Successfully reported this slideshow.
Upcoming SlideShare
×

# RUTILEA社内勉強会第3回 「意外な統計」

132 views

Published on

RUTILEA社内で定期的に行っている勉強会の第3回です．

Published in: Science
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### RUTILEA社内勉強会第3回 「意外な統計」

1. 1. '¥EHt2¥Fn¥t, ¥ ¥ ¥ ¥¥I
2. 2. ' IIOutlinee. # l Z s c o r e v i a robust s t a t i s t i c s # 2 Bayesian perspective
3. 3. # l Z s c o r e v i a robust s t a t i s t i c s Z z=¥¥Y# He,I f z > 3 , w e regard × i t a s a n outlier. But, this method could be unstable. |CA# t r u e observation i 6,27, 6.34, 6,25, 6,31, 6.28 mistake observation: 6,27, 6,34, 6.25, 63, I , 6.28 -
4. 4. ( l Non robust s t a t i s t i c s c a n n o t detect outliers' i n the c a s e of s m a l l samples." Actuall, m e a n ( x ) = T I L X = 17.65 Std ( X ) = 2 5 . 4 1 Z = - 0 . 4 5 , - 0 . 4 5 , - 0 . 4 5 , # - 0 , 4 5 W e w i l l modify this conventional s t a t i s t i c s with robust s t a t i s t i c s . m e a n → median S td → median absolute deviation (MAD)
5. 5. median (X) 6. 2 5 I 6.27 E # E b. 3 4 E 63,10 stable e s t i m a t o r M A D (X) = 1.48 med: ahl X i - m e d i a n 1411 = 0 , 0 4 4 (true Std i s 0.035) stable e s t i m a t o r Robust z s c o r e - 0 . 2 2 E 1,35 E - O . 6 7 E / 2 7 7, 5 E O, O
6. 6. Discussion a n d Conclusion * I n the c a s e of small dataset, normal s t a t i s t i c s i s affected by outliers to o heavily. * The influence could be asseseid by the influence analysis. Ref, M i a hubert, et.cl. 2017.
7. 7. # 2 Bayesian perspective t a t t e r . 45¥'T¥¥.fi#fiEiEHILf.. Stage 2 n A ' ' v e E.th k £ 4 . . . i n ¥.it#finIttFaIEiEHnT.aeti's. 71"'. I ' -43k\$'" X":b#A.Effi I k 3 prob, = 99 % 71"i t " t ' s " H D " A" : 2 ¥ . . e ¥ k # At k a prob.: 9 9 % 2 -'it. tat's t i t h e " K c i n a FIFE¥42" X " i z " c-2;D'.
8. 8. PCII.fi#4E/f'EtET's't't) 9 9 % 0.1% PEET'¥4± HE.EE#st4fPCtnEtEeB4IlEfEstI)PCEaf'¥-41) = I n = L PGHEF.IM#tI) PCA:.AE#EE4E)tP(A:it2u,fEtEf'EHI) 0.1%4994 99.9% × 0.1% (P(¥±ft¥t±) = 0.1%533.) ¥.tt#atn3eg.gy. P = - = 9,016% 1. 098% YE.f.fyge.nl?l?
9. 9. 7.tt#AaFEtEnh5I- TEeiIiaETFieII'Its Tn.'F¥¥ 99% a.i÷÷÷±÷ ÷÷÷÷÷÷÷÷ ÷÷.".IE?::EEimiaT3 p i ¥ % , g = n 9 . 9 -I x 99 t - 9 9 . 9 × 3 0 = § = 0 . 3 % THE'En.:#oil %.ae#Ektinu2.tiEZniHaFEiA'EtEuE. # ¥ t.TT#a3FiFEEEth, 0.3%17.17
10. 10. M2"E¥# P P i . P H # P oP( Y i ) = )I Bayese update↳ → Planewyaj.pl#l0Po P(newYi) i ' t h ' ' EL'¥G h t t , Iri'LEE'¥44,8'" -44. F''- '7¥42#' ' I ¥7232 ¥EiEE¥* a 4 ¥ 4 2 - - ¥ 1 9 ' 'Ref. k¥2,Fife'¥Eif¥t4¥ I t
11. 11. Co h c l n s i o n B T ' t 2 " E-¥fi te c ' l Eat i n " . F i * I n Fife'¥5'' 4 2 ¥ t 3. A TEFiFEEL't ' I n Ea u EE.In i.FEEt . T '42" EL#h s 'iff'IA. A F K h ta 3 F'' - '7 t i if I ' I I 'Est's ¥'t#GET 5¥ o r YET'¥'t'Ite I F E u n 3.