RestingState
Chi-Lin Yu
Library
library(randomForest);library(leaps);library(pROC);library(ggplot2);
library(reshape2);library(plotly);library(ltm);library(dplyr);library(plyr)
library(bestglm)
predict.regsubsets <- function (object ,newdata ,id ,...) {
form=as.formula (object$call [[2]])
mat=model.matrix (form ,newdata )
coefi =coef(object ,id=id)
xvars =names (coefi )
mat[,xvars ]%*% coefi
}Data
Subject 2 is an outlier, so we deleted it.
19 subjects remain
Create a factor variable
dta <- readRDS("ML_NIRS_Connectivity_MeanVar.Rdata")[-12,c(2,10:39)]
dta1 <- dta
dta$Word_C <-as.factor(ifelse(dta$Word > median(dta$Word), "H","L"))
head(dta[,c(1:4,32)]) Word Sex Age Channel_2_Channel_1 Word_C
1 125 M 10.41 0.2485940 H
2 102 M 9.95 0.7715194 L
3 57 M 10.22 0.8711941 L
4 88 M 9.68 0.2212408 L
5 114 F 10.35 0.3854612 H
6 74 F 10.37 0.7481600 Ldta2 <- dta[,-1]
rownames(dta2) <- 1:nrow(dta2)
dta1 <- dta1[,c(2:31,1)]dta1 : regression
dim(dta1)[1] 19 31head(dta1) Sex Age Channel_2_Channel_1 Channel_3_Channel_1 Channel_3_Channel_2
1 M 10.41 0.2485940 0.46288574 0.21175610
2 M 9.95 0.7715194 -0.20377880 -0.29934220
3 M 10.22 0.8711941 0.23371935 0.20358104
4 M 9.68 0.2212408 0.06037749 0.08020694
5 F 10.35 0.3854612 0.29656393 0.15374033
6 F 10.37 0.7481600 0.46951380 0.23374250
Channel_4_Channel_1 Channel_4_Channel_2 Channel_4_Channel_3
1 0.7039091 -0.04930048 0.4604179
2 -0.2355694 -0.41759950 0.7629680
3 0.1320238 0.08566067 0.3161932
4 -0.1288285 0.04661314 0.1997940
5 0.4443495 0.03459522 0.3626908
6 0.3856371 0.31281710 0.5825679
Channel_5_Channel_1 Channel_5_Channel_2 Channel_5_Channel_3
1 0.7009494 0.2035324 0.51403430
2 0.7717407 0.8092355 -0.49009980
3 0.8439191 0.8784945 0.28403479
4 -0.1007590 0.3922983 -0.03923779
5 0.6462124 0.5197564 0.38399364
6 0.7916407 0.5007837 0.72978350
Channel_5_Channel_4 Channel_6_Channel_1 Channel_6_Channel_2
1 0.4112742 0.411660113 0.49688579
2 -0.4043635 0.613281200 0.83455350
3 0.2647561 0.678072007 0.87501035
4 -0.2381991 0.007969316 -0.09428076
5 0.3985602 0.260205190 0.55150128
6 0.4010637 0.106755900 0.32546680
Channel_6_Channel_3 Channel_6_Channel_4 Channel_6_Channel_5
1 -0.15116778 0.11765056 0.4423296
2 -0.45905630 -0.40614350 0.9480414
3 0.22815328 0.32551799 0.8741519
4 -0.05030743 -0.13522252 -0.1144503
5 -0.02480146 0.08635908 0.5882912
6 0.36968820 0.37587110 0.2972336
Channel_7_Channel_1 Channel_7_Channel_2 Channel_7_Channel_3
1 0.700666539 0.17455800 0.60011525
2 -0.184380200 -0.50874760 0.53369450
3 -0.008307771 -0.05236511 0.50517990
4 0.177693210 -0.03449846 0.05798242
5 0.132750980 -0.28640862 0.27003615
6 0.496956700 0.12642850 0.83869470
Channel_7_Channel_4 Channel_7_Channel_5 Channel_7_Channel_6
1 0.82182529 0.61792821 0.2722755
2 0.60017280 -0.25840960 -0.3543049
3 0.44000084 0.29512903 0.1070221
4 0.05554032 0.04993730 -0.2077076
5 0.81571089 0.06635884 -0.2516587
6 0.39024960 0.71139930 0.1850840
Channel_8_Channel_1 Channel_8_Channel_2 Channel_8_Channel_3
1 0.3582581 -0.140995464 0.29597684
2 -0.2318880 -0.361179400 0.29057710
3 -0.0918582 -0.008965472 0.20687536
4 0.4150704 0.077495848 -0.06399662
5 0.3767846 0.061195420 0.04938052
6 0.1906364 0.101353800 0.72356260
Channel_8_Channel_4 Channel_8_Channel_5 Channel_8_Channel_6
1 0.6785552 0.3329433 -0.008028079
2 0.6313585 -0.2051132 -0.184942600
3 0.7476095 0.1667268 0.344600225
4 0.3314869 -0.3403798 0.075392439
5 0.7057353 0.3773816 0.198273800
6 0.5645786 0.4028124 0.601079600
Channel_8_Channel_7 Word
1 0.7204461 125
2 0.5734672 102
3 0.5064076 57
4 -0.1080041 88
5 0.5233526 114
6 0.7166430 74dta2 : Classification
dim(dta2)[1] 19 31head(dta2) Sex Age Channel_2_Channel_1 Channel_3_Channel_1 Channel_3_Channel_2
1 M 10.41 0.2485940 0.46288574 0.21175610
2 M 9.95 0.7715194 -0.20377880 -0.29934220
3 M 10.22 0.8711941 0.23371935 0.20358104
4 M 9.68 0.2212408 0.06037749 0.08020694
5 F 10.35 0.3854612 0.29656393 0.15374033
6 F 10.37 0.7481600 0.46951380 0.23374250
Channel_4_Channel_1 Channel_4_Channel_2 Channel_4_Channel_3
1 0.7039091 -0.04930048 0.4604179
2 -0.2355694 -0.41759950 0.7629680
3 0.1320238 0.08566067 0.3161932
4 -0.1288285 0.04661314 0.1997940
5 0.4443495 0.03459522 0.3626908
6 0.3856371 0.31281710 0.5825679
Channel_5_Channel_1 Channel_5_Channel_2 Channel_5_Channel_3
1 0.7009494 0.2035324 0.51403430
2 0.7717407 0.8092355 -0.49009980
3 0.8439191 0.8784945 0.28403479
4 -0.1007590 0.3922983 -0.03923779
5 0.6462124 0.5197564 0.38399364
6 0.7916407 0.5007837 0.72978350
Channel_5_Channel_4 Channel_6_Channel_1 Channel_6_Channel_2
1 0.4112742 0.411660113 0.49688579
2 -0.4043635 0.613281200 0.83455350
3 0.2647561 0.678072007 0.87501035
4 -0.2381991 0.007969316 -0.09428076
5 0.3985602 0.260205190 0.55150128
6 0.4010637 0.106755900 0.32546680
Channel_6_Channel_3 Channel_6_Channel_4 Channel_6_Channel_5
1 -0.15116778 0.11765056 0.4423296
2 -0.45905630 -0.40614350 0.9480414
3 0.22815328 0.32551799 0.8741519
4 -0.05030743 -0.13522252 -0.1144503
5 -0.02480146 0.08635908 0.5882912
6 0.36968820 0.37587110 0.2972336
Channel_7_Channel_1 Channel_7_Channel_2 Channel_7_Channel_3
1 0.700666539 0.17455800 0.60011525
2 -0.184380200 -0.50874760 0.53369450
3 -0.008307771 -0.05236511 0.50517990
4 0.177693210 -0.03449846 0.05798242
5 0.132750980 -0.28640862 0.27003615
6 0.496956700 0.12642850 0.83869470
Channel_7_Channel_4 Channel_7_Channel_5 Channel_7_Channel_6
1 0.82182529 0.61792821 0.2722755
2 0.60017280 -0.25840960 -0.3543049
3 0.44000084 0.29512903 0.1070221
4 0.05554032 0.04993730 -0.2077076
5 0.81571089 0.06635884 -0.2516587
6 0.39024960 0.71139930 0.1850840
Channel_8_Channel_1 Channel_8_Channel_2 Channel_8_Channel_3
1 0.3582581 -0.140995464 0.29597684
2 -0.2318880 -0.361179400 0.29057710
3 -0.0918582 -0.008965472 0.20687536
4 0.4150704 0.077495848 -0.06399662
5 0.3767846 0.061195420 0.04938052
6 0.1906364 0.101353800 0.72356260
Channel_8_Channel_4 Channel_8_Channel_5 Channel_8_Channel_6
1 0.6785552 0.3329433 -0.008028079
2 0.6313585 -0.2051132 -0.184942600
3 0.7476095 0.1667268 0.344600225
4 0.3314869 -0.3403798 0.075392439
5 0.7057353 0.3773816 0.198273800
6 0.5645786 0.4028124 0.601079600
Channel_8_Channel_7 Word_C
1 0.7204461 H
2 0.5734672 L
3 0.5064076 L
4 -0.1080041 L
5 0.5233526 H
6 0.7166430 LRegression : dta1
Variable Selection
fit_lm <- list()
R2_lm <- data.frame(R2 = NA, variable = NA)
aR2_lm <- data.frame(aR2 = NA, variable = NA)
p_lm <- data.frame(pvalue = NA, variable = NA)
for (i in 1:30){
fit_lm[[i]] <- summary(fit <- lm(Word~.,
data = dta1[,c(i,31)]))
names(fit_lm)[i] <- colnames(dta1)[i]
yhat <- predict(fit,data = dta1[,c(i,31)],type = "response")
R2_lm <- rbind(R2_lm,
data.frame(R2 = fit_lm[[i]]$r.squared,
variable = colnames(dta1)[i]))
aR2_lm <- rbind(aR2_lm,
data.frame(aR2 = fit_lm[[i]]$adj.r.squared,
variable = colnames(dta1)[i]))
p_lm <- rbind(p_lm, data.frame(pvalue = fit_lm[[i]]$coefficient[2,4],
variable = colnames(dta1)[i]))
}Variable Selection
R2 > 0.07 : 6 variables
head(vs <- na.omit(cbind(p_lm[order(p_lm$pvalue),c(2,1)],
R2_lm[order(-R2_lm$R2),c(2,1)],
aR2_lm[order(-aR2_lm$aR2),c(2,1)]))[,c(1,2,4,6)],10) variable pvalue R2 aR2
30 Channel_8_Channel_6 0.04796165 0.21085134 0.164430832
29 Channel_8_Channel_5 0.14345477 0.12157590 0.069903893
31 Channel_8_Channel_7 0.24141640 0.07975418 0.025622076
13 Channel_5_Channel_4 0.24694482 0.07798054 0.023744103
12 Channel_5_Channel_3 0.26345264 0.07294288 0.018410111
9 Channel_4_Channel_3 0.26976994 0.07111060 0.016470050
28 Channel_8_Channel_4 0.28794471 0.06610719 0.011172321
23 Channel_7_Channel_5 0.32297046 0.05745242 0.002008439
4 Channel_2_Channel_1 0.36667231 0.04816139 -0.007829121
7 Channel_4_Channel_1 0.37525910 0.04650344 -0.009584594dta1_vs<- dta1[,c("Word",filter(vs, R2>0.07)$variable)]
head(dta1_vs) Word Channel_8_Channel_6 Channel_8_Channel_5 Channel_8_Channel_7
1 125 -0.008028079 0.3329433 0.7204461
2 102 -0.184942600 -0.2051132 0.5734672
3 57 0.344600225 0.1667268 0.5064076
4 88 0.075392439 -0.3403798 -0.1080041
5 114 0.198273800 0.3773816 0.5233526
6 74 0.601079600 0.4028124 0.7166430
Channel_5_Channel_4 Channel_5_Channel_3 Channel_4_Channel_3
1 0.4112742 0.51403430 0.4604179
2 -0.4043635 -0.49009980 0.7629680
3 0.2647561 0.28403479 0.3161932
4 -0.2381991 -0.03923779 0.1997940
5 0.3985602 0.38399364 0.3626908
6 0.4010637 0.72978350 0.5825679GLM
Best subset selection
limit : 6 variables
nmax = 6
bs_r2 <- matrix(NA,1000,nmax,dimnames =list(NULL , paste (1:nmax) ))
for (k in 1:1000){
set.seed(k)
idc_test <- sample(1:nrow(dta1_vs),6)
idc_train <- -idc_test
best.fit <- regsubsets(Word~. ,data=dta1_vs[idc_train,],
method ="exhaustive",nvmax= nmax)
for(i in 1:nmax) {
yhat <- predict(best.fit,newdata = dta1_vs[idc_test,],
id=i,type = "response")
y <- dta1_vs[idc_test,]$Word
bs_r2 [k,i] = 1 - mean((y - yhat)^2)/var(y)
}
}
sort(apply(bs_r2 ,2, mean,na.rm =T)) 4 6 5 3 2 1
-2.302816 -2.286349 -2.227113 -1.985276 -1.398768 -1.084220 best.fit <- regsubsets(Word~. ,data=dta1_vs,
method ="exhaustive",nvmax= nmax)
coef(best.fit,1) (Intercept) Channel_8_Channel_6
105.07076 -53.16316 GLM
1 variable Ch8_Ch6
rs_mat_lm <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- sample(1:nrow(dta1_vs),6)
idc_train <- -idc_test
