( ) ( ) ( NSC M )

Transcription

1 ( ) ( ) ( NSC M )

2 2 ( 1) Minitab SPlus ( 1):

3

4 4 2 (1980) ( 1952 ) (Significant difference (Two sample) (Change-point problem (1980) ( t-test) (Chi-square test)

5 5 ( 2 P ( ) P P- value

6 Literary style Stylometry Augustus de Morgan G. Udny Yule George Zipf (Pattern) Frederick Mosteller David Wallace (1984) (Bayesian techniques) (The Federalist Papers) Alexander Hamilton James Madison John Jay Hamilton Madison Masteller Wallace 55 Hamilton 90 1 Madison Shakespeare Bradley Efron Ronald Thisted C.B.Williams(1975) (Bacon) (Prose) (Verse)

7 7 Mendenhall B.J.R.Bailey(1990) (Function words or contextfree words) (Binomial distribution), (Articles) (Chi-square test) A.F.Bissell(1995) Weighted Cumulative Sums Weighted Variance Estimation 26 a the 2.2 : (Populations) (Two sample) ; Change-point problem (Time Series Analysis) (Discriminant Annlysis)

8 8 (Linear Discriminant function) (Quality Control) ( ) (Fixed Sample Size) David V. Hinkley Elizabeth A. Hinkley(1970) (Maximum likelihood estimate MLE) (Asymptotic distribution)

9 9 (Likelihood Ratio Tests) A. N. Pettitt(1980) (Conditional test) (Simulation) MLE K. J. Worsley (1983) (Cumulative Sum test CUSUM test) E.S. Page(1954) MLE H. Chernoff S. Zack(1964) 1 (Bayes test) (Critical value) (Power function) David V. Hinkley (1971) MLE S. Zacks (1991) B. E. Brodsky B. S. Darkhovsky (1993) 3.1 ( ) ( ) ( )

10 10 DBase IV 3.2 ( ) ( 3) ( ) % 1.6% ( ) 19.3%( ) ~ ~ ~ ~ ~1, ,001~1, ,201~1, ,401~1, ,601~1, ,

11 , 56.8% % z ( ) + = = +, n 1 = 80 n 2 p 1 = 40 p 2 P Η 0 : p 1 = p 2 V.S. Η 1: p1 > p2 P Η 0 : p 1 = p 2 V.S. Η 1: p1 p2 P ( Two-

12 12 sided test) Poem Index (Function Words)

13 (1980) ( ) ~ (8.03) (5.00) (28.51) (20.83) (7.54) 81~ (8.73) (6.34) (29.38) (23.29) (10.06) 1~ (8.25) (5.43) (28.79) (21.31) (8.35)

14 ( ) (1) % 3 65% z (

15 ) ( ) t C Index t : = = Value= Value=0.000

16 16 (2) t : 8.61 = = Value= Value=0.000 (3) t : = = Value= Value=

17 ~

18 Y Y ( Y n P$ ) χ ij j j = n P$ i = 1 j = 1 Y $ 1j + Y2j Pj =, j = 12,,..., n = 80, n = j j 2 = P P ~60 61~ ~ ~ ~ χ 2 =21.34 P ~60 61~ ~

19 19 1~40 41~ C Index : True Group Put into Group total Squared Distance between Group=

20 F F n1+ n2 p 1 nn 1 2 n n p n + n ( + 2) D = > F pn, n p ( ) n n 1 = 80 2 = 40 P=13 D= P K.J.Worsley 1983 CUSUM Likelihood Ratio Likelihood Ratio 0 CUSUM X i iid ( ) ~ B n, p i i, 0 p 1 i for i = 12,,..., 120 n i i i p i p H0: pi = p i = 12,,..., 120 v.s. H1: pi = { p i = 1,..., k i = k + 1,..., 120 p p m i i M N = = 120 i = i = 1 m n i i M N K K = = K i = 1 K i = 1 m n i i i = 1, 2,..., 120 CUSUM

21 21 Q K = M r M K N K σ 2 P M 2 N K 2 0 =, σ = P0 ( 1 P0 ) rk =, SK = rk( 1 rk) N N 2 QK Q 2 K k S K Pearson χ 2 ( ) 4.1 : Utility Function

22 22 7/ (1980)

23 23 ( ) ( ) ( ) 4.2 (Species Problem) (Capture-Recapture Model) (population) (1994)

24 24 ( ) : (1) : 1., (1980)," ",. 2. (1977)," ",. 3. (1983)," ",. 4. (1984)," ",. 5. (1994)," ",. 6. (David Steelman, 1994)," -- ",. (2) : 1.Bailey, B. J. R.(1990)"A Model for Function Word Counts", Applied Statistics, 39, pp Bissel, A. F.(1995)"Weighted Cumulative Sums for Text Analysis using Word Counts", Journal of Royal Statistics, Series A, 158, pp Brodsky, B. E. and Darkhovsky, B. S.(1993)"Nonparameteric Methods in Changepoint problems", Academic Publishers. 4.Chernoff, H. and Zacks, S.(1964)"Estimating the current mean of a Normal Distribution which is Subject to Changes in Times", Annals of Mathematical Statistics, 35, pp Efron, B. and Thisted, R.(1976)"Estimating the Number of Unseen Species: How many Words did Shakespeare Know?", Biometrika, 63, pp Hinkley, D. V. and Hinkley, E. A.(1970)"Inference about the Change-point in a Sequence of Binomial Variables", Biometrika, 57, pp Hinkley, D. V.(1971)"Inference about the Change-point from Cumulative Sum Tests", Biometrika, 58, pp

25 8.Holmes, D.(1995)"Who was the Author?", Journal of Royal Statistics News, Vol. 23, No. 2, pp Horvath, L.(1989)"The Limit Distributions of Likelihood Ratio and Cumulative Sum Tests for a Change in a Binomial Probability", Journal of Multivariate Analysis, 31, pp Karlgren, B. (1952), "New Excursions in Chinese Grammar", in Bulletin of the museum of Far Eastern Antiquities (Stockholm), No. 24, pp Mosteller F. and Wallace D.L.(1984),"Applied Bayesian and Classical Inferrence:The Case of The Federalist Papers",Springer-Verlag. 12.Pettitt A. N.(1979)"A Nonparametric Approach to the Change-point Problem", Applied Statistics, 28, pp Pettitt A. N.(1980)"A Simple Cumulative Sum Type Statistic for the Change-point Problem with Zero-one Observations", Biometrika,67,pp Smith, A.F.M.(1975)"A Bayesian Approach to Inference about a Change-point in a Sequence of Random Variables", Biometrika,62,pp Thisted,R.and Efron, B.(1987)"Did Shakespeare Write a Newly-discovered Poem?", Biometrika, 74, pp Sichel, H.S.(1986)"Word Frequency Distributions and Type-token Characteristics", The Mathematical Scientist, 11, pp Williams, C. B.(1975)"Mendenhall's Studies of Word-length Distribution in the Works of Shakespeare and Bacon", Biometrika,62,pp Worsley, K.J.(1983)"The Power of Likelihood Ratio and Cumulative Sum Tests for a Change in a Binomial Probability", Biometrika,70,pp Yue, C.J.(1994)"Bayesian Sequential Tests for Comparing the Species Richness of Two Populations", Ph.D. thesis, Univ. of Wisconsin-Madison. 20.Zacks, S.(1991)"Detection and Change-point Problems", Handbook of Sequential Analysis, Mercel and Dekker.