메뉴 건너뛰기




Volumn 34, Issue 1, 2006, Pages 42-77

Extended statistical modeling under symmetry; the link toward quantum mechanics

Author keywords

Born's formula; Complementarity; Complete sufficient statistics; Gleason's theorem; Group representation; Hilbert space; Model reduction; Quantum mechanics; Quantum theory; Symmetry; Transition probability

Indexed keywords


EID: 33744811702     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000868     Document Type: Article
Times cited : (6)

References (63)
  • 1
    • 49549134109 scopus 로고
    • Nonrelativistic quantum mechanics as a noncommutative Markov process
    • MR0484170
    • ACCARDI, L. (1976). Nonrelativistic quantum mechanics as a noncommutative Markov process. Advances in Math. 20 329-366. MR0484170
    • (1976) Advances in Math. , vol.20 , pp. 329-366
    • Accardi, L.1
  • 2
    • 33744787294 scopus 로고    scopus 로고
    • ACCARDI, L. and HEYDE, C. C., eds. Springer, New York. MR1632689
    • ACCARDI, L. and HEYDE, C. C., eds. (1998). Probability Towards 2000. Lecture Notes in Statist. 128. Springer, New York. MR1632689
    • (1998) Probability Towards 2000. Lecture Notes in Statist. , vol.128
  • 3
    • 84858892335 scopus 로고    scopus 로고
    • Comment on "Simple counterexamples against the conditionality principle"
    • by I. S. Heiland [Amer. Statist. 49 (1995) 351-356]. MR1368487
    • AITKIN, M. (1996). Comment on "Simple counterexamples against the conditionality principle," by I. S. Heiland [Amer. Statist. 49 (1995) 351-356]. Amer. Statist. 50 384-385. MR1368487
    • (1996) Amer. Statist. , vol.50 , pp. 384-385
    • Aitkin, M.1
  • 4
    • 0002213302 scopus 로고
    • Strata for randomized experiments
    • MR1094275
    • BAILEY, R. A. (1991). Strata for randomized experiments (with discussion). J. Roy. Statist. Soc. Ser. B 53 27-78. MR1094275
    • (1991) J. Roy. Statist. Soc. Ser. B , vol.53 , pp. 27-78
    • Bailey, R.A.1
  • 5
    • 0009113102 scopus 로고
    • Diversity of evidence and Birnbaum's theorem
    • MR1363227
    • BARNDORFF-NIELSEN, O. E. (1995). Diversity of evidence and Birnbaum's theorem (with discussion). Scand. J. Statist. 22 513-522. MR1363227
    • (1995) Scand. J. Statist. , vol.22 , pp. 513-522
    • Barndorff-Nielsen, O.E.1
  • 6
    • 0034705250 scopus 로고    scopus 로고
    • Fisher information in quantum statistics
    • MR1768745
    • BARNDORFF-NIELSEN, O. E. and GILL, R. D. (2000). Fisher information in quantum statistics. J. Phys. A 33 4481-4490. MR1768745
    • (2000) J. Phys. A , vol.33 , pp. 4481-4490
    • Barndorff-Nielsen, O.E.1    Gill, R.D.2
  • 10
    • 0034552507 scopus 로고    scopus 로고
    • Quantum probabilities and paradoxes of the quantum century
    • MR 1805845
    • BELAVKIN, V. P. (2000). Quantum probabilities and paradoxes of the quantum century. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 577-610. MR 1805845
    • (2000) Infin. Dimens. Anal. Quantum Probab. Relat. Top. , vol.3 , pp. 577-610
    • Belavkin, V.P.1
  • 13
    • 35948974968 scopus 로고
    • A suggested interpretation of the quantum theory in terms of "hidden" variables. I
    • MR0046287
    • BOHM, D. (1952). A suggested interpretation of the quantum theory in terms of "hidden" variables. I. Phys. Rev. 85 166-179. MR0046287
    • (1952) Phys. Rev. , vol.85 , pp. 166-179