fit <- lm(Word~Channel_8_Channel_6,data = dta1_vs[idc_train,])
yhat <- predict(fit,newdata = dta1_vs[idc_test,],type = "response")
y <- dta1_vs[idc_test,]$Word
rs_mat_lm[k,] = 1 - mean((y - yhat)^2)/var(y)
}
mean(rs_mat_lm)[1] -0.6092389quantile(rs_mat_lm,probs = c(0.025,0.975)) 2.5% 97.5%
-5.5763401 0.4659623 GLM
1 variable Ch8_Ch6
Classification
dta1_vs_c <- dta1_vs
dta1_vs_c$Word_c <- as.factor(ifelse(dta1_vs$Word > median(dta1_vs$Word), "H","L"))
dta1_vs_c <- dta1_vs_c[,-1]
auc_mat_glm_c <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta1_vs_c$Word_c == "H"), 3),
sample(which(dta1_vs_c$Word_c == "L"), 3))
idc_train <- -idc_test
fit <- glm(Word_c~Channel_8_Channel_6,data = dta1_vs_c[idc_train,],family = "binomial")
yhat <- predict(fit,newdata = dta1_vs_c[idc_test,],type = "response")
y <- dta1_vs_c[idc_test,]$Word
auc_mat_glm_c[k,] = pROC::auc(y,yhat)
}
mean( auc_mat_glm_c)[1] 0.6695556quantile( auc_mat_glm_c,probs = c(0.025,0.975)) 2.5% 97.5%
0.4444444 1.0000000 RF
Default metry and nodesize
rs_mat_rf <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- sample(1:nrow(dta1_vs),6)
idc_train <- -idc_test
fit <- randomForest(Word~. ,
data = dta1_vs[idc_train,],
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta1_vs[idc_test,],type = "response")
y <- dta1_vs[idc_test,]$Word
rs_mat_rf[k,] = 1 - mean((y - yhat)^2)/var(y)
}
mean(rs_mat_rf)[1] -0.5409942quantile(rs_mat_rf,probs = c(0.025,0.975)) 2.5% 97.5%
-4.0545783 0.3578068 RF
Default metry and nodesize
classification
dta1_vs_c <- dta1_vs
dta1_vs_c$Word_c <- as.factor(ifelse(dta1_vs$Word > median(dta1_vs$Word), "H","L"))
dta1_vs_c <- dta1_vs_c[,-1]
auc_mat_rf_c <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta1_vs_c$Word_c == "H"), 3),
sample(which(dta1_vs_c$Word_c == "L"), 3))
idc_train <- -idc_test
fit <- randomForest(Word_c~. ,
data = dta1_vs_c[idc_train,],
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta1_vs_c[idc_test,],type = "prob")[,2]
y <- dta1_vs_c[idc_test,]$Word
auc_mat_rf_c[k,] = pROC::auc(y,yhat)
}
mean(auc_mat_rf_c)[1] 0.7144444quantile(auc_mat_rf_c,probs = c(0.025,0.975)) 2.5% 97.5%
0.4444444 1.0000000 # rf tune nodesize and mtryComparison
mean(rs_mat_lm)[1] -0.6092389mean(auc_mat_glm_c)[1] 0.6695556mean(rs_mat_rf) # # rf tune nodesize and mtry[1] -0.5409942mean(auc_mat_rf_c) # # rf tune nodesize and mtry[1] 0.7144444Comparison
pdta <- data.frame(RS_LM = rs_mat_lm,AUC_LM = auc_mat_glm_c,
RS_RF = rs_mat_rf, AUC_RF = auc_mat_rf_c)
pdta <- melt(pdta)
ggplot(pdta, aes(value))+
geom_density()+
facet_wrap(~variable,scales = "free")+
theme_bw()
Classification : dta2
Variable Selection
p value and AUC from linear model
fit_lm <- list()
auc_lm <- data.frame(AUC = NA, variable = NA)
p_lm <- data.frame(pvalue = NA, variable = NA)
for (i in 1:30){
fit_lm[[i]] <- summary(fit <- glm(Word_C~.,
data = dta2[,c(i,31)],family = "binomial"))
names(fit_lm)[i] <- colnames(dta2)[i]
yhat <- predict(fit,data = dta2[,c(i,31)],type = "response")
auc_lm <- rbind(auc_lm,
data.frame(AUC = pROC::auc(dta2$Word_C,yhat),
variable = colnames(dta2)[i]))
p_lm <- rbind(p_lm, data.frame(pvalue = fit_lm[[i]]$coefficient[2,4], variable = colnames(dta2)[i]))
}Variable Selection
AUC > 0.75 : 3 variables
head(na.omit(cbind(p_lm[order(p_lm$pvalue),c(2,1)],
vs <- auc_lm[order(-auc_lm$AUC),c(2,1)])),10) variable pvalue variable AUC
29 Channel_8_Channel_5 0.04705111 Channel_4_Channel_1 0.7777778
7 Channel_4_Channel_1 0.05937883 Channel_8_Channel_5 0.7777778
8 Channel_4_Channel_2 0.08392544 Channel_5_Channel_4 0.7555556
13 Channel_5_Channel_4 0.09553314 Channel_3_Channel_1 0.7444444
12 Channel_5_Channel_3 0.09629423 Channel_7_Channel_1 0.7444444
19 Channel_7_Channel_1 0.10024331 Channel_5_Channel_3 0.7333333
5 Channel_3_Channel_1 0.11573316 Channel_4_Channel_2 0.7222222
23 Channel_7_Channel_5 0.14191010 Channel_2_Channel_1 0.7111111
6 Channel_3_Channel_2 0.16463977 Channel_7_Channel_5 0.7111111
4 Channel_2_Channel_1 0.18213073 Channel_7_Channel_2 0.6888889dta2_vs<- dta2[,c("Word_C",filter(vs,AUC > 0.75)$variable)]
# >0.75 3
# >0.74 5
head(dta2_vs) Word_C Channel_4_Channel_1 Channel_8_Channel_5 Channel_5_Channel_4
1 H 0.7039091 0.3329433 0.4112742
2 L -0.2355694 -0.2051132 -0.4043635
3 L 0.1320238 0.1667268 0.2647561
4 L -0.1288285 -0.3403798 -0.2381991
5 H 0.4443495 0.3773816 0.3985602
6 L 0.3856371 0.4028124 0.4010637GLM
Best subset selection, nvmax : 5 variables
bs_auc_i <- matrix(NA,1000,3,dimnames =list(NULL , paste (1:3)))
# more than 1000 ?
for (k in 1:1000){
set.seed(k)
print(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
best.fit <- bestglm(dta2_vs[idc_train,c(2:4,1)],
IC="AIC",method ="exhaustive",family=binomial,nvmax = 3)
yhat <- predict(best.fit$BestModel,newdata = dta2_vs[idc_test,c(2:4,1)],
type = "response")
n = nrow(as.data.frame(best.fit$BestModel$coefficients)) - 1
bs_auc_i[k,n] = pROC::auc(dta2_vs[idc_test,]$Word_C,as.numeric(yhat))
}[1] 1
Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
[1] 39
Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
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Morgan-Tatar search since family is non-gaussian.
[1] 46
Morgan-Tatar search since family is non-gaussian.
[1] 47
Morgan-Tatar search since family is non-gaussian.
[1] 48
Morgan-Tatar search since family is non-gaussian.
[1] 49
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[1] 50
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[1] 51
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[1] 52
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[1] 53
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[1] 54
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[1] 55
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[1] 56
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[1] 57
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[1] 58
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[1] 59
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[1] 60
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[1] 61
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[1] 62
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[1] 63
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[1] 64
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[1] 65
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[1] 66
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[1] 67
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[1] 68
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[1] 69
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[1] 70
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[1] 71
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[1] 72
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[1] 73
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[1] 74
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[1] 75
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[1] 76
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[1] 77
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[1] 78
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[1] 79
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[1] 80
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[1] 81
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[1] 82
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[1] 83
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[1] 84
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[1] 85
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[1] 86
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[1] 87
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[1] 88
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[1] 89
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[1] 90
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[1] 91
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[1] 92
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[1] 93
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[1] 94
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[1] 95
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[1] 96
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[1] 97
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[1] 98
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[1] 99
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[1] 100
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[1] 101
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[1] 102
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[1] 103
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[1] 104
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[1] 105
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[1] 106
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[1] 107
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[1] 108
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[1] 109
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[1] 110
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[1] 111
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[1] 112
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[1] 113
