60 (W30)? 1. ( ) 2. ( ) web site URL ( :41 ) 1/ 77

Size: px
Start display at page:

Download "60 (W30)? 1. ( ) 2. ( ) web site URL ( :41 ) 1/ 77"

Transcription

1 60 (W30)? 1. ( ) kubo@ees.hokudai.ac.jp 2. ( ) web site URL ( :41 ) 1/ 77

2 ! : :? ( :41 ) 2/ 77

3 ( :41 ) 3/ 77!!

4 ( :41 ) 4/ 77 ( )!

5 ( :41 ) 5/ 77 : offset : :???

6 ( :41 ) 6/ 77 GLM

7 ( :41 ) 7/ 77 : R OS free software S R

8 ( :41 ) 8/ 77

9 ( :41 ) 9/ 77

10 ( :41 ) 10/ 77

11 ( :41 ) 11/ 77

12 ( :41 ) 12/ 77

13 ( :41 ) 13/ 77

14 ( :41 ) 14/ 77

15 : : ( ) ( :41 ) 15/ 77

16 ( :41 ) 16/ 77 ( : offset

17 何でも割算! , 2, 3! x /x ( :41 ) 17/ 77

18 ? /? : ? ( ) ( :41 ) 18/ 77

19 ( :41 ) 19/ 77 : specific leaf area (SLA) : offset : N k :

20 ( :41 ) 20/ 77 (1) offset

21 ( :41 ) 21/ 77 :? x {0.1, 0.2,, 1.0} 10 glm(..., family = poisson)

22 ?!! x A = /! glm() offset ( :41 ) 22/ 77

23 ( :41 ) 23/ 77 vs plot(d$x, d$y / d$area) d$y/d$area d$x

24 GLM! family: poisson, link : "log" : y ~ x offset : log(area) z = a + b x + log(area) a, b λ log(λ) = z λ = exp(z) = exp(a + b x + log(area)) λ : ( :41 ) 24/ 77

25 ( :41 ) 25/ 77 (2)

26 ( :41 ) 26/ 77 (1 = ) seed size [ ] ( )

27 ( :41 ) 27/ 77 ( ) seed size seed size 1. ( 4 ) 2. ; {0, 1} 3. ( or or & )

28 ( :41 ) 28/ 77? 1 / / 200! seed size? 1? (? )

29 ( :41 ) 29/ 77 R glm() : seed size (x) or q q = exp( (a + bx)) (logistic ) a b R glm() ( )

30 ( :41 ) 30/ 77 (binomial distribution)? y i {0, 1, 2,, N} (paramter: q, N) ( ) N q y (1 q) N y y Nq Nq(1 q) probability prob = 0.2 prob = 0.5 prob = : N y y

31 ( :41 ) 31/ 77 R glm() :? ( z): x link : logit family: binomial,

32 ( :41 ) 32/ 77 ( ) Ending 1.0 germination prob seed size!!? :!

33 ( :41 ) 33/ 77 (ESJ59 : glm()

34 : OK ( :41 ) 34/ 77

35 ( :41 ) 35/ 77 (Poisson distribution)? lambda = 1.4 y {0, 1, 2,, } (paramter: λ) λ y exp( λ) 0.0 lambda = y! probability λ λ lambda = : y

36 ( :41 ) 36/ glm() log-linear model

37 : > d2 <- read.csv("d2.csv") # > (ct2 <- xtabs(y ~ x + Spc, data = d2)) Spc x A B > plot(ct2, col = c("orange", "blue")) ct2 0 1 B Spc A ( :41 ) 37/ 77 x

38 GLM ( ) A ( ) y A,x Pois(λ A,x) log(λ A,x) = α A + β A x > summary(glm(y ~ x, data = d2[d2$spc == "A",], family = poisson) > # SpcA (......) Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 x ( :41 ) 38/ 77

39 ( :41 ) 39/ 77 GLM ( ) B y B,x Pois(λ B,x) log(λ B,x) = α B + β B x > summary(glm(y ~ x, data = d2[d2$spc == "B",], family = poisson) > # SpcB (......) Estimate Std. Error z value Pr(> z ) (Intercept) < 2e-16 x e-05?

40 ( :41 ) 40/ 77 log(λ A,x ) = x log(λ B,x ) = x lambda_a lambda_b x x AIC AIC λ A,x = α A + β A x 19.3 λ B,x = α B + β B x 17.1 λ A,x = α A 30.1 λ B,x = α B 32.4!

41 ( :41 ) 41/ 77 GLM GLM GLM: logit(q A,x) = a A + b A x 1 q A,x = 1 + exp[ (a A + b A x)] : log(λ A,x) = α A + β A x λ A,x = exp(α A + β A x) λ B,x = exp(α B + β B x) A? λ A,x λ A,x + λ B,x = = exp(α A + β A x) exp(α A + β A x) + exp(α B + β B x) exp[α B α A + (β B β A )x]

42 : GLM GLM GLM q A,x = exp[ (a A + b A x)] GLM ( ) λ A,x λ A,x + λ B,x = exp[α B α A + (β B β A )x] GLM GLM a A = α A α B b A = β A β B ( :41 ) 42/ 77

43 : GLM GLM GLM a A = = α A α B b A = = β A β B > GLM (A ) > glm(ct2 ~ c(0, 1), data = d2, family = binomial) (Intercept) c(0, 1) > GLM (A ) > glm(y ~ x, data = d2[d2$spc == "A",], family = poisson) (Intercept) x > GLM (B ) > glm(y ~ x, data = d2[d2$spc == "B",], family = poisson) (Intercept) x ( :41 ) 43/ 77

44 : GLM GLM GLM (A ) GLM (B ) lambda_a x lambda_* = lambda_b x 0 1 x = q_a 0 1 GLM (A + B ) 0 1 x ( :41 ) 44/ 77

45 ( :41 ) 45/ glm() GLM R package

46 : 2 3 Spc x A B C > plot(ct3, col = c("orange", "blue", "green")) ct3 0 1 C B Spc A ( :41 ) 46/ 77 x

47 ( :41 ) 47/ 77 GLM ( ) > glm(y ~ x * Spc, data = d3, family = poisson) (......) Coefficients: (Intercept) x SpcB SpcC x:spcb x:spcc GLM y A,x Pois(λ A,x ) log(λ A,x ) = α A + β A x α A = 5.66 α B = α C = β A = β B = β C =

48 GLM GLM lambda_a (A ) (B ) (C ) 0 1 x + + lambda_* lambda_b x = 0 1 x lambda_b = 0 1 x lambda_* 0 1 GLM 0 1 x ( :41 ) 48/ 77

49 ( :41 ) 49/ GLM GLMM!

