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<!DOCTYPE html>
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<head>
<title>Predictive Mapping with R</title>
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class: center, middle, inverse, title-slide
# Predictive Mapping with R
## Part III: Naive Bayesian
### Martin Hinz
### 4.2.2019
---
class: inverse, center, middle
# Naive Bayesian
---
## Introducing Bayesian classifier
.tiny[
```r
library(e1071)
soiltype <- sample(c("Chernozem", "Brown soil"), size=20, replace=T)
settlement_c <- sample(c(T,F), size=sum(soiltype=="Chernozem"), prob = c(0.8,0.2), replace=T)
settlement_b <- sample(c(T,F), size=sum(soiltype=="Brown soil"), prob = c(0.2,0.8), replace=T)
set_soil <- data.frame(soiltype = soiltype)
set_soil$settlement[soiltype=="Chernozem"] <- settlement_c
set_soil$settlement[soiltype=="Brown soil"] <- settlement_b
```
]
.pull-left[
.tiny[
```r
table(set_soil)
```
```
## settlement
## soiltype FALSE TRUE
## Brown soil 10 3
## Chernozem 1 6
```
```r
prop.table(table(set_soil), margin = 2)
```
```
## settlement
## soiltype FALSE TRUE
## Brown soil 0.90909091 0.33333333
## Chernozem 0.09090909 0.66666667
```
]]
.pull-right[
.tiny[
```r
naiveBayes(settlement ~ soiltype,
data = set_soil)
```
```
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## FALSE TRUE
## 0.55 0.45
##
## Conditional probabilities:
## soiltype
## Y Brown soil Chernozem
## FALSE 0.90909091 0.09090909
## TRUE 0.33333333 0.66666667
```
]]
---
## Introducing Bayesian classifier
.tiny[
```r
bm <- naiveBayes(settlement ~ soiltype,
data = set_soil)
predict(bm, newdata = set_soil)
```
```
## [1] TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [12] FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
```
```r
predict(bm, newdata = set_soil, type = "raw")
```
```
## FALSE TRUE
## [1,] 0.1428571 0.8571429
## [2,] 0.1428571 0.8571429
## [3,] 0.7692308 0.2307692
## [4,] 0.1428571 0.8571429
## [5,] 0.7692308 0.2307692
## [6,] 0.7692308 0.2307692
## [7,] 0.7692308 0.2307692
## [8,] 0.1428571 0.8571429
## [9,] 0.7692308 0.2307692
## [10,] 0.7692308 0.2307692
## [11,] 0.7692308 0.2307692
## [12,] 0.7692308 0.2307692
## [13,] 0.1428571 0.8571429
## [14,] 0.7692308 0.2307692
## [15,] 0.7692308 0.2307692
## [16,] 0.1428571 0.8571429
## [17,] 0.1428571 0.8571429
## [18,] 0.7692308 0.2307692
## [19,] 0.7692308 0.2307692
## [20,] 0.7692308 0.2307692
```
]
---
## Introducing Bayesian classifier
Add another predictor
.tiny[
```r
aspect_s <- sample(c("N","S"), size=sum(set_soil$settlement), prob = c(0.8,0.2), replace=T)
aspect_n <- sample(c("N","S"), size=sum(!set_soil$settlement), prob = c(0.2,0.8), replace=T)
set_soil$aspect[set_soil$settlement] <- aspect_s
set_soil$aspect[!set_soil$settlement] <- aspect_n
```
]
.tiny[
```r
bm <- naiveBayes(settlement ~ soiltype + aspect,
data = set_soil)
bm
```
```
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## FALSE TRUE
## 0.55 0.45
##
## Conditional probabilities:
## soiltype
## Y Brown soil Chernozem
## FALSE 0.90909091 0.09090909
## TRUE 0.33333333 0.66666667
##
## aspect
## Y N S
## FALSE 0.2727273 0.7272727
## TRUE 0.8888889 0.1111111
```
]
---
## Introducing Bayesian classifier
resulting combined probabilities
.tiny[
```r
cbind(predict(bm, newdata = set_soil, type = "raw"), as.character(set_soil$soiltype), set_soil$aspect)
```
```
## FALSE TRUE
## [1,] "0.0486486486486487" "0.951351351351351" "Chernozem" "N"
## [2,] "0.521739130434783" "0.478260869565217" "Chernozem" "S"
## [3,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [4,] "0.0486486486486487" "0.951351351351351" "Chernozem" "N"
## [5,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [6,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [7,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [8,] "0.0486486486486487" "0.951351351351351" "Chernozem" "N"
## [9,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [10,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [11,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [12,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [13,] "0.521739130434783" "0.478260869565217" "Chernozem" "S"
## [14,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [15,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
## [16,] "0.0486486486486487" "0.951351351351351" "Chernozem" "N"
## [17,] "0.0486486486486487" "0.951351351351351" "Chernozem" "N"
## [18,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [19,] "0.50561797752809" "0.49438202247191" "Brown soil" "N"
## [20,] "0.956175298804781" "0.0438247011952191" "Brown soil" "S"
```
]
---
## Resetting the stage
.tiny[
Loading Libraries
```r
library(sp)
library(raster)
```
```
##
## Attaching package: 'raster'
```
```
## The following object is masked from 'package:e1071':
##
## interpolate
```
```r
library(mapview)
```
Reading Data
```r
load("data/pred_data2.RData")
source("scripts/model_gain.R")
evidence$aspect <- factor(evidence$aspect)
evidence$site_b <- factor(evidence$site)
env_data.df <- as.data.frame(env_data)
env_data.df$aspect <- factor(env_data.df$aspect)
```
]
---
## Doing the calculation
```r
fit.bayes <- naiveBayes(site_b ~ tpi + slope + aspect,
data=evidence)
```
Model description (trivial):
If something is a site depends on the tpi, the slope and the aspect (as factor). We use our evidence.
