A. Calero, K.H. Lee, J.P. Sethna, and R.A. Cerione (unpublished).
12. J.E. Bailey, Nat. Biotechnol. 19, 503 (2001).
13. A.B. Vojtek and C.J. Der, J. Biol. Chem. 273, 19925 (1998).
14. K. Schulz, K. Beven, and B. Huwe, Soil Sci. Soc. Am. J. 63, 1934 (1999).
15. B.W. Frost and M.J. Kishi, Prog. Oceanogr. 43, 317 (1999).
16. S. Doney, Global Biogeochem. Cycles 13, 705 (1999).
17. M.J.R. Fasham, H.W. Ducklow, and S.M. McKelvie, J. Mar. Res. 48, 591 (1990).
18. C.C. Hill and J.P. Sethna (unpublished).
19. In our real system we had no data for the PI3K loop and used methods described in this manuscript to determine if the loop should be included given the data. Thus, for the "perfect" model we generated no data for this loop in order to use the model as a test case for the model selection methods, as we used it as a test case for other methods. However, the perfect model is unenlightening in this respect because model selection methods in a sense tell us what we already know, i.e., that the loop was present when the data were generated and are hence necessary.
20. D.W. Marquardt, J. Soc. Ind. Appl. Math. 11, 431 (1963).
21. R. Fletcher, Practical Methods of Optimization, 2nd ed. (Wiley, Chichester, 1987).
22. Our methods identify typical, but not all, members of the ensemble. New data outside the error bars may, in principle, be consistent with the existing model but restrict the parameters to a formerly insignificant subregion.
23. k's are quadratic in the cost and can be integrated out of the partition function (see text); they play the role of uninteresting "nuisance parameters" in the Bayesian language.
24. I.T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).
25. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, New York, 1996).
26. M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999).
27. M.P. Nightingale and C.J. Umrigar (unpublished).
28. C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, NJ, 1956).
29. L. Wasserman, J. Math. Psychol. 44, 92 (2000).
30. S.J. Press, Bayesian Statistics: Principles, Models, and Applications (Wiley, New York, 1989).
31. R.E. Kass and A.E. Raftery, J. Am. Stat. Assoc. 90, 773 (1995).
32. G. Schwartz, Ann. Stat. 6, 461 (1978).
33. R.E. Kass and L. Wasserman, J. Am. Stat. Assoc. 90, 928, (1995).
34. H. Akaike, in 2nd International Symposium on Information Theory, edited by B.N. Petrov and F. Csaki (Akademia Kiado, Budapest, 1973), pp. 267-281.
35. H. Bozdogan, J. Math. Psychol. 44, 62 (2000).
36. R. McCulloch and P.E. Rossi, J. Econometr. 49, 141 (1991).
37. C.H. Bennett, J. Comput. Phys. 22, 245 (1976).