50 : 3 9! Spc x A B C D E F G H I > plot(ct9, col = c( )) cts 0 1 IHG F E D C Spc B A ( :41 ) 50/ 77 x

51 GLM ( ) > ct9 Spc x A B C D E F G H I > summary(glm(y ~ x * Spc, data = d9, family = poisson)) (Intercept) x SpcB SpcC SpcD SpcE SpcF SpcG SpcH SpcI x:spcb x:spcc x:spcd x:spce x:spcf x:spcg x:spch x:spci H! ( :41 ) 51/ 77

52 ( :41 ) 52/ 77 glm() GLMM!??! Spc?: 9 Spc ( )

53 ( :41 ) 53/ 77 σ best GLMM > (fit.glmm <- glmmml(y ~ x, data = d9, cluster = Spc, family = poisson)) ( ) > fit.glmm$posterior.modes [1] [6] individual small posterior prior σ large σ

54 ( ) データ ( 応答変数 ) 各個体の種子数 Y[i] 個 ポアソン分布平均 lambda[i] 全個体共通 a0 無情報事前分布 b0 データ ( 説明変数 ) X[i] 傾きの差 b[spc[i]] 切片の差 a[spc[i]] 階層事前分布 s[1] 切片差のばらつき 階層事前分布 s[2] 傾き差のばらつき 無情報事前分布 ( 超事前分布 ) WinBUGS (MCMC ) BUGS WinBUGS R ( :41 ) 54/ 77

55 ( :41 ) 55/ 77 ( )??

56 ( :41 ) 56/ 77 : λ = 30 λ = = ! p = {0.60, 0.40}

57 ( :41 ) 57/ 77 : λ = 30 λ = 20 λ = = = ! p = {0.50, 0.33, 0.17}

58 ( :41 ) 58/ 77 (Gamma distribution)? y 0 (paramter: r, s) p(y s, r) = rs Γ(s) ys 1 exp( ry) s/r s/r 2

59 : 1 : (0.6, 0.4) (0.325, 0.675) : (0.5, 0.3, 0.1) (0.28, 0.54, 0.18) 0.6 a = 12, b = 8 a = 6, b = 4 a = 1.2, b = 0.8 a = 0.6, b = y y y y ( :41 ) 59/ 77

60 OK? = = ? p = {0.60, 0.40} ( :41 ) 60/ 77

61 OK? = = = , 0.286? p = {0.50, 0.33, 0.17} ( :41 ) 61/ 77

62 ( :41 ) 62/ 77?? OK : R glm(y ~ x, family = Gamma) ( ): θ = 1/r =

63 > ALake <- ArcticLake > ALake$Y <- DR_data(ALake[,1:3]) > DirichReg(Y ~ depth + I(depth^2), ALake) Coefficients for variable no. 1: sand (Intercept) depth I(depth^2) Coefficients for variable no. 2: silt (Intercept) depth I(depth^2) Coefficients for variable no. 3: clay (Intercept) depth I(depth^2) ( :41 ) 63/ 77 R library(dirichletreg) package GLM

64 ( :41 ) 64/ 77 library(dirichletreg) random effects?

65 ( :41 ) 65/ 77 (ESJ57

66 ( :41 ) 66/ 77 : above ground mass Y 重量 y x below ground mass X

67 ( :41 ) 67/ 77 : q w 観測できない世界観測できる世界 parameter process observation 無情報事前分布 w q 1- q y x Y X 地上部地下部 階層的事前分布 個体差 測定時の誤差 重量 y x

68 BUGS code (process ) for (i in 1:N) { Y[i] ~ dnorm(y[i], Tau.err) # X[i] ~ dnorm(x[i], Tau.err) # y[i] <- q[i] * w[i] x[i] <- (1 - q[i]) * w[i] # logit(q[i]) <- a + b * log.w[i] + re[i] w[i] <- exp(log.w[i]) # log.w[i] + log.w[i] ~ dnorm(0, Tau.noninformative) #!! ( ) ( :41 ) 68/ 77

69 ( :41 ) 69/ 77 : MCMC 1. BUGS code (model1.txt) 2. R (runbus1.r) 3. R runbus1.r (source("runbugs1.r")) 4. R library(r2winbugs) WinBUGS 5. WinBUGS Markov chain Monte Carlo (MCMC) 6. R

70 ( :41 ) 70/ 77 : w b MCMC

71 ( :41 ) 71/ 77 above ground mass Y 重量 y x below ground mass X (median) (95% CI)

72 ( :41 ) 72/ 77

73 ( :41 ) 73/ 77 C-N (coverage) GIS

74 ( :41 ) 74/ 77 : offset : :??

75 ( :41 ) 75/ 77

76 60 (W30)? 1. ( ) kubo@ees.hokudai.ac.jp 2. ( ) web site URL ( :41 ) 76/ 77

77 ( :41 ) 77/ 77

kubostat2017j p.2 CSV CSV (!) d2.csv d2.csv,, 286,0,A 85,0,B 378,1,A 148,1,B ( :27 ) 10/ 51 kubostat2017j (http://goo.gl/76c4i

kubostat2017j p.2 CSV CSV (!) d2.csv d2.csv,, 286,0,A 85,0,B 378,1,A 148,1,B ( :27 ) 10/ 51 kubostat2017j (http://goo.gl/76c4i kubostat2017j p.1 2017 (j) Categorical Data Analsis kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2017 11 15 : 2017 11 08 17:11 kubostat2017j (http://goo.gl/76c4i) 2017 (j) 2017 11 15 1 / 63 A B C D E F G

More information

一般化線形 (混合) モデル (2) - ロジスティック回帰と GLMM

一般化線形 (混合) モデル (2) - ロジスティック回帰と GLMM .. ( ) (2) GLMM kubo@ees.hokudai.ac.jp I http://goo.gl/rrhzey 2013 08 27 : 2013 08 27 08:29 kubostat2013ou2 (http://goo.gl/rrhzey) ( ) (2) 2013 08 27 1 / 74 I.1 N k.2 binomial distribution logit link function.3.4!