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[1] 114
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[1] 115
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[1] 116
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[1] 117
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[1] 118
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[1] 119
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[1] 120
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[1] 121
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[1] 122
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[1] 123
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[1] 136
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[1] 137
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[1] 138
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[1] 139
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[1] 140
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[1] 141
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[1] 142
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[1] 143
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[1] 144
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[1] 145
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[1] 146
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[1] 147
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[1] 148
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[1] 149
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[1] 150
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[1] 151
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[1] 152
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[1] 153
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[1] 154
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[1] 155
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[1] 156
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[1] 157
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[1] 158
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[1] 159
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[1] 160
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[1] 161
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[1] 162
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[1] 163
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[1] 164
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[1] 165
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[1] 166
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[1] 167
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[1] 168
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[1] 169
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[1] 170
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[1] 171
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[1] 172
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[1] 173
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[1] 174
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[1] 175
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[1] 176
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[1] 177
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[1] 178
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[1] 179
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[1] 180
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[1] 181
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[1] 182
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[1] 183
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[1] 184
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[1] 185
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[1] 186
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[1] 187
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[1] 188
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[1] 189
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[1] 190
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[1] 191
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[1] 192
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[1] 193
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[1] 194
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[1] 195
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[1] 196
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[1] 197
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[1] 198
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[1] 199
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[1] 200
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[1] 201
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[1] 202
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[1] 203
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[1] 204
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[1] 206
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[1] 207
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[1] 208
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[1] 209
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[1] 210
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[1] 211
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[1] 212
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[1] 213
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[1] 214
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[1] 215
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[1] 216
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[1] 217
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[1] 219
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[1] 220
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[1] 221
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[1] 222
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[1] 223
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[1] 224
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[1] 225
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[1] 226
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[1] 227
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[1] 228
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[1] 229
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[1] 230
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[1] 231
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[1] 232
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[1] 233
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[1] 234
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[1] 235
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[1] 236
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[1] 237
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[1] 238
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[1] 239
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[1] 240
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[1] 241
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[1] 242
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[1] 243
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[1] 244
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[1] 245
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[1] 246
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[1] 247
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[1] 248
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[1] 249
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[1] 250
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[1] 251
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[1] 252
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[1] 253
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[1] 254
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[1] 255
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[1] 256
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[1] 257
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[1] 258
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[1] 259
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[1] 260
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[1] 261
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[1] 262
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[1] 263
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[1] 264
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[1] 265
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[1] 266
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[1] 267
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[1] 268
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[1] 269
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[1] 270
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[1] 271
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[1] 272
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[1] 273
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[1] 274
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[1] 275
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[1] 276
Morgan-Tatar search since family is non-gaussian.
[1] 277
Morgan-Tatar search since family is non-gaussian.
