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Volumn 205, Issue 1-4, 2005, Pages 207-214

Some implications of renormalization group theoretical ideas to statistics

Author keywords

Data analysis; Renormalization; Statistics

Indexed keywords

ALGORITHMS; DATA MINING; DATA REDUCTION; DIFFERENTIAL EQUATIONS; LEARNING SYSTEMS; PATTERN RECOGNITION; PERTURBATION TECHNIQUES; POPULATION STATISTICS; STATISTICS;

EID: 19944395196     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.02.001     Document Type: Article
Times cited : (2)

References (27)
  • 1
    • 0001805648 scopus 로고
    • Scaling, universality and renormalization group theory
    • Springer, Berlin
    • e.g. M.E. Fisher, Scaling, Universality and Renormalization Group Theory, Lecture Notes in Physics, vol. 186, Springer, Berlin, 1986
    • (1986) Lecture Notes in Physics , vol.186
    • Fisher, M.E.1
  • 6
    • 19944400206 scopus 로고    scopus 로고
    • note
    • This point of view including the idea of pursuit of stability was presented in the Cherry Bud Workshop at Yokohama held on March 2004; the paper is an outgrowth of the workshop presentation.
  • 9
    • 32144435012 scopus 로고    scopus 로고
    • N.S. Namachchivaya, Y.K. Lin (Eds.) Kluwer Academic Publishers
    • See, also L. Arnold, in: N.S. Namachchivaya, Y.K. Lin (Eds.), IUTAM on Nonlinear Stochastic Dynamics, Kluwer Academic Publishers, 2003, 5.
    • (2003) IUTAM on Nonlinear Stochastic Dynamics , pp. 5
    • Arnold, L.1
  • 12
    • 19944420227 scopus 로고    scopus 로고
    • note
    • This is only formal. 〈 f 〉 A may not even be continuous, and the reduced equation may not have any solution in some cases. The meaning of the approximation of the true solution x (t) in terms of A (t) is also quite delicate. Mathematically, we expect the modulus of the discrepancy integrated over [ 0, t / ε ] converges to zero as ε → 0
  • 13
    • 19944392036 scopus 로고    scopus 로고
    • note
    • The interpretation of this stochastic equation is delicate. Our interpretation (conjecture) is, under the condition that the averaged equation (2.7) is well behaved, that ∫ d t (x ̇ - 〈 f 〉) 2 / 2 ε b (A) is the rate function for the large deviation of the true solution from, A (t). That is, we interpret the Langevin equation (2.11) as a shorthand notation of the large deviation, principle
  • 17
    • 0001813888 scopus 로고
    • An invariance principle for certain probability limit theorems
    • M.D. Donsker An invariance principle for certain probability limit theorems Mem. Am. Math. Soc. 6 1951
    • (1951) Mem. Am. Math. Soc. , Issue.6
    • Donsker, M.D.1
  • 21
    • 19944379907 scopus 로고    scopus 로고
    • note
    • This statement is equivalent to asserting that probability theory is used to describe the possible world consistent with the given empirical data, because objective probability must be consistent with empirical frequencies. One might say that Bayesian or subjective interpretation of probability is possible and free from frequencies, so the above assertion is incomplete.
  • 22
    • 19944368517 scopus 로고    scopus 로고
    • note
    • Here, the reader may wonder why we use only the inequality relations instead of more quantitative concepts such as distances to describe dissimilarities. It is our general belief that converting the dissimilarity information in terms of qualitative inequalities makes the analysis method much more robust against corrupted and/or missing data. Thus, our proposal is: converting all the quantitative data into a set of qualitative relations that could recover the quantitative relations if the original data is quantitative must be a general strategy in data analysis.
  • 23
    • 19944370211 scopus 로고    scopus 로고
    • note
    • We know that the requirement is enough to recover a geometrical object if the number of points in the object is not too small (e.g., not less than 20).
  • 27
    • 85039094755 scopus 로고    scopus 로고
    • Advance Access published on February 22 doi:10.1093/bioinformatics/ bti067
    • Y.-h. Taguchi, Y. Oono, Bioinformatics, Advance Access published on February 22, 2005; doi:10.1093/bioinformatics/ bti067.
    • (2005) Bioinformatics
    • Taguchi, Y.-H.1    Oono, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.