More information

12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? ( :51 ) 2/ 71

12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? ( :51 ) 2/ 71 2010-12-02 (2010 12 02 10 :51 ) 1/ 71 GCOE 2010-12-02 WinBUGS kubo@ees.hokudai.ac.jp http://goo.gl/bukrb 12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? 2010-12-02 (2010 12

More information

kubostat2015e p.2 how to specify Poisson regression model, a GLM GLM how to specify model, a GLM GLM logistic probability distribution Poisson distrib

kubostat2015e p.2 how to specify Poisson regression model, a GLM GLM how to specify model, a GLM GLM logistic probability distribution Poisson distrib kubostat2015e p.1 I 2015 (e) GLM kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2015 07 22 2015 07 21 16:26 kubostat2015e (http://goo.gl/76c4i) 2015 (e) 2015 07 22 1 / 42 1 N k 2 binomial distribution logit

More information

kubostat2017e p.1 I 2017 (e) GLM logistic regression : : :02 1 N y count data or

kubostat2017e p.1 I 2017 (e) GLM logistic regression : : :02 1 N y count data or kubostat207e p. I 207 (e) GLM kubo@ees.hokudai.ac.jp https://goo.gl/z9ycjy 207 4 207 6:02 N y 2 binomial distribution logit link function 3 4! offset kubostat207e (https://goo.gl/z9ycjy) 207 (e) 207 4

More information

/ 55 2 : : (GLM) 1. 1/23 ( )? GLM? (GLM ) 2.! 1/25 ( ) ffset (GLM )

/ 55 2 : : (GLM) 1. 1/23 ( )? GLM? (GLM ) 2.! 1/25 ( ) ffset (GLM ) 2012 01 25 1/ 55 ( II) : (2012 1 ) 2 2 (GLM) 2012 01 25! kub@ees.hkudai.ac.jp http://g.gl/76c4i 2012 01 25 2/ 55 2 : : (GLM) 1. 1/23 ( )? GLM? (GLM ) 2.! 1/25 ( ) ffset (GLM ) 2012 01 25 3/ 55 1. : 2.

More information

/ 60 : 1. GLM? 2. A: (pwer functin) x y?

/ 60 : 1. GLM? 2. A: (pwer functin) x y? 2009-03-17 1/ 60 (2009-03-17) GLM 1. GLM :, link,, deviance (20 ) 2. GLM : (60 ) 3. GLM ( ): ffset (40 ) http://hsh.ees.hkudai.ac.jp/ kub/ce/ecsj2009.html 2009-03-17 2/ 60 : 1. GLM? 2. A: (pwer functin)

More information

講義のーと : データ解析のための統計モデリング. 第3回

講義のーと :  データ解析のための統計モデリング. 第3回 Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20

More information

kubostat2017c p (c) Poisson regression, a generalized linear model (GLM) : :

kubostat2017c p (c) Poisson regression, a generalized linear model (GLM) : : kubostat2017c p.1 2017 (c), a generalized linear model (GLM) : kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2017 11 14 : 2017 11 07 15:43 kubostat2017c (http://goo.gl/76c4i) 2017 (c) 2017 11 14 1 / 47 agenda

More information

kubo2015ngt6 p.2 ( ( (MLE 8 y i L(q q log L(q q 0 ˆq log L(q / q = 0 q ˆq = = = * ˆq = 0.46 ( 8 y 0.46 y y y i kubo (ht

kubo2015ngt6 p.2 ( ( (MLE 8 y i L(q q log L(q q 0 ˆq log L(q / q = 0 q ˆq = = = * ˆq = 0.46 ( 8 y 0.46 y y y i kubo (ht kubo2015ngt6 p.1 2015 (6 MCMC kubo@ees.hokudai.ac.jp, @KuboBook http://goo.gl/m8hsbm 1 ( 2 3 4 5 JAGS : 2015 05 18 16:48 kubo (http://goo.gl/m8hsbm 2015 (6 1 / 70 kubo (http://goo.gl/m8hsbm 2015 (6 2 /

More information

k2 ( :35 ) ( k2) (GLM) web web 1 :

k2 ( :35 ) ( k2) (GLM) web   web   1 : 2012 11 01 k2 (2012-10-26 16:35 ) 1 6 2 (2012 11 01 k2) (GLM) kubo@ees.hokudai.ac.jp web http://goo.gl/wijx2 web http://goo.gl/ufq2 1 : 2 2 4 3 7 4 9 5 : 11 5.1................... 13 6 14 6.1......................

More information

kubostat7f p GLM! logistic regression as usual? N? GLM GLM doesn t work! GLM!! probabilit distribution binomial distribution : : β + β x i link functi

kubostat7f p GLM! logistic regression as usual? N? GLM GLM doesn t work! GLM!! probabilit distribution binomial distribution : : β + β x i link functi kubostat7f p statistaical models appeared in the class 7 (f) kubo@eeshokudaiacjp https://googl/z9cjy 7 : 7 : The development of linear models Hierarchical Baesian Model Be more flexible Generalized Linear

More information

講義のーと : データ解析のための統計モデリング. 第5回

講義のーと :  データ解析のための統計モデリング. 第5回 Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20