[1] 278
Morgan-Tatar search since family is non-gaussian.
[1] 279
Morgan-Tatar search since family is non-gaussian.
[1] 280
Morgan-Tatar search since family is non-gaussian.
[1] 281
Morgan-Tatar search since family is non-gaussian.
[1] 282
Morgan-Tatar search since family is non-gaussian.
[1] 283
Morgan-Tatar search since family is non-gaussian.
[1] 284
Morgan-Tatar search since family is non-gaussian.
[1] 285
Morgan-Tatar search since family is non-gaussian.
[1] 286
Morgan-Tatar search since family is non-gaussian.
[1] 287
Morgan-Tatar search since family is non-gaussian.
[1] 288
Morgan-Tatar search since family is non-gaussian.
[1] 289
Morgan-Tatar search since family is non-gaussian.
[1] 290
Morgan-Tatar search since family is non-gaussian.
[1] 291
Morgan-Tatar search since family is non-gaussian.
[1] 292
Morgan-Tatar search since family is non-gaussian.
[1] 293
Morgan-Tatar search since family is non-gaussian.
[1] 294
Morgan-Tatar search since family is non-gaussian.
[1] 295
Morgan-Tatar search since family is non-gaussian.
[1] 296
Morgan-Tatar search since family is non-gaussian.
[1] 297
Morgan-Tatar search since family is non-gaussian.
[1] 298
Morgan-Tatar search since family is non-gaussian.
[1] 299
Morgan-Tatar search since family is non-gaussian.
[1] 300
Morgan-Tatar search since family is non-gaussian.
[1] 301
Morgan-Tatar search since family is non-gaussian.
[1] 302
Morgan-Tatar search since family is non-gaussian.
[1] 303
Morgan-Tatar search since family is non-gaussian.
[1] 304
Morgan-Tatar search since family is non-gaussian.
[1] 305
Morgan-Tatar search since family is non-gaussian.
[1] 306
Morgan-Tatar search since family is non-gaussian.
[1] 307
Morgan-Tatar search since family is non-gaussian.
[1] 308
Morgan-Tatar search since family is non-gaussian.
[1] 309
Morgan-Tatar search since family is non-gaussian.
[1] 310
Morgan-Tatar search since family is non-gaussian.
[1] 311
Morgan-Tatar search since family is non-gaussian.
[1] 312
Morgan-Tatar search since family is non-gaussian.
[1] 313
Morgan-Tatar search since family is non-gaussian.
[1] 314
Morgan-Tatar search since family is non-gaussian.
[1] 315
Morgan-Tatar search since family is non-gaussian.
[1] 316
Morgan-Tatar search since family is non-gaussian.
[1] 317
Morgan-Tatar search since family is non-gaussian.
[1] 318
Morgan-Tatar search since family is non-gaussian.
[1] 319
Morgan-Tatar search since family is non-gaussian.
[1] 320
Morgan-Tatar search since family is non-gaussian.
[1] 321
Morgan-Tatar search since family is non-gaussian.
[1] 322
Morgan-Tatar search since family is non-gaussian.
[1] 323
Morgan-Tatar search since family is non-gaussian.
[1] 324
Morgan-Tatar search since family is non-gaussian.
[1] 325
Morgan-Tatar search since family is non-gaussian.
[1] 326
Morgan-Tatar search since family is non-gaussian.
[1] 327
Morgan-Tatar search since family is non-gaussian.
[1] 328
Morgan-Tatar search since family is non-gaussian.
[1] 329
Morgan-Tatar search since family is non-gaussian.
[1] 330
Morgan-Tatar search since family is non-gaussian.
[1] 331
Morgan-Tatar search since family is non-gaussian.
[1] 332
Morgan-Tatar search since family is non-gaussian.
[1] 333
Morgan-Tatar search since family is non-gaussian.
[1] 334
Morgan-Tatar search since family is non-gaussian.
[1] 335
Morgan-Tatar search since family is non-gaussian.
[1] 336
Morgan-Tatar search since family is non-gaussian.
[1] 337
Morgan-Tatar search since family is non-gaussian.
[1] 338
Morgan-Tatar search since family is non-gaussian.
[1] 339
Morgan-Tatar search since family is non-gaussian.
[1] 340
Morgan-Tatar search since family is non-gaussian.
[1] 341
Morgan-Tatar search since family is non-gaussian.
[1] 342
Morgan-Tatar search since family is non-gaussian.
[1] 343
Morgan-Tatar search since family is non-gaussian.
[1] 344
Morgan-Tatar search since family is non-gaussian.
[1] 345
Morgan-Tatar search since family is non-gaussian.
[1] 346
Morgan-Tatar search since family is non-gaussian.
[1] 347
Morgan-Tatar search since family is non-gaussian.
[1] 348
Morgan-Tatar search since family is non-gaussian.
[1] 349
Morgan-Tatar search since family is non-gaussian.
[1] 350
Morgan-Tatar search since family is non-gaussian.
[1] 351
Morgan-Tatar search since family is non-gaussian.
[1] 352
Morgan-Tatar search since family is non-gaussian.
[1] 353
Morgan-Tatar search since family is non-gaussian.
[1] 354
Morgan-Tatar search since family is non-gaussian.
[1] 355
Morgan-Tatar search since family is non-gaussian.
[1] 356
Morgan-Tatar search since family is non-gaussian.
[1] 357
Morgan-Tatar search since family is non-gaussian.
[1] 358
Morgan-Tatar search since family is non-gaussian.
[1] 359
Morgan-Tatar search since family is non-gaussian.
[1] 360
Morgan-Tatar search since family is non-gaussian.
[1] 361
Morgan-Tatar search since family is non-gaussian.
[1] 362
Morgan-Tatar search since family is non-gaussian.
[1] 363
Morgan-Tatar search since family is non-gaussian.
[1] 364
Morgan-Tatar search since family is non-gaussian.
[1] 365
Morgan-Tatar search since family is non-gaussian.
[1] 366
Morgan-Tatar search since family is non-gaussian.
[1] 367
Morgan-Tatar search since family is non-gaussian.
[1] 368
Morgan-Tatar search since family is non-gaussian.
[1] 369
Morgan-Tatar search since family is non-gaussian.
[1] 370
Morgan-Tatar search since family is non-gaussian.
[1] 371
Morgan-Tatar search since family is non-gaussian.
[1] 372
Morgan-Tatar search since family is non-gaussian.
[1] 373
Morgan-Tatar search since family is non-gaussian.
[1] 374
Morgan-Tatar search since family is non-gaussian.
[1] 375
Morgan-Tatar search since family is non-gaussian.
[1] 376
Morgan-Tatar search since family is non-gaussian.
[1] 377
Morgan-Tatar search since family is non-gaussian.
[1] 378
Morgan-Tatar search since family is non-gaussian.
[1] 379
Morgan-Tatar search since family is non-gaussian.
[1] 380
Morgan-Tatar search since family is non-gaussian.
[1] 381
Morgan-Tatar search since family is non-gaussian.
[1] 382
Morgan-Tatar search since family is non-gaussian.
[1] 383
Morgan-Tatar search since family is non-gaussian.
[1] 384
Morgan-Tatar search since family is non-gaussian.
[1] 385
Morgan-Tatar search since family is non-gaussian.
[1] 386
Morgan-Tatar search since family is non-gaussian.
[1] 387
Morgan-Tatar search since family is non-gaussian.
[1] 388
Morgan-Tatar search since family is non-gaussian.
[1] 389
Morgan-Tatar search since family is non-gaussian.
[1] 390
Morgan-Tatar search since family is non-gaussian.
[1] 391
Morgan-Tatar search since family is non-gaussian.
[1] 392
Morgan-Tatar search since family is non-gaussian.
[1] 393
Morgan-Tatar search since family is non-gaussian.
[1] 394
Morgan-Tatar search since family is non-gaussian.
[1] 395
Morgan-Tatar search since family is non-gaussian.
[1] 396
Morgan-Tatar search since family is non-gaussian.
[1] 397
Morgan-Tatar search since family is non-gaussian.
[1] 398
Morgan-Tatar search since family is non-gaussian.
[1] 399
Morgan-Tatar search since family is non-gaussian.
[1] 400
Morgan-Tatar search since family is non-gaussian.