    • Bohm, D.1
  • 14
    • 11944267780 scopus 로고
    • Primary manifestation of symmetry. Origin of quantal indeterminacy
    • MR1328825
    • BOHR, A. and ULFBECK, O. (1995). Primary manifestation of symmetry. Origin of quantal indeterminacy. Rev. Modern Phys. 67 1-35. MR1328825
    • (1995) Rev. Modern Phys. , vol.67 , pp. 1-35
    • Bohr, A.1    Ulfbeck, O.2
  • 15
    • 0039075727 scopus 로고
    • Can quantum-mechanical description of physical reality be considered complete?
    • BOHR, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48 696-702.
    • (1935) Phys. Rev. , vol.48 , pp. 696-702
    • Bohr, N.1
  • 17
    • 0142188672 scopus 로고    scopus 로고
    • Quantum states and generalized observables: A simple proof of Gleason's theorem
    • MR2037239
    • BUSCH, P. (2003). Quantum states and generalized observables: A simple proof of Gleason's theorem. Phys. Rev. Lett. 91 120403. MR2037239
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 120403
    • Busch, P.1
  • 18
    • 1542380590 scopus 로고    scopus 로고
    • Gleason-type derivations of the quantum probability rule for generalized measurements
    • Available at arxiv.org/abs/quant-ph/0306179. MR2054121
    • CAVES, C. M., FUCHS, C. A., MANNE, K. K. and RENES, J. M. (2004). Gleason-type derivations of the quantum probability rule for generalized measurements. Found. Phys. 34 193-209. Available at arxiv.org/abs/quant-ph/ 0306179. MR2054121
    • (2004) Found. Phys. , vol.34 , pp. 193-209
    • Caves, C.M.1    Fuchs, C.A.2    Manne, K.K.3    Renes, J.M.4
  • 19
    • 0043027690 scopus 로고    scopus 로고
    • Quantum probabilities as Bayesian probabilities
    • Available at arxiv.org/abs/quant-ph/0106133
    • CAVES, C. M., FUCHS, C. A. and SCHACK, R. (2002). Quantum probabilities as Bayesian probabilities. Phys. Rev. A 65 022305. Available at arxiv.org/abs/quant-ph/0106133.
    • (2002) Phys. Rev. A , vol.65 , pp. 022305
    • Caves, C.M.1    Fuchs, C.A.2    Schack, R.3
  • 20
    • 35949022025 scopus 로고
    • The transactional interpretation of quantum mechanics
    • MR0854444
    • CRAMER, J. C. (1986). The transactional interpretation of quantum mechanics. Rev. Modern Phys. 58 647-687. MR0854444
    • (1986) Rev. Modern Phys. , vol.58 , pp. 647-687
    • Cramer, J.C.1
  • 21
    • 1542742382 scopus 로고    scopus 로고
    • Causal inference without counterfactuals
    • MR1803167
    • DAWID, A. P. (2000). Causal inference without counterfactuals (with discussion). J. Amer. Statist. Assoc. 95 407-448. MR1803167
    • (2000) J. Amer. Statist. Assoc. , vol.95 , pp. 407-448
    • Dawid, A.P.1
  • 22
    • 33746443314 scopus 로고    scopus 로고
    • Quantum theory of probability and decisions
    • MR1807058
    • DEUTSCH, D. (1999). Quantum theory of probability and decisions. Proc. Roy. Soc. Lond. Ser. A 455 3129-3197. MR1807058
    • (1999) Proc. Roy. Soc. Lond. Ser. A , vol.455 , pp. 3129-3197
    • Deutsch, D.1
  • 25
    • 36149025875 scopus 로고
    • "Relative state" formulation of quantum mechanics
    • MR0094159
    • EVERETT, H. III (1957). "Relative state" formulation of quantum mechanics. Rev. Mod. Phys. 29454-462. MR0094159
    • (1957) Rev. Mod. Phys. , vol.29 , pp. 454-462
    • Everett III, H.1
  • 28
    • 84967619569 scopus 로고    scopus 로고
    • On an argument of David Deutsch