More information

kubo2017sep16a p.1 ( 1 ) : : :55 kubo ( ( 1 ) / 10

kubo2017sep16a p.1 ( 1 ) :   : :55 kubo (  ( 1 ) / 10 kubo2017sep16a p.1 ( 1 ) kubo@ees.hokudai.ac.jp 2017 09 16 : http://goo.gl/8je5wh : 2017 09 13 16:55 kubo (http://goo.gl/ufq2) ( 1 ) 2017 09 16 1 / 106 kubo (http://goo.gl/ufq2) ( 1 ) 2017 09 16 2 / 106

More information

kubostat1g p. MCMC binomial distribution q MCMC : i N i y i p(y i q = ( Ni y i q y i (1 q N i y i, q {y i } q likelihood q L(q {y i } = i=1 p(y i q 1

kubostat1g p. MCMC binomial distribution q MCMC : i N i y i p(y i q = ( Ni y i q y i (1 q N i y i, q {y i } q likelihood q L(q {y i } = i=1 p(y i q 1 kubostat1g p.1 1 (g Hierarchical Bayesian Model kubo@ees.hokudai.ac.jp http://goo.gl/7ci The development of linear models Hierarchical Bayesian Model Be more flexible Generalized Linear Mixed Model (GLMM

More information

/22 R MCMC R R MCMC? 3. Gibbs sampler : kubo/

/22 R MCMC R R MCMC? 3. Gibbs sampler :   kubo/ 2006-12-09 1/22 R MCMC R 1. 2. R MCMC? 3. Gibbs sampler : kubo@ees.hokudai.ac.jp http://hosho.ees.hokudai.ac.jp/ kubo/ 2006-12-09 2/22 : ( ) : : ( ) : (?) community ( ) 2006-12-09 3/22 :? 1. ( ) 2. ( )

More information

,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i

,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i Armitage.? SAS.2 µ, µ 2, µ 3 a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 µ, µ 2, µ 3 log a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 * 2 2. y t y y y Poisson y * ,, Poisson 3 3. t t y,, y n Nµ,

More information

/ *1 *1 c Mike Gonzalez, October 14, Wikimedia Commons.

/ *1 *1 c Mike Gonzalez, October 14, Wikimedia Commons. 2010 05 22 1/ 35 2010 2010 05 22 *1 kubo@ees.hokudai.ac.jp *1 c Mike Gonzalez, October 14, 2007. Wikimedia Commons. 2010 05 22 2/ 35 1. 2. 3. 2010 05 22 3/ 35 : 1.? 2. 2010 05 22 4/ 35 1. 2010 05 22 5/

More information

: Bradley-Terry Burczyk

: Bradley-Terry Burczyk 58 (W15) 2011 03 09 kubo@ees.hokudai.ac.jp http://goo.gl/edzle 2011 03 09 (2011 03 09 19 :32 ) : Bradley-Terry Burczyk ? ( ) 1999 2010 9 R : 7 (1) 8 7??! 15 http://www.atmarkit.co.jp/fcoding/articles/stat/07/stat07a.html

More information

: (GLMM) (pseudo replication) ( ) ( ) & Markov Chain Monte Carlo (MCMC)? /30

: (GLMM) (pseudo replication) ( ) ( ) & Markov Chain Monte Carlo (MCMC)? /30 PlotNet 6 ( ) 2006-01-19 TOEF(1998 2004), AM, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) 1. 2. - - : kubo@ees.hokudai.ac.jp http://hosho.ees.hokudai.ac.jp/ kubo/show/2006/plotnet/

More information

(2/24) : 1. R R R

(2/24) : 1. R R R R? http://hosho.ees.hokudai.ac.jp/ kubo/ce/2004/ : kubo@ees.hokudai.ac.jp (2/24) : 1. R 2. 3. R R (3/24)? 1. ( ) 2. ( I ) : (p ) : cf. (power) p? (4/24) p ( ) I p ( ) I? ( ) (5/24)? 0 2 4 6 8 A B A B (control)

More information

k3 ( :07 ) 2 (A) k = 1 (B) k = 7 y x x 1 (k2)?? x y (A) GLM (k

k3 ( :07 ) 2 (A) k = 1 (B) k = 7 y x x 1 (k2)?? x y (A) GLM (k 2012 11 01 k3 (2012-10-24 14:07 ) 1 6 3 (2012 11 01 k3) kubo@ees.hokudai.ac.jp web http://goo.gl/wijx2 web http://goo.gl/ufq2 1 3 2 : 4 3 AIC 6 4 7 5 8 6 : 9 7 11 8 12 8.1 (1)........ 13 8.2 (2) χ 2....................

More information

kubostat2017b p.1 agenda I 2017 (b) probability distribution and maximum likelihood estimation :

kubostat2017b p.1 agenda I 2017 (b) probability distribution and maximum likelihood estimation : kubostat2017b p.1 agenda I 2017 (b) probabilit distribution and maimum likelihood estimation kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2017 11 14 : 2017 11 07 15:43 1 : 2 3? 4 kubostat2017b (http://goo.gl/76c4i)

More information

今回 次回の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ Danger!! (危 1) 時系列データの GLM あてはめ (危 2) 時系列Yt 時系列 Xt 各時刻の個体数 気温 とか これは次回)

今回 次回の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ Danger!! (危 1) 時系列データの GLM あてはめ (危 2) 時系列Yt 時系列 Xt 各時刻の個体数 気温 とか これは次回) 生態学の時系列データ解析でよく見る あぶない モデリング 久保拓弥 mailto:kubo@ees.hokudai.ac.jp statistical model for time-series data 2017-07-03 kubostat2017 (h) 1/59 今回 次回の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ Danger!! (危 1) 時系列データの

More information

1 15 R Part : website:

1 15 R Part : website: 1 15 R Part 4 2017 7 24 4 : website: email: http://www3.u-toyama.ac.jp/kkarato/ kkarato@eco.u-toyama.ac.jp 1 2 2 3 2.1............................... 3 2.2 2................................. 4 2.3................................