[1] 401
Morgan-Tatar search since family is non-gaussian.
[1] 402
Morgan-Tatar search since family is non-gaussian.
[1] 403
Morgan-Tatar search since family is non-gaussian.
[1] 404
Morgan-Tatar search since family is non-gaussian.
[1] 405
Morgan-Tatar search since family is non-gaussian.
[1] 406
Morgan-Tatar search since family is non-gaussian.
[1] 407
Morgan-Tatar search since family is non-gaussian.
[1] 408
Morgan-Tatar search since family is non-gaussian.
[1] 409
Morgan-Tatar search since family is non-gaussian.
[1] 410
Morgan-Tatar search since family is non-gaussian.
[1] 411
Morgan-Tatar search since family is non-gaussian.
[1] 412
Morgan-Tatar search since family is non-gaussian.
[1] 413
Morgan-Tatar search since family is non-gaussian.
[1] 414
Morgan-Tatar search since family is non-gaussian.
[1] 415
Morgan-Tatar search since family is non-gaussian.
[1] 416
Morgan-Tatar search since family is non-gaussian.
[1] 417
Morgan-Tatar search since family is non-gaussian.
[1] 418
Morgan-Tatar search since family is non-gaussian.
[1] 419
Morgan-Tatar search since family is non-gaussian.
[1] 420
Morgan-Tatar search since family is non-gaussian.
[1] 421
Morgan-Tatar search since family is non-gaussian.
[1] 422
Morgan-Tatar search since family is non-gaussian.
[1] 423
Morgan-Tatar search since family is non-gaussian.
[1] 424
Morgan-Tatar search since family is non-gaussian.
[1] 425
Morgan-Tatar search since family is non-gaussian.
[1] 426
Morgan-Tatar search since family is non-gaussian.
[1] 427
Morgan-Tatar search since family is non-gaussian.
[1] 428
Morgan-Tatar search since family is non-gaussian.
[1] 429
Morgan-Tatar search since family is non-gaussian.
[1] 430
Morgan-Tatar search since family is non-gaussian.
[1] 431
Morgan-Tatar search since family is non-gaussian.
[1] 432
Morgan-Tatar search since family is non-gaussian.
[1] 433
Morgan-Tatar search since family is non-gaussian.
[1] 434
Morgan-Tatar search since family is non-gaussian.
[1] 435
Morgan-Tatar search since family is non-gaussian.
[1] 436
Morgan-Tatar search since family is non-gaussian.
[1] 437
Morgan-Tatar search since family is non-gaussian.
[1] 438
Morgan-Tatar search since family is non-gaussian.
[1] 439
Morgan-Tatar search since family is non-gaussian.
[1] 440
Morgan-Tatar search since family is non-gaussian.
[1] 441
Morgan-Tatar search since family is non-gaussian.
[1] 442
Morgan-Tatar search since family is non-gaussian.
[1] 443
Morgan-Tatar search since family is non-gaussian.
[1] 444
Morgan-Tatar search since family is non-gaussian.
[1] 445
Morgan-Tatar search since family is non-gaussian.
[1] 446
Morgan-Tatar search since family is non-gaussian.
[1] 447
Morgan-Tatar search since family is non-gaussian.
[1] 448
Morgan-Tatar search since family is non-gaussian.
[1] 449
Morgan-Tatar search since family is non-gaussian.
[1] 450
Morgan-Tatar search since family is non-gaussian.
[1] 451
Morgan-Tatar search since family is non-gaussian.
[1] 452
Morgan-Tatar search since family is non-gaussian.
[1] 453
Morgan-Tatar search since family is non-gaussian.
[1] 454
Morgan-Tatar search since family is non-gaussian.
[1] 455
Morgan-Tatar search since family is non-gaussian.
[1] 456
Morgan-Tatar search since family is non-gaussian.
[1] 457
Morgan-Tatar search since family is non-gaussian.
[1] 458
Morgan-Tatar search since family is non-gaussian.
[1] 459
Morgan-Tatar search since family is non-gaussian.
[1] 460
Morgan-Tatar search since family is non-gaussian.
[1] 461
Morgan-Tatar search since family is non-gaussian.
[1] 462
Morgan-Tatar search since family is non-gaussian.
[1] 463
Morgan-Tatar search since family is non-gaussian.
[1] 464
Morgan-Tatar search since family is non-gaussian.
[1] 465
Morgan-Tatar search since family is non-gaussian.
[1] 466
Morgan-Tatar search since family is non-gaussian.
[1] 467
Morgan-Tatar search since family is non-gaussian.
[1] 468
Morgan-Tatar search since family is non-gaussian.
[1] 469
Morgan-Tatar search since family is non-gaussian.
[1] 470
Morgan-Tatar search since family is non-gaussian.
[1] 471
Morgan-Tatar search since family is non-gaussian.
[1] 472
Morgan-Tatar search since family is non-gaussian.
[1] 473
Morgan-Tatar search since family is non-gaussian.
[1] 474
Morgan-Tatar search since family is non-gaussian.
[1] 475
Morgan-Tatar search since family is non-gaussian.
[1] 476
Morgan-Tatar search since family is non-gaussian.
[1] 477
Morgan-Tatar search since family is non-gaussian.
[1] 478
Morgan-Tatar search since family is non-gaussian.
[1] 479
Morgan-Tatar search since family is non-gaussian.
[1] 480
Morgan-Tatar search since family is non-gaussian.
[1] 481
Morgan-Tatar search since family is non-gaussian.
[1] 482
Morgan-Tatar search since family is non-gaussian.
[1] 483
Morgan-Tatar search since family is non-gaussian.
[1] 484
Morgan-Tatar search since family is non-gaussian.
[1] 485
Morgan-Tatar search since family is non-gaussian.
[1] 486
Morgan-Tatar search since family is non-gaussian.
[1] 487
Morgan-Tatar search since family is non-gaussian.
[1] 488
Morgan-Tatar search since family is non-gaussian.
[1] 489
Morgan-Tatar search since family is non-gaussian.
[1] 490
Morgan-Tatar search since family is non-gaussian.
[1] 491
Morgan-Tatar search since family is non-gaussian.
[1] 492
Morgan-Tatar search since family is non-gaussian.
[1] 493
Morgan-Tatar search since family is non-gaussian.
[1] 494
Morgan-Tatar search since family is non-gaussian.
[1] 495
Morgan-Tatar search since family is non-gaussian.
[1] 496
Morgan-Tatar search since family is non-gaussian.
[1] 497
Morgan-Tatar search since family is non-gaussian.
[1] 498
Morgan-Tatar search since family is non-gaussian.
[1] 499
Morgan-Tatar search since family is non-gaussian.
[1] 500
Morgan-Tatar search since family is non-gaussian.
[1] 501
Morgan-Tatar search since family is non-gaussian.
[1] 502
Morgan-Tatar search since family is non-gaussian.
[1] 503
Morgan-Tatar search since family is non-gaussian.
[1] 504
Morgan-Tatar search since family is non-gaussian.
[1] 505
Morgan-Tatar search since family is non-gaussian.
[1] 506
Morgan-Tatar search since family is non-gaussian.
[1] 507
Morgan-Tatar search since family is non-gaussian.
[1] 508
Morgan-Tatar search since family is non-gaussian.
[1] 509
Morgan-Tatar search since family is non-gaussian.
[1] 510
Morgan-Tatar search since family is non-gaussian.
[1] 511
Morgan-Tatar search since family is non-gaussian.
[1] 512
Morgan-Tatar search since family is non-gaussian.
[1] 513
Morgan-Tatar search since family is non-gaussian.
[1] 514
Morgan-Tatar search since family is non-gaussian.
[1] 515
Morgan-Tatar search since family is non-gaussian.
[1] 516
Morgan-Tatar search since family is non-gaussian.
[1] 517
Morgan-Tatar search since family is non-gaussian.
[1] 518
Morgan-Tatar search since family is non-gaussian.
[1] 519
Morgan-Tatar search since family is non-gaussian.
[1] 520
Morgan-Tatar search since family is non-gaussian.
[1] 521
Morgan-Tatar search since family is non-gaussian.
[1] 522
Morgan-Tatar search since family is non-gaussian.
[1] 523
Morgan-Tatar search since family is non-gaussian.