    • (M. Schürmann and U. Franz, eds.). World Scientific, Singapore
    • GILL, R. D. (2005). On an argument of David Deutsch. In Quantum Probability and Infinite Dimensional Analysis (M. Schürmann and U. Franz, eds.) 277-292. World Scientific, Singapore.
    • (2005) Quantum Probability and Infinite Dimensional Analysis , pp. 277-292
    • Gill, R.D.1
  • 29
    • 0035528171 scopus 로고    scopus 로고
    • Causal inference for complex longitudinal data
    • MR1891746
    • GILL, R. D. and ROBINS, J. M. (2001). Causal inference for complex longitudinal data. Ann. Statist. 29 1785-1811. MR1891746
    • (2001) Ann. Statist. , vol.29 , pp. 1785-1811
    • Gill, R.D.1    Robins, J.M.2
  • 30
    • 0000278073 scopus 로고
    • Measures on the closed subspaces of a Hilbert space
    • MR0096113
    • GLEASON, A. (1957). Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6 885-893. MR0096113
    • (1957) J. Math. Mech. , vol.6 , pp. 885-893
    • Gleason, A.1
  • 33
    • 84858889850 scopus 로고    scopus 로고
    • Discussion of "What is a statistical model?" by P. McCullagh
    • MR 1936320
    • HELLAND, I. S. (2002). Discussion of "What is a statistical model?" by P. McCullagh. Ann. Statist. 30 1286-1289. MR 1936320
    • (2002) Ann. Statist. , vol.30 , pp. 1286-1289
    • Helland, I.S.1
  • 34
    • 10244263650 scopus 로고    scopus 로고
    • Statistical inference under symmetry
    • HELLAND, I. S. (2004). Statistical inference under symmetry. Internat. Statist. Rev. 72 409-422.
    • (2004) Internat. Statist. Rev. , vol.72 , pp. 409-422
    • Helland, I.S.1
  • 35
    • 78751697972 scopus 로고    scopus 로고
    • Quantum theory as a statistical theory under symmetry
    • (A. Khrennikov, ed.). Amer. Inst. Physics, Melville. NY. Revised version available at arxiv.org/abs/quant-ph/0411174
    • HELLAND, I. S. (2005). Quantum theory as a statistical theory under symmetry. In Foundations of Probability and Physics 3 (A. Khrennikov, ed.) 127-149. Amer. Inst. Physics, Melville. NY. Revised version available at arxiv.org/abs/quant-ph/0411174.
    • (2005) Foundations of Probability and Physics , vol.3 , pp. 127-149
    • Helland, I.S.1
  • 39
  • 41
    • 0004047518 scopus 로고    scopus 로고
    • Oxford Univ. Press, New York. MR1419991
    • LAURITZEN, S. (1996). Graphical Models. Oxford Univ. Press, New York. MR1419991
    • (1996) Graphical Models
    • Lauritzen, S.1
  • 43
    • 84972541088 scopus 로고
    • Quantum statistical inference
    • MR1250150
    • MALLEY, J. D. and HORNSTEIN, J. (1993). Quantum statistical inference. Statist. Sci. 8 433-457. MR1250150
    • (1993) Statist. Sci. , vol.8 , pp. 433-457
    • Malley, J.D.1    Hornstein, J.2
  • 44
    • 0042788746 scopus 로고    scopus 로고
    • What is a statistical model?
    • MR1936320
    • MCCULLAGH, P. (2002). What is a statistical model? (with discussion). Ann. Statist. 30 1225-1310. MR1936320
    • (2002) Ann. Statist. , vol.30 , pp. 1225-1310
    • McCullagh, P.1
  • 46
    • 0004226939 scopus 로고
    • Van Nostrand, Princeton, NJ. MR0175995
    • NACHBIN, L. (1965). The Haar Integral. Van Nostrand, Princeton, NJ. MR0175995
    • (1965) The Haar Integral
    • Nachbin, L.1
  • 48
    • 0001058698 scopus 로고
    • On the application of probability theory to agricultural experiments. Essay on principles
    • Section 9