More information

講義のーと : データ解析のための統計モデリング. 第2回

講義のーと :  データ解析のための統計モデリング. 第2回 Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20

More information

kubostat2018d p.2 :? bod size x and fertilization f change seed number? : a statistical model for this example? i response variable seed number : { i

kubostat2018d p.2 :? bod size x and fertilization f change seed number? : a statistical model for this example? i response variable seed number : { i kubostat2018d p.1 I 2018 (d) model selection and kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2018 06 25 : 2018 06 21 17:45 1 2 3 4 :? AIC : deviance model selection misunderstanding kubostat2018d (http://goo.gl/76c4i)

More information

今日の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ (危 1) 時系列データの GLM あてはめ (危 2) 時系列Yt 時系列 Xt 各時刻の個体数 気温 とか

今日の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ (危 1) 時系列データの GLM あてはめ (危 2) 時系列Yt 時系列 Xt 各時刻の個体数 気温 とか 時系列データ解析でよく見る あぶない モデリング 久保拓弥 (北海道大 環境科学) 1/56 今日の要点 あぶない 時系列データ解析は やめましょう! 統計モデル のあてはめ (危 1) 時系列データの GLM あてはめ (危 2) 時系列Yt 時系列 Xt 各時刻の個体数 気温 とか (危 1) 時系列データを GLM で (危 2) 時系列Yt 時系列 Xt 相関は因果関係ではない 問題の一部

More information

kubostat2018a p.1 統計モデリング入門 2018 (a) The main language of this class is 生物多様性学特論 Japanese Sorry An overview: Statistical Modeling 観測されたパターンを説明する統計モデル

kubostat2018a p.1 統計モデリング入門 2018 (a) The main language of this class is 生物多様性学特論 Japanese Sorry An overview: Statistical Modeling 観測されたパターンを説明する統計モデル p.1 統計モデリング入門 2018 (a) The main language of this class is 生物多様性学特論 Japanese Sorry An overview: Statistical Modeling 観測されたパターンを説明する統計モデル 久保拓弥 (北海道大 環境科学) Why in Japanese? because even in Japanese, statistics

More information

統計モデリング入門 2018 (a) 生物多様性学特論 An overview: Statistical Modeling 観測されたパターンを説明する統計モデル 久保拓弥 (北海道大 環境科学) 統計モデリング入門 2018a 1

統計モデリング入門 2018 (a) 生物多様性学特論 An overview: Statistical Modeling 観測されたパターンを説明する統計モデル 久保拓弥 (北海道大 環境科学) 統計モデリング入門 2018a 1 統計モデリング入門 2018 (a) 生物多様性学特論 An overview: Statistical Modeling 観測されたパターンを説明する統計モデル 久保拓弥 (北海道大 環境科学) kubo@ees.hokudai.ac.jp 1/56 The main language of this class is Japanese Sorry Why in Japanese? because

More information

2009 5 1...1 2...3 2.1...3 2.2...3 3...10 3.1...10 3.1.1...10 3.1.2... 11 3.2...14 3.2.1...14 3.2.2...16 3.3...18 3.4...19 3.4.1...19 3.4.2...20 3.4.3...21 4...24 4.1...24 4.2...24 4.3 WinBUGS...25 4.4...28

More information

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,. 24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)

More information

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3 13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >

More information

²¾ÁÛ¾õ¶·É¾²ÁË¡¤Î¤¿¤á¤Î¥Ñ¥Ã¥±¡¼¥¸DCchoice ¡Ê»ÃÄêÈÇ¡Ë

²¾ÁÛ¾õ¶·É¾²ÁË¡¤Î¤¿¤á¤Î¥Ñ¥Ã¥±¡¼¥¸DCchoice ¡Ê»ÃÄêÈÇ¡Ë DCchoice ( ) R 2013 2013 11 30 DCchoice package R 2013/11/30 1 / 19 1 (CV) CV 2 DCchoice WTP 3 DCchoice package R 2013/11/30 2 / 19 (Contingent Valuation; CV) WTP CV WTP WTP 1 1989 2 DCchoice package R

More information

Use R

Use R Use R! 2008/05/23( ) Index Introduction (GLM) ( ) R. Introduction R,, PLS,,, etc. 2. Correlation coefficient (Pearson s product moment correlation) r = Sxy Sxx Syy :, Sxy, Sxx= X, Syy Y 1.96 95% R cor(x,

More information

2 / 39

2 / 39 W707 s-taiji@is.titech.ac.jp 1 / 39 2 / 39 1 2 3 3 / 39 q f (x; α) = α j B j (x). j=1 min α R n+2 n ( d (Y i f (X i ; α)) 2 2 ) 2 f (x; α) + λ dx 2 dx. i=1 f B j 4 / 39 : q f (x) = α j B j (x). j=1 : x

More information

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P 6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P

More information

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10

More information

(lm) lm AIC 2 / 1

(lm) lm AIC 2 / 1 W707 s-taiji@is.titech.ac.jp 1 / 1 (lm) lm AIC 2 / 1 : y = β 1 x 1 + β 2 x 2 + + β d x d + β d+1 + ϵ (ϵ N(0, σ 2 )) y R: x R d : β i (i = 1,..., d):, β d+1 : ( ) (d = 1) y = β 1 x 1 + β 2 + ϵ (d > 1) y

More information

& 3 3 ' ' (., (Pixel), (Light Intensity) (Random Variable). (Joint Probability). V., V = {,,, V }. i x i x = (x, x,, x V ) T. x i i (State Variable),

& 3 3 ' ' (., (Pixel), (Light Intensity) (Random Variable). (Joint Probability). V., V = {,,, V }. i x i x = (x, x,, x V ) T. x i i (State Variable), .... Deeping and Expansion of Large-Scale Random Fields and Probabilistic Image Processing Kazuyuki Tanaka The mathematical frameworks of probabilistic image processing are formulated by means of Markov

More information

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,. (1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..