---
## Resulting Model
.tiny[
```r
fit.bayes
```
```
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## FALSE TRUE
## 0.93810445 0.06189555
##
## Conditional probabilities:
## tpi
## Y [,1] [,2]
## FALSE -0.9293701 78.22160
## TRUE -19.2822300 26.47506
##
## slope
## Y [,1] [,2]
## FALSE 9.268849 8.023070
## TRUE 3.275290 2.711175
##
## aspect
## Y 1 2 3 4 5 6
## FALSE 0.13195876 0.12061856 0.11855670 0.14226804 0.09484536 0.10927835
## TRUE 0.01562500 0.15625000 0.01562500 0.09375000 0.21875000 0.25000000
## aspect
## Y 7 8
## FALSE 0.12474227 0.15773196
## TRUE 0.04687500 0.20312500
```
]
---
## Repredicting our evidence
.tiny[
.pull-left[
```r
pcdata.bayes.raw <- predict(fit.bayes,
newdata = evidence,
* type="raw")
pcdata.bayes.raw
```
```
## FALSE TRUE
## [1,] 0.4983422 5.016578e-01
## [2,] 0.7193047 2.806953e-01
## [3,] 0.5372025 4.627975e-01
## [4,] 0.5372025 4.627975e-01
## [5,] 0.9872989 1.270108e-02
## [6,] 0.3719656 6.280344e-01
## [7,] 0.3530095 6.469905e-01
## [8,] 0.3762769 6.237231e-01
## [9,] 0.6337556 3.662444e-01
## [10,] 0.8374614 1.625386e-01
## [11,] 0.6302694 3.697306e-01
## [12,] 0.7992606 2.007394e-01
## [13,] 0.4034972 5.965028e-01
## [14,] 0.5462047 4.537953e-01
## [15,] 0.5310865 4.689135e-01
## [16,] 0.4212243 5.787757e-01
## [17,] 0.3746631 6.253369e-01
## [18,] 0.5330024 4.669976e-01
## [19,] 0.4042117 5.957883e-01
## [20,] 0.7299769 2.700231e-01
## [21,] 0.4662446 5.337554e-01
## [22,] 0.6042074 3.957926e-01
## [23,] 0.3762769 6.237231e-01
## [24,] 0.3597841 6.402159e-01
## [25,] 0.4220412 5.779588e-01
## [26,] 0.7390901 2.609099e-01
## [27,] 0.3719656 6.280344e-01
## [28,] 0.5029445 4.970555e-01
## [29,] 0.3947632 6.052368e-01
## [30,] 0.7684449 2.315551e-01
## [31,] 0.3994348 6.005652e-01
## [32,] 0.3994348 6.005652e-01
## [33,] 0.8677742 1.322258e-01
## [34,] 0.4976970 5.023030e-01
## [35,] 0.7193047 2.806953e-01
## [36,] 0.7382371 2.617629e-01
## [37,] 0.4467905 5.532095e-01
## [38,] 0.7193047 2.806953e-01
## [39,] 0.4034972 5.965028e-01
## [40,] 0.9999999 5.634363e-08
## [41,] 0.6337556 3.662444e-01
## [42,] 0.9374049 6.259506e-02
## [43,] 0.5408298 4.591702e-01
## [44,] 0.5938658 4.061342e-01
## [45,] 0.7320978 2.679022e-01
## [46,] 0.4212243 5.787757e-01
## [47,] 0.4034972 5.965028e-01
## [48,] 0.7684449 2.315551e-01
## [49,] 0.6337556 3.662444e-01
## [50,] 0.6337556 3.662444e-01
## [51,] 0.9124525 8.754750e-02
## [52,] 0.4014621 5.985379e-01
## [53,] 0.3871034 6.128966e-01
## [54,] 0.5721978 4.278022e-01
## [55,] 0.9997120 2.879681e-04
## [56,] 0.9841762 1.582376e-02
## [57,] 0.4032998 5.967002e-01
## [58,] 0.4212243 5.787757e-01
## [59,] 0.8015759 1.984241e-01
## [60,] 0.5140536 4.859464e-01
## [61,] 0.5605499 4.394501e-01
## [62,] 0.4921045 5.078955e-01
## [63,] 0.4212243 5.787757e-01
## [64,] 0.7193047 2.806953e-01
## [65,] 0.4500468 5.499532e-01
## [66,] 1.0000000 6.329120e-18
## [67,] 1.0000000 5.745524e-11
## [68,] 0.6953380 3.046620e-01
## [69,] 0.9989215 1.078487e-03
## [70,] 1.0000000 7.856779e-13
## [71,] 0.4768496 5.231504e-01
## [72,] 0.9424246 5.757536e-02
## [73,] 0.9997870 2.130044e-04
## [74,] 0.7484381 2.515619e-01
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## [76,] 0.6752529 3.247471e-01