[1] 524
Morgan-Tatar search since family is non-gaussian.
[1] 525
Morgan-Tatar search since family is non-gaussian.
[1] 526
Morgan-Tatar search since family is non-gaussian.
[1] 527
Morgan-Tatar search since family is non-gaussian.
[1] 528
Morgan-Tatar search since family is non-gaussian.
[1] 529
Morgan-Tatar search since family is non-gaussian.
[1] 530
Morgan-Tatar search since family is non-gaussian.
[1] 531
Morgan-Tatar search since family is non-gaussian.
[1] 532
Morgan-Tatar search since family is non-gaussian.
[1] 533
Morgan-Tatar search since family is non-gaussian.
[1] 534
Morgan-Tatar search since family is non-gaussian.
[1] 535
Morgan-Tatar search since family is non-gaussian.
[1] 536
Morgan-Tatar search since family is non-gaussian.
[1] 537
Morgan-Tatar search since family is non-gaussian.
[1] 538
Morgan-Tatar search since family is non-gaussian.
[1] 539
Morgan-Tatar search since family is non-gaussian.
[1] 540
Morgan-Tatar search since family is non-gaussian.
[1] 541
Morgan-Tatar search since family is non-gaussian.
[1] 542
Morgan-Tatar search since family is non-gaussian.
[1] 543
Morgan-Tatar search since family is non-gaussian.
[1] 544
Morgan-Tatar search since family is non-gaussian.
[1] 545
Morgan-Tatar search since family is non-gaussian.
[1] 546
Morgan-Tatar search since family is non-gaussian.
[1] 547
Morgan-Tatar search since family is non-gaussian.
[1] 548
Morgan-Tatar search since family is non-gaussian.
[1] 549
Morgan-Tatar search since family is non-gaussian.
[1] 550
Morgan-Tatar search since family is non-gaussian.
[1] 551
Morgan-Tatar search since family is non-gaussian.
[1] 552
Morgan-Tatar search since family is non-gaussian.
[1] 553
Morgan-Tatar search since family is non-gaussian.
[1] 554
Morgan-Tatar search since family is non-gaussian.
[1] 555
Morgan-Tatar search since family is non-gaussian.
[1] 556
Morgan-Tatar search since family is non-gaussian.
[1] 557
Morgan-Tatar search since family is non-gaussian.
[1] 558
Morgan-Tatar search since family is non-gaussian.
[1] 559
Morgan-Tatar search since family is non-gaussian.
[1] 560
Morgan-Tatar search since family is non-gaussian.
[1] 561
Morgan-Tatar search since family is non-gaussian.
[1] 562
Morgan-Tatar search since family is non-gaussian.
[1] 563
Morgan-Tatar search since family is non-gaussian.
[1] 564
Morgan-Tatar search since family is non-gaussian.
[1] 565
Morgan-Tatar search since family is non-gaussian.
[1] 566
Morgan-Tatar search since family is non-gaussian.
[1] 567
Morgan-Tatar search since family is non-gaussian.
[1] 568
Morgan-Tatar search since family is non-gaussian.
[1] 569
Morgan-Tatar search since family is non-gaussian.
[1] 570
Morgan-Tatar search since family is non-gaussian.
[1] 571
Morgan-Tatar search since family is non-gaussian.
[1] 572
Morgan-Tatar search since family is non-gaussian.
[1] 573
Morgan-Tatar search since family is non-gaussian.
[1] 574
Morgan-Tatar search since family is non-gaussian.
[1] 575
Morgan-Tatar search since family is non-gaussian.
[1] 576
Morgan-Tatar search since family is non-gaussian.
[1] 577
Morgan-Tatar search since family is non-gaussian.
[1] 578
Morgan-Tatar search since family is non-gaussian.
[1] 579
Morgan-Tatar search since family is non-gaussian.
[1] 580
Morgan-Tatar search since family is non-gaussian.
[1] 581
Morgan-Tatar search since family is non-gaussian.
[1] 582
Morgan-Tatar search since family is non-gaussian.
[1] 583
Morgan-Tatar search since family is non-gaussian.
[1] 584
Morgan-Tatar search since family is non-gaussian.
[1] 585
Morgan-Tatar search since family is non-gaussian.
[1] 586
Morgan-Tatar search since family is non-gaussian.
[1] 587
Morgan-Tatar search since family is non-gaussian.
[1] 588
Morgan-Tatar search since family is non-gaussian.
[1] 589
Morgan-Tatar search since family is non-gaussian.
[1] 590
Morgan-Tatar search since family is non-gaussian.
[1] 591
Morgan-Tatar search since family is non-gaussian.
[1] 592
Morgan-Tatar search since family is non-gaussian.
[1] 593
Morgan-Tatar search since family is non-gaussian.
[1] 594
Morgan-Tatar search since family is non-gaussian.
[1] 595
Morgan-Tatar search since family is non-gaussian.
[1] 596
Morgan-Tatar search since family is non-gaussian.
[1] 597
Morgan-Tatar search since family is non-gaussian.
[1] 598
Morgan-Tatar search since family is non-gaussian.
[1] 599
Morgan-Tatar search since family is non-gaussian.
[1] 600
Morgan-Tatar search since family is non-gaussian.
[1] 601
Morgan-Tatar search since family is non-gaussian.
[1] 602
Morgan-Tatar search since family is non-gaussian.
[1] 603
Morgan-Tatar search since family is non-gaussian.
[1] 604
Morgan-Tatar search since family is non-gaussian.
[1] 605
Morgan-Tatar search since family is non-gaussian.
[1] 606
Morgan-Tatar search since family is non-gaussian.
[1] 607
Morgan-Tatar search since family is non-gaussian.
[1] 608
Morgan-Tatar search since family is non-gaussian.
[1] 609
Morgan-Tatar search since family is non-gaussian.
[1] 610
Morgan-Tatar search since family is non-gaussian.
[1] 611
Morgan-Tatar search since family is non-gaussian.
[1] 612
Morgan-Tatar search since family is non-gaussian.
[1] 613
Morgan-Tatar search since family is non-gaussian.
[1] 614
Morgan-Tatar search since family is non-gaussian.
[1] 615
Morgan-Tatar search since family is non-gaussian.
[1] 616
Morgan-Tatar search since family is non-gaussian.
[1] 617
Morgan-Tatar search since family is non-gaussian.
[1] 618
Morgan-Tatar search since family is non-gaussian.
[1] 619
Morgan-Tatar search since family is non-gaussian.
[1] 620
Morgan-Tatar search since family is non-gaussian.
[1] 621
Morgan-Tatar search since family is non-gaussian.
[1] 622
Morgan-Tatar search since family is non-gaussian.
[1] 623
Morgan-Tatar search since family is non-gaussian.
[1] 624
Morgan-Tatar search since family is non-gaussian.
[1] 625
Morgan-Tatar search since family is non-gaussian.
[1] 626
Morgan-Tatar search since family is non-gaussian.
[1] 627
Morgan-Tatar search since family is non-gaussian.
[1] 628
Morgan-Tatar search since family is non-gaussian.
[1] 629
Morgan-Tatar search since family is non-gaussian.
[1] 630
Morgan-Tatar search since family is non-gaussian.
[1] 631
Morgan-Tatar search since family is non-gaussian.
[1] 632
Morgan-Tatar search since family is non-gaussian.
[1] 633
Morgan-Tatar search since family is non-gaussian.
[1] 634
Morgan-Tatar search since family is non-gaussian.
[1] 635
Morgan-Tatar search since family is non-gaussian.
[1] 636
Morgan-Tatar search since family is non-gaussian.
[1] 637
Morgan-Tatar search since family is non-gaussian.
[1] 638
Morgan-Tatar search since family is non-gaussian.
[1] 639
Morgan-Tatar search since family is non-gaussian.
[1] 640
Morgan-Tatar search since family is non-gaussian.
[1] 641
Morgan-Tatar search since family is non-gaussian.
[1] 642
Morgan-Tatar search since family is non-gaussian.
[1] 643
Morgan-Tatar search since family is non-gaussian.
[1] 644
Morgan-Tatar search since family is non-gaussian.
[1] 645
Morgan-Tatar search since family is non-gaussian.
[1] 646
Morgan-Tatar search since family is non-gaussian.