More information

最小2乗法

最小2乗法 2 2012 4 ( ) 2 2012 4 1 / 42 X Y Y = f (X ; Z) linear regression model X Y slope X 1 Y (X, Y ) 1 (X, Y ) ( ) 2 2012 4 2 / 42 1 β = β = β (4.2) = β 0 + β (4.3) ( ) 2 2012 4 3 / 42 = β 0 + β + (4.4) ( )

More information

1 Tokyo Daily Rainfall (mm) Days (mm)

1 Tokyo Daily Rainfall (mm) Days (mm) ( ) r-taka@maritime.kobe-u.ac.jp 1 Tokyo Daily Rainfall (mm) 0 100 200 300 0 10000 20000 30000 40000 50000 Days (mm) 1876 1 1 2013 12 31 Tokyo, 1876 Daily Rainfall (mm) 0 50 100 150 0 100 200 300 Tokyo,

More information

1 環境統計学ぷらす 第 5 回 一般 ( 化 ) 線形混合モデル 高木俊 2013/11/21

1 環境統計学ぷらす 第 5 回 一般 ( 化 ) 線形混合モデル 高木俊 2013/11/21 1 環境統計学ぷらす 第 5 回 一般 ( 化 ) 線形混合モデル 高木俊 shun.takagi@sci.toho-u.ac.jp 2013/11/21 2 予定 第 1 回 : Rの基礎と仮説検定 第 2 回 : 分散分析と回帰 第 3 回 : 一般線形モデル 交互作用 第 4.1 回 : 一般化線形モデル 第 4.2 回 : モデル選択 (11/29?) 第 5 回 : 一般化線形混合モデル

More information

H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =

H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat = H BioS t (i) treat treat data d; input patno treat treat; cards; 3 8 7 4 8 8 5 5 6 3 ; run; (i) treat treat data d; input group patno period treat y; label group patno period ; cards; 3 8 3 7 4 8 4 8 5

More information

第13回:交差項を含む回帰・弾力性の推定

第13回:交差項を含む回帰・弾力性の推定 13 2018 7 27 1 / 31 1. 2. 2 / 31 y i = β 0 + β X x i + β Z z i + β XZ x i z i + u i, E(u i x i, z i ) = 0, E(u i u j x i, z i ) = 0 (i j), V(u i x i, z i ) = σ 2, i = 1, 2,, n x i z i 1 3 / 31 y i = β

More information

tokei01.dvi

tokei01.dvi 2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN

More information

untitled

untitled MCMC 2004 23 1 I. MCMC 1. 2. 3. 4. MH 5. 6. MCMC 2 II. 1. 2. 3. 4. 5. 3 I. MCMC 1. 2. 3. 4. MH 5. 4 1. MCMC 5 2. A P (A) : P (A)=0.02 A B A B Pr B A) Pr B A c Pr B A)=0.8, Pr B A c =0.1 6 B A 7 8 A, :

More information

10:30 12:00 P.G. vs vs vs 2

10:30 12:00 P.G. vs vs vs 2 1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B

More information

Excelにおける回帰分析(最小二乗法)の手順と出力

Excelにおける回帰分析(最小二乗法)の手順と出力 Microsoft Excel Excel 1 1 x y x y y = a + bx a b a x 1 3 x 0 1 30 31 y b log x α x α x β 4 version.01 008 3 30 Website:http://keijisaito.info, E-mail:master@keijisaito.info 1 Excel Excel.1 Excel Excel

More information

Dirichlet process mixture Dirichlet process mixture 2 /40 MIRU2008 :

Dirichlet process mixture Dirichlet process mixture 2 /40 MIRU2008 : Dirichlet Process : joint work with: Max Welling (UC Irvine), Yee Whye Teh (UCL, Gatsby) http://kenichi.kurihara.googlepages.com/miru_workshop.pdf 1 /40 MIRU2008 : Dirichlet process mixture Dirichlet process

More information

untitled

untitled 3 3. (stochastic differential equations) { dx(t) =f(t, X)dt + G(t, X)dW (t), t [,T], (3.) X( )=X X(t) : [,T] R d (d ) f(t, X) : [,T] R d R d (drift term) G(t, X) : [,T] R d R d m (diffusion term) W (t)

More information

スライド 1

スライド 1 WinBUGS 入門 水産資源学におけるベイズ統計の応用ワークショップ 2007 年 8 月 2-3 日, 中央水研 遠洋水産研究所外洋資源部 鯨類管理研究室 岡村寛 WinBUGS とは BUGS (Bayesian Inference Using Gibbs Sampling) の Windows バージョン フリーのソフトウェア Gibbs samplingを利用した事後確率からのサンプリングを行う

More information

( 28 ) ( ) ( ) 0 This note is c 2016, 2017 by Setsuo Taniguchi. It may be used for personal or classroom purposes, but not for commercial purp

( 28 ) ( ) ( ) 0 This note is c 2016, 2017 by Setsuo Taniguchi. It may be used for personal or classroom purposes, but not for commercial purp ( 28) ( ) ( 28 9 22 ) 0 This ote is c 2016, 2017 by Setsuo Taiguchi. It may be used for persoal or classroom purposes, but ot for commercial purposes. i (http://www.stat.go.jp/teacher/c2epi1.htm ) = statistics

More information

( 30 ) 30 4 5 1 4 1.1............................................... 4 1.............................................. 4 1..1.................................. 4 1.......................................

More information

みっちりGLM

みっちりGLM 2015/3/27 12:00-13:00 日本草地学会若手 R 統計企画 ( 信州大学農学部 ) R と一般化線形モデル入門 山梨県富士山科学研究所 安田泰輔 謝辞 : 日本草地学会若手の会の皆様 発表の機会を頂き たいへんありがとうございます! 茨城大学 学生時代 自己紹介 ベータ二項分布を用いた種の空間分布の解析 所属 : 山梨県富士山科学研究所 最近の研究テーマ 近接リモートセンシングによる半自然草地のモニタリング手法開発

More information

こんにちは由美子です

こんにちは由美子です 1 2 . sum Variable Obs Mean Std. Dev. Min Max ---------+----------------------------------------------------- var1 13.4923077.3545926.05 1.1 3 3 3 0.71 3 x 3 C 3 = 0.3579 2 1 0.71 2 x 0.29 x 3 C 2 = 0.4386