    • NEYMAN, J. (1923). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Ann. Agricultural Sciences 10 1-51.
    • (1923) Ann. Agricultural Sciences , vol.10 , pp. 1-51
    • Neyman, J.1
  • 49
    • 84972526326 scopus 로고
    • Translated MR1092986
    • [Translated in Statist. Sci. 5 (1990) 465-472]. MR1092986
    • (1990) Statist. Sci. , vol.5 , pp. 465-472
  • 51
    • 0004213845 scopus 로고    scopus 로고
    • Cambridge Univ. Press. MR1744773
    • PEARL, J. (2000). Causality. Cambridge Univ. Press. MR1744773
    • (2000) Causality
    • Pearl, J.1
  • 52
    • 0039762121 scopus 로고
    • The philosophy of Niels Bohr
    • (A. P. French and P. J. Kennedy, eds.). Harvard Univ. Press
    • PETERSEN, A. (1985). The philosophy of Niels Bohr. In Niels Bohr. A Centenary Volume (A. P. French and P. J. Kennedy, eds.) 299-310. Harvard Univ. Press.
    • (1985) Niels Bohr. A Centenary Volume , pp. 299-310
    • Petersen, A.1
  • 53
    • 46149139403 scopus 로고
    • A new approach to causal inference in mortality studies with a sustained exposure period - Application to control of the healthy worker survivor effect
    • MR0877758
    • ROBINS, J. (1986). A new approach to causal inference in mortality studies with a sustained exposure period - Application to control of the healthy worker survivor effect. Math. Modelling 7 1393-1512. MR0877758
    • (1986) Math. Modelling , vol.7 , pp. 1393-1512
    • Robins, J.1
  • 54
    • 0023592958 scopus 로고
    • Addendum to "A new approach to causal inference in mortality studies with a sustained exposure period - Application to control of the healthy worker survivor effect"
    • MR0922792
    • ROBINS, J. (1987). Addendum to "A new approach to causal inference in mortality studies with a sustained exposure period - Application to control of the healthy worker survivor effect." Comput. Math. Appl 14 923-945. MR0922792
    • (1987) Comput. Math. Appl , vol.14 , pp. 923-945
    • Robins, J.1
  • 55
    • 0002531157 scopus 로고
    • Bayesian inference for causal effects: The role of randomization
    • MR0472152
    • RUBIN, D. B. (1978). Bayesian inference for causal effects: The role of randomization. Ann. Statist. 6 34-58. MR0472152
    • (1978) Ann. Statist. , vol.6 , pp. 34-58
    • Rubin, D.B.1
  • 58
    • 84858905086 scopus 로고    scopus 로고
    • Seven principles of quantum mechanics
    • Växjö Univ. Press. MR2039739. Available at arxiv.org/abs/quant- ph/0212126
    • VOLOVICH, I. V. (2003). Seven principles of quantum mechanics. In Foundations of Probability and Physics 2 569-575. Växjö Univ. Press. MR2039739. Available at arxiv.org/abs/quant-ph/0212126.
    • (2003) Foundations of Probability and Physics , vol.2 , pp. 569-575
    • Volovich, I.V.1
  • 61
    • 0039466157 scopus 로고
    • Hilbert's sixth problem: Mathematical treatment of the axioms of physics
    • (F. E. Browder, ed.). Amer. Math. Soc., Providence, RI. MR0436800
    • WIGHTMAN, A. S. (1976). Hilbert's sixth problem: Mathematical treatment of the axioms of physics. In Mathematical Developments Arising from Hilbert Problems (F. E. Browder, ed.) 147-240. Amer. Math. Soc., Providence, RI. MR0436800
    • (1976) Mathematical Developments Arising from Hilbert Problems , pp. 147-240
    • Wightman, A.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.