[1] 647
Morgan-Tatar search since family is non-gaussian.
[1] 648
Morgan-Tatar search since family is non-gaussian.
[1] 649
Morgan-Tatar search since family is non-gaussian.
[1] 650
Morgan-Tatar search since family is non-gaussian.
[1] 651
Morgan-Tatar search since family is non-gaussian.
[1] 652
Morgan-Tatar search since family is non-gaussian.
[1] 653
Morgan-Tatar search since family is non-gaussian.
[1] 654
Morgan-Tatar search since family is non-gaussian.
[1] 655
Morgan-Tatar search since family is non-gaussian.
[1] 656
Morgan-Tatar search since family is non-gaussian.
[1] 657
Morgan-Tatar search since family is non-gaussian.
[1] 658
Morgan-Tatar search since family is non-gaussian.
[1] 659
Morgan-Tatar search since family is non-gaussian.
[1] 660
Morgan-Tatar search since family is non-gaussian.
[1] 661
Morgan-Tatar search since family is non-gaussian.
[1] 662
Morgan-Tatar search since family is non-gaussian.
[1] 663
Morgan-Tatar search since family is non-gaussian.
[1] 664
Morgan-Tatar search since family is non-gaussian.
[1] 665
Morgan-Tatar search since family is non-gaussian.
[1] 666
Morgan-Tatar search since family is non-gaussian.
[1] 667
Morgan-Tatar search since family is non-gaussian.
[1] 668
Morgan-Tatar search since family is non-gaussian.
[1] 669
Morgan-Tatar search since family is non-gaussian.
[1] 670
Morgan-Tatar search since family is non-gaussian.
[1] 671
Morgan-Tatar search since family is non-gaussian.
[1] 672
Morgan-Tatar search since family is non-gaussian.
[1] 673
Morgan-Tatar search since family is non-gaussian.
[1] 674
Morgan-Tatar search since family is non-gaussian.
[1] 675
Morgan-Tatar search since family is non-gaussian.
[1] 676
Morgan-Tatar search since family is non-gaussian.
[1] 677
Morgan-Tatar search since family is non-gaussian.
[1] 678
Morgan-Tatar search since family is non-gaussian.
[1] 679
Morgan-Tatar search since family is non-gaussian.
[1] 680
Morgan-Tatar search since family is non-gaussian.
[1] 681
Morgan-Tatar search since family is non-gaussian.
[1] 682
Morgan-Tatar search since family is non-gaussian.
[1] 683
Morgan-Tatar search since family is non-gaussian.
[1] 684
Morgan-Tatar search since family is non-gaussian.
[1] 685
Morgan-Tatar search since family is non-gaussian.
[1] 686
Morgan-Tatar search since family is non-gaussian.
[1] 687
Morgan-Tatar search since family is non-gaussian.
[1] 688
Morgan-Tatar search since family is non-gaussian.
[1] 689
Morgan-Tatar search since family is non-gaussian.
[1] 690
Morgan-Tatar search since family is non-gaussian.
[1] 691
Morgan-Tatar search since family is non-gaussian.
[1] 692
Morgan-Tatar search since family is non-gaussian.
[1] 693
Morgan-Tatar search since family is non-gaussian.
[1] 694
Morgan-Tatar search since family is non-gaussian.
[1] 695
Morgan-Tatar search since family is non-gaussian.
[1] 696
Morgan-Tatar search since family is non-gaussian.
[1] 697
Morgan-Tatar search since family is non-gaussian.
[1] 698
Morgan-Tatar search since family is non-gaussian.
[1] 699
Morgan-Tatar search since family is non-gaussian.
[1] 700
Morgan-Tatar search since family is non-gaussian.
[1] 701
Morgan-Tatar search since family is non-gaussian.
[1] 702
Morgan-Tatar search since family is non-gaussian.
[1] 703
Morgan-Tatar search since family is non-gaussian.
[1] 704
Morgan-Tatar search since family is non-gaussian.
[1] 705
Morgan-Tatar search since family is non-gaussian.
[1] 706
Morgan-Tatar search since family is non-gaussian.
[1] 707
Morgan-Tatar search since family is non-gaussian.
[1] 708
Morgan-Tatar search since family is non-gaussian.
[1] 709
Morgan-Tatar search since family is non-gaussian.
[1] 710
Morgan-Tatar search since family is non-gaussian.
[1] 711
Morgan-Tatar search since family is non-gaussian.
[1] 712
Morgan-Tatar search since family is non-gaussian.
[1] 713
Morgan-Tatar search since family is non-gaussian.
[1] 714
Morgan-Tatar search since family is non-gaussian.
[1] 715
Morgan-Tatar search since family is non-gaussian.
[1] 716
Morgan-Tatar search since family is non-gaussian.
[1] 717
Morgan-Tatar search since family is non-gaussian.
[1] 718
Morgan-Tatar search since family is non-gaussian.
[1] 719
Morgan-Tatar search since family is non-gaussian.
[1] 720
Morgan-Tatar search since family is non-gaussian.
[1] 721
Morgan-Tatar search since family is non-gaussian.
[1] 722
Morgan-Tatar search since family is non-gaussian.
[1] 723
Morgan-Tatar search since family is non-gaussian.
[1] 724
Morgan-Tatar search since family is non-gaussian.
[1] 725
Morgan-Tatar search since family is non-gaussian.
[1] 726
Morgan-Tatar search since family is non-gaussian.
[1] 727
Morgan-Tatar search since family is non-gaussian.
[1] 728
Morgan-Tatar search since family is non-gaussian.
[1] 729
Morgan-Tatar search since family is non-gaussian.
[1] 730
Morgan-Tatar search since family is non-gaussian.
[1] 731
Morgan-Tatar search since family is non-gaussian.
[1] 732
Morgan-Tatar search since family is non-gaussian.
[1] 733
Morgan-Tatar search since family is non-gaussian.
[1] 734
Morgan-Tatar search since family is non-gaussian.
[1] 735
Morgan-Tatar search since family is non-gaussian.
[1] 736
Morgan-Tatar search since family is non-gaussian.
[1] 737
Morgan-Tatar search since family is non-gaussian.
[1] 738
Morgan-Tatar search since family is non-gaussian.
[1] 739
Morgan-Tatar search since family is non-gaussian.
[1] 740
Morgan-Tatar search since family is non-gaussian.
[1] 741
Morgan-Tatar search since family is non-gaussian.
[1] 742
Morgan-Tatar search since family is non-gaussian.
[1] 743
Morgan-Tatar search since family is non-gaussian.
[1] 744
Morgan-Tatar search since family is non-gaussian.
[1] 745
Morgan-Tatar search since family is non-gaussian.
[1] 746
Morgan-Tatar search since family is non-gaussian.
[1] 747
Morgan-Tatar search since family is non-gaussian.
[1] 748
Morgan-Tatar search since family is non-gaussian.
[1] 749
Morgan-Tatar search since family is non-gaussian.
[1] 750
Morgan-Tatar search since family is non-gaussian.
[1] 751
Morgan-Tatar search since family is non-gaussian.
[1] 752
Morgan-Tatar search since family is non-gaussian.
[1] 753
Morgan-Tatar search since family is non-gaussian.
[1] 754
Morgan-Tatar search since family is non-gaussian.
[1] 755
Morgan-Tatar search since family is non-gaussian.
[1] 756
Morgan-Tatar search since family is non-gaussian.
[1] 757
Morgan-Tatar search since family is non-gaussian.
[1] 758
Morgan-Tatar search since family is non-gaussian.
[1] 759
Morgan-Tatar search since family is non-gaussian.
[1] 760
Morgan-Tatar search since family is non-gaussian.
[1] 761
Morgan-Tatar search since family is non-gaussian.
[1] 762
Morgan-Tatar search since family is non-gaussian.
[1] 763
Morgan-Tatar search since family is non-gaussian.
[1] 764
Morgan-Tatar search since family is non-gaussian.
[1] 765
Morgan-Tatar search since family is non-gaussian.
[1] 766
Morgan-Tatar search since family is non-gaussian.
[1] 767
Morgan-Tatar search since family is non-gaussian.
[1] 768
Morgan-Tatar search since family is non-gaussian.
[1] 769
Morgan-Tatar search since family is non-gaussian.