More information

1 911 9001030 9:00 A B C D E F G H I J K L M 1A0900 1B0900 1C0900 1D0900 1E0900 1F0900 1G0900 1H0900 1I0900 1J0900 1K0900 1L0900 1M0900 9:15 1A0915 1B0915 1C0915 1D0915 1E0915 1F0915 1G0915 1H0915 1I0915

More information

(pdf) (cdf) Matlab χ ( ) F t

(pdf) (cdf) Matlab χ ( ) F t (, ) (univariate) (bivariate) (multi-variate) Matlab Octave Matlab Matlab/Octave --...............3. (pdf) (cdf)...3.4....4.5....4.6....7.7. Matlab...8.7.....9.7.. χ ( )...0.7.3.....7.4. F....7.5. t-...3.8....4.8.....4.8.....5.8.3....6.8.4....8.8.5....8.8.6....8.9....9.9.....9.9.....0.9.3....0.9.4.....9.5.....0....3

More information

y i OLS [0, 1] OLS x i = (1, x 1,i,, x k,i ) β = (β 0, β 1,, β k ) G ( x i β) 1 G i 1 π i π i P {y i = 1 x i } = G (

y i OLS [0, 1] OLS x i = (1, x 1,i,, x k,i ) β = (β 0, β 1,, β k ) G ( x i β) 1 G i 1 π i π i P {y i = 1 x i } = G ( 7 2 2008 7 10 1 2 2 1.1 2............................................. 2 1.2 2.......................................... 2 1.3 2........................................ 3 1.4................................................

More information

80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x

80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x 80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =

More information

201711grade1ouyou.pdf

201711grade1ouyou.pdf 2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2

More information

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-7 O1-8 O1-9 O1-10 O1-11 O1-12 O1-13 O1-14 O1-15 O1-16 O1-17 O1-18 O1-19 O1-20 O1-21 O1-22 O1-23 O1-24 O1-25 O1-26 O1-27 O1-28 O1-29 O1-30 O1-31 O1-32 O1-33 O1-34 O1-35

More information

09基礎分析講習会

09基礎分析講習会 データ解析の意味を理解しないでパソコンで計算して 序論 誤差解析 何のために も意味がない 以下の本でちゃんと勉強しよう R. A. Millikan ミリカン 水滴の蒸発 大学院生H. Fletcher 水滴を油滴に 博士論文単名 140の観測のうち49個除外 データ削除 実験データを正しく扱うために 化学同人編集部編 油滴実験 Regener がもともとThompsonの実験室(Cambridge

More information

分布

分布 (normal distribution) 30 2 Skewed graph 1 2 (variance) s 2 = 1/(n-1) (xi x) 2 x = mean, s = variance (variance) (standard deviation) SD = SQR (var) or 8 8 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 8 0 1 8 (probability

More information

untitled

untitled 2 : n =1, 2,, 10000 0.5125 0.51 0.5075 0.505 0.5025 0.5 0.4975 0.495 0 2000 4000 6000 8000 10000 2 weak law of large numbers 1. X 1,X 2,,X n 2. µ = E(X i ),i=1, 2,,n 3. σi 2 = V (X i ) σ 2,i=1, 2,,n ɛ>0

More information

Microsoft PowerPoint - GLMMexample_ver pptx

Microsoft PowerPoint - GLMMexample_ver pptx Linear Mixed Model ( 以下 混合モデル ) の短い解説 この解説のPDFは http://www.lowtem.hokudai.ac.jp/plantecol/akihiro/sumida-index.html の お勉強 のページにあります. ver 20121121 と との間に次のような関係が見つかったとしよう 全体的な傾向に対する回帰直線を点線で示した ところが これらのデータは実は異なる

More information

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í Markov 2009 10 2 Markov 2009 10 2 1 / 25 1 (GA) 2 GA 3 4 Markov 2009 10 2 2 / 25 (GA) (GA) L ( 1) I := {0, 1} L f : I (0, ) M( 2) S := I M GA (GA) f (i) i I Markov 2009 10 2 3 / 25 (GA) ρ(i, j), i, j I

More information

自由集会時系列part2web.key

自由集会時系列part2web.key spurious correlation spurious regression xt=xt-1+n(0,σ^2) yt=yt-1+n(0,σ^2) n=20 type1error(5%)=0.4703 no trend 0 1000 2000 3000 4000 p for r xt=xt-1+n(0,σ^2) random walk random walk variable -5 0 5 variable

More information

1 2 Visual SLAM 2 Visual SLAM

1 2 Visual SLAM 2 Visual SLAM 00D8102006F 2004 3 1 2 Visual SLAM 2 Visual SLAM 1 1 2 2 2.1 2 2.2 2 2.3 2 3 4 3.1 4 3.2 Kedall 4 3.3 Poisso 5 3.4 M/M/c 6 4 12 4.1 12 4.2 13 4.3 16 4.4 Visual SLAM 20 4.4.1 Visual SLAM 20 4.4.2 20 4.4.3

More information

: (EQS) /EQUATIONS V1 = 30*V F1 + E1; V2 = 25*V *F1 + E2; V3 = 16*V *F1 + E3; V4 = 10*V F2 + E4; V5 = 19*V99

: (EQS) /EQUATIONS V1 = 30*V F1 + E1; V2 = 25*V *F1 + E2; V3 = 16*V *F1 + E3; V4 = 10*V F2 + E4; V5 = 19*V99 218 6 219 6.11: (EQS) /EQUATIONS V1 = 30*V999 + 1F1 + E1; V2 = 25*V999 +.54*F1 + E2; V3 = 16*V999 + 1.46*F1 + E3; V4 = 10*V999 + 1F2 + E4; V5 = 19*V999 + 1.29*F2 + E5; V6 = 17*V999 + 2.22*F2 + E6; CALIS.