[1] 770
Morgan-Tatar search since family is non-gaussian.
[1] 771
Morgan-Tatar search since family is non-gaussian.
[1] 772
Morgan-Tatar search since family is non-gaussian.
[1] 773
Morgan-Tatar search since family is non-gaussian.
[1] 774
Morgan-Tatar search since family is non-gaussian.
[1] 775
Morgan-Tatar search since family is non-gaussian.
[1] 776
Morgan-Tatar search since family is non-gaussian.
[1] 777
Morgan-Tatar search since family is non-gaussian.
[1] 778
Morgan-Tatar search since family is non-gaussian.
[1] 779
Morgan-Tatar search since family is non-gaussian.
[1] 780
Morgan-Tatar search since family is non-gaussian.
[1] 781
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Morgan-Tatar search since family is non-gaussian.sort(apply(bs_auc_i,2, mean,na.rm =T)) 3 2 1
0.5497076 0.5844839 0.7185561 GLM
Best subset selection, best : 1 variables
best.fit <- bestglm(dta2_vs[,c(2:4,1)],
IC="AIC",method ="exhaustive",family=binomial,nvmax = 1)##???)Morgan-Tatar search since family is non-gaussian.summary(best.fit$BestModel)
Call:
glm(formula = y ~ ., family = family, data = Xi, weights = weights)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.7242 -0.9143 0.3820 0.8524 2.0069
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.8311 0.6805 1.221 0.2220
Channel_8_Channel_5 -3.8347 1.9310 -1.986 0.0471 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 26.287 on 18 degrees of freedom
Residual deviance: 20.690 on 17 degrees of freedom
AIC: 24.69
Number of Fisher Scoring iterations: 4GLM
Lm : Ch8_Ch5
auc_mat_lm <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
# Channel_8_Channel_5
fit <- glm(Word_C~Channel_8_Channel_5,
data = dta2_vs[idc_train,],family = "binomial")
yhat <- predict(fit,newdata = dta2_vs[idc_test,],type = "response")
auc_mat_lm[k,] <- pROC::auc(dta2_vs[idc_test,]$Word_C,yhat)
}
mean(auc_mat_lm) # 0.791[1] 0.7911667quantile(auc_mat_lm,probs = c(0.025,0.975)) # 0.5555556 1.0000000 2.5% 97.5%
0.5555556 1.0000000 RF
Default mtry and nodesize
auc_mat_rf_3 <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
fit <- randomForest(Word_C~. ,
data = dta2_vs[idc_train,],
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta2[idc_test,],type = "prob")[,2]
auc_mat_rf_3[k,] <- pROC::auc(dta2_vs[idc_test,]$Word_C,yhat)
}
mean(auc_mat_rf_3) [1] 0.7997778quantile(auc_mat_rf_3,probs = c(0.025,0.975)) 2.5% 97.5%
0.5 1.0 RF
mtry = 1 ; nodesize = 7
auc_mat_rf_3_tune <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
fit <- randomForest(Word_C~. ,
data = dta2_vs[idc_train,],
mtry = 1 ,nodesize = 7,
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta2[idc_test,],type = "prob")[,2]
auc_mat_rf_3_tune[k,] <- pROC::auc(dta2_vs[idc_test,]$Word_C,yhat)
}
mean(auc_mat_rf_3_tune) [1] 0.8253889quantile(auc_mat_rf_3_tune,probs = c(0.025,0.975)) 2.5% 97.5%
0.5555556 1.0000000 # 9 var = 0.729
# 7 var = 0.726
# 6 var = 0.748
# 5 var = 0.779
#### mtry = 1 ,nodesize = 4 ; 0.797
# 3 var = 0.799
#### mtry = 1 ,nodesize = 7 ; 0.8253889
# 2 var = 0.7333889RF 2
AUC > 0.74 : 5 variables
Default metry and nodesize
head(na.omit(cbind(p_lm[order(p_lm$pvalue),c(2,1)],
vs <- auc_lm[order(-auc_lm$AUC),c(2,1)])),10) variable pvalue variable AUC
29 Channel_8_Channel_5 0.04705111 Channel_4_Channel_1 0.7777778
7 Channel_4_Channel_1 0.05937883 Channel_8_Channel_5 0.7777778
8 Channel_4_Channel_2 0.08392544 Channel_5_Channel_4 0.7555556
13 Channel_5_Channel_4 0.09553314 Channel_3_Channel_1 0.7444444
12 Channel_5_Channel_3 0.09629423 Channel_7_Channel_1 0.7444444
19 Channel_7_Channel_1 0.10024331 Channel_5_Channel_3 0.7333333
5 Channel_3_Channel_1 0.11573316 Channel_4_Channel_2 0.7222222
23 Channel_7_Channel_5 0.14191010 Channel_2_Channel_1 0.7111111
6 Channel_3_Channel_2 0.16463977 Channel_7_Channel_5 0.7111111
4 Channel_2_Channel_1 0.18213073 Channel_7_Channel_2 0.6888889dta2_vs<- dta2[,c("Word_C",filter(vs,AUC > 0.74)$variable)]
auc_mat_rf_5 <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
fit <- randomForest(Word_C~. ,
data = dta2_vs[idc_train,],
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta2[idc_test,],type = "prob")[,2]
auc_mat_rf_5[k,] <- pROC::auc(dta2_vs[idc_test,]$Word_C,yhat)
}
mean(auc_mat_rf_5) [1] 0.7790556quantile(auc_mat_rf_5,probs = c(0.025,0.975)) 2.5% 97.5%
0.4444444 1.0000000 RF 2
AUC > 0.74 : 5 variables
mtry = 1 ,nodesize = 7
auc_mat_rf_5_tune <- matrix(NA,1000,1)
for (k in 1:1000){
set.seed(k)
idc_test <- c(sample(which(dta2_vs$Word_C == "H"), 3),
sample(which(dta2_vs$Word_C == "L"), 3))
idc_train <- -idc_test
fit <- randomForest(Word_C~. ,
data = dta2_vs[idc_train,],
mtry = 1 ,nodesize = 4,##
ntree = 10001,importance = F)
yhat <- predict(fit,newdata = dta2[idc_test,],type = "prob")[,2]
auc_mat_rf_5_tune[k,] <- pROC::auc(dta2_vs[idc_test,]$Word_C,yhat)
}
mean(auc_mat_rf_5_tune) [1] 0.797quantile(auc_mat_rf_5_tune,probs = c(0.025,0.975)) 2.5% 97.5%
0.4444444 1.0000000 Comparsion
plotdta <- data.frame(GLM_1 = auc_mat_lm,
RF_3 = auc_mat_rf_3,
RF_3t = auc_mat_rf_3_tune,
RF_5 = auc_mat_rf_5,
RF_5t = auc_mat_rf_5_tune)
apply(plotdta,2,mean) GLM_1 RF_3 RF_3t RF_5 RF_5t
0.7911667 0.7997778 0.8253889 0.7790556 0.7970000 apply(plotdta,2,quantile,probs = 0.025) GLM_1 RF_3 RF_3t RF_5 RF_5t
0.5555556 0.5000000 0.5555556 0.4444444 0.4444444 apply(plotdta,2,quantile,probs = 0.975)GLM_1 RF_3 RF_3t RF_5 RF_5t
1 1 1 1 1 Comparsion
p <- melt(plotdta)
colnames(p)[1:2] <- c("Model","AUC")
Fig1 <- ggplot(p,aes(AUC,fill = Model, col = Model))+
geom_density(alpha = 0.3)+
theme_bw()+
xlab("AUC")
mdta <- ddply(p, "Model", summarise, average=mean(AUC))
prodta <- ddply(p,"Model",summarise,
Q.025 = quantile(AUC,probs = c(0.025)),
Q.975 = quantile(AUC,probs = c(0.975)))
Fig2 <- Fig1+
facet_grid(Model~.)+
geom_vline(data=mdta , aes(xintercept=average),
linetype="dashed", size=1, colour="red")+
geom_vline(data = prodta,aes(xintercept=Q.025),
linetype="dashed", size=1, colour="darkgoldenrod")+
geom_vline(data = prodta,aes(xintercept=Q.975),
linetype="dashed", size=1, colour="darkgoldenrod")
ggplotly(Fig1)Fig2