More information

GLM PROC GLM y = Xβ + ε y X β ε ε σ 2 E[ε] = 0 var[ε] = σ 2 I σ 2 0 σ 2 =... 0 σ 2 σ 2 I ε σ 2 y E[y] =Xβ var[y] =σ 2 I PROC GLM

GLM PROC GLM y = Xβ + ε y X β ε ε σ 2 E[ε] = 0 var[ε] = σ 2 I σ 2 0 σ 2 =... 0 σ 2 σ 2 I ε σ 2 y E[y] =Xβ var[y] =σ 2 I PROC GLM PROC MIXED ( ) An Introdunction to PROC MIXED Junji Kishimoto SAS Institute Japan / Keio Univ. SFC / Univ. of Tokyo e-mail address: jpnjak@jpn.sas.com PROC MIXED PROC GLM PROC MIXED,,,, 1 1.1 PROC MIXED

More information

H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I

H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I H BioS (i) I treat II treat data d; input group patno treat treat; cards; 8 7 4 8 8 5 5 6 ; run; I II sum data d; set d; sum treat + treat; run; sum proc gplot data d; plot sum * group ; symbol c black

More information

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4 20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d

More information

2. 2 I,II,III) 2 x expx) = lim + x 3) ) expx) e x 3) x. ) {a } a a 2 a 3...) a b b {a } α : lim a = α b) ) [] 2 ) f x) = + x ) 4) x > 0 {f x)} x > 0,

2. 2 I,II,III) 2 x expx) = lim + x 3) ) expx) e x 3) x. ) {a } a a 2 a 3...) a b b {a } α : lim a = α b) ) [] 2 ) f x) = + x ) 4) x > 0 {f x)} x > 0, . 207 02 02 a x x ) a x x a x x a x x ) a x x [] 3 3 sup) if) [3] 3 [4] 5.4 ) e x e x = lim + x ) ) e x e x log x = log e x) a > 0) x a x = e x log a 2) 2. 2 I,II,III) 2 x expx) = lim + x 3) ) expx) e

More information

JMP V4 による生存時間分析

JMP V4 による生存時間分析 V4 1 SAS 2000.11.18 4 ( ) (Survival Time) 1 (Event) Start of Study Start of Observation Died Died Died Lost End Time Censor Died Died Censor Died Time Start of Study End Start of Observation Censor

More information

°ÌÁê¿ô³ØII

°ÌÁê¿ô³ØII July 14, 2007 Brouwer f f(x) = x x f(z) = 0 2 f : S 2 R 2 f(x) = f( x) x S 2 3 3 2 - - - 1. X x X U(x) U(x) x U = {U(x) x X} X 1. U(x) A U(x) x 2. A U(x), A B B U(x) 3. A, B U(x) A B U(x) 4. A U(x),

More information

201711grade2.pdf

201711grade2.pdf 2017 11 26 1 2 28 3 90 4 5 A 1 2 3 4 Web Web 6 B 10 3 10 3 7 34 8 23 9 10 1 2 3 1 (A) 3 32.14 0.65 2.82 0.93 7.48 (B) 4 6 61.30 54.68 34.86 5.25 19.07 (C) 7 13 5.89 42.18 56.51 35.80 50.28 (D) 14 20 0.35

More information

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

Microsoft PowerPoint - Rを利用した回帰分析.pptx

Microsoft PowerPoint - Rを利用した回帰分析.pptx R を利 した回帰分析 中央水産研究所 岡村 寛 水産資源学における統計解析 漁業 調査データ解析 CPUE 標準化 資源のトレンド 体 組成のモード分解 成 式などの生物パラメータの推定 資源評価モデルによる個体群評価 ほとんどがパラメータの推定問題 今日の概要 前半 ( 岡村 ) 単回帰 重回帰モデル一般化線形 ( 混合 加法 ) モデルプロダクションモデル,VPA など 最小二乗法 最尤法 ベイズ推定

More information

p.1/22

p.1/22 p.1/22 & & & & Excel / p.2/22 & & & & Excel / p.2/22 ( ) ( ) p.3/22 ( ) ( ) Baldi Web p.3/22 ( ) ( ) Baldi Web ( ) ( ) ( p.3/22 ) Text Mining for Clementine True Teller Text Mining Studio Text Miner Trustia

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7

More information

確率論と統計学の資料

確率論と統計学の資料 5 June 015 ii........................ 1 1 1.1...................... 1 1........................... 3 1.3... 4 6.1........................... 6................... 7 ii ii.3.................. 8.4..........................

More information

untitled

untitled 18 1 2,000,000 2,000,000 2007 2 2 2008 3 31 (1) 6 JCOSSAR 2007pp.57-642007.6. LCC (1) (2) 2 10mm 1020 14 12 10 8 6 4 40,50,60 2 0 1998 27.5 1995 1960 40 1) 2) 3) LCC LCC LCC 1 1) Vol.42No.5pp.29-322004.5.

More information

Ł\”ƒ.dvi

Ł\”ƒ.dvi , , 1 1 9 11 9 12 10 13 11 14 14 15 15 16 19 2 21 21 21 22 23 221 23 222 24 223 27 23 30 231 2PLM 31 232 CCM 31 233 2PLCM 33 234 34 235 35 3 51 31 51 32 53 321 53 322 54 323 2 BTM 54 2 324 55 325 MCMC

More information

報告書

報告書 1 2 3 4 5 6 7 or 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2.65 2.45 2.31 2.30 2.29 1.95 1.79 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 60 55 60 75 25 23 6064 65 60 1015

More information

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )

5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j ) 5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y

More information

2 1,, x = 1 a i f i = i i a i f i. media ( ): x 1, x 2,..., x,. mode ( ): x 1, x 2,..., x,., ( ). 2., : box plot ( ): x variace ( ): σ 2 = 1 (x k x) 2

2 1,, x = 1 a i f i = i i a i f i. media ( ): x 1, x 2,..., x,. mode ( ): x 1, x 2,..., x,., ( ). 2., : box plot ( ): x variace ( ): σ 2 = 1 (x k x) 2 1 1 Lambert Adolphe Jacques Quetelet (1796 1874) 1.1 1 1 (1 ) x 1, x 2,..., x ( ) x a 1 a i a m f f 1 f i f m 1.1 ( ( )) 155 160 160 165 165 170 170 175 175 180 180 185 x 157.5 162.5 167.5 172.5 177.5

More information