## [77,] 0.5304728 4.695272e-01
## [78,] 0.9999999 1.126220e-07
## [79,] 0.9174948 8.250516e-02
## [80,] 0.9365559 6.344412e-02
## [81,] 0.9269101 7.308991e-02
## [82,] 0.7607296 2.392704e-01
## [83,] 0.4710185 5.289815e-01
## [84,] 0.9933304 6.669617e-03
## [85,] 0.7874711 2.125289e-01
## [86,] 1.0000000 2.871345e-09
## [87,] 0.9365888 6.341117e-02
## [88,] 0.5057701 4.942299e-01
## [89,] 1.0000000 1.010619e-09
## [90,] 0.9908962 9.103781e-03
## [91,] 0.6204856 3.795144e-01
## [92,] 1.0000000 4.711954e-21
## [93,] 0.9984442 1.555831e-03
## [94,] 0.5928195 4.071805e-01
## [95,] 0.5326522 4.673478e-01
## [96,] 1.0000000 3.614784e-12
## [97,] 0.6695622 3.304378e-01
## [98,] 0.9999982 1.752916e-06
## [99,] 0.8430265 1.569735e-01
## [100,] 0.9999999 7.418492e-08
## [101,] 0.3702023 6.297977e-01
## [102,] 0.9999999 1.194275e-07
## [103,] 0.8059527 1.940473e-01
## [104,] 0.9999989 1.050409e-06
## [105,] 0.9999998 2.439184e-07
## [106,] 0.8636647 1.363353e-01
## [107,] 0.5997266 4.002734e-01
## [108,] 0.5196147 4.803853e-01
## [109,] 0.9982402 1.759758e-03
## [110,] 0.9390365 6.096347e-02
## [111,] 1.0000000 1.506149e-10
## [112,] 1.0000000 2.561877e-29
## [113,] 0.9999987 1.255138e-06
## [114,] 1.0000000 1.587198e-09
## [115,] 0.9643389 3.566107e-02
## [116,] 1.0000000 6.087979e-11
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## [118,] 1.0000000 1.682101e-10
## [119,] 0.9999997 3.209917e-07
## [120,] 0.9935285 6.471518e-03
## [121,] 0.7484851 2.515149e-01
## [122,] 1.0000000 4.730729e-18
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## [124,] 0.4679492 5.320508e-01
## [125,] 0.9991514 8.485951e-04
## [126,] 1.0000000 1.500743e-13
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## [128,] 0.3506623 6.493377e-01
## [129,] 0.5314951 4.685049e-01
## [130,] 0.7396609 2.603391e-01
## [131,] 1.0000000 7.467163e-23
## [132,] 0.9942883 5.711709e-03
## [133,] 0.9998306 1.693971e-04
## [134,] 1.0000000 1.112347e-10
## [135,] 0.9999995 4.918910e-07
## [136,] 0.6247507 3.752493e-01
## [137,] 1.0000000 1.211423e-13
## [138,] 0.7344326 2.655674e-01
## [139,] 1.0000000 3.382795e-11
## [140,] 0.7089063 2.910937e-01
## [141,] 0.7165871 2.834129e-01
## [142,] 0.9998687 1.312558e-04
## [143,] 1.0000000 6.217466e-15
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## [145,] 1.0000000 3.058180e-08
## [146,] 0.9998875 1.124504e-04
## [147,] 0.9523704 4.762960e-02
## [148,] 0.4971231 5.028769e-01
## [149,] 0.9165106 8.348941e-02
## [150,] 0.3545037 6.454963e-01
## [151,] 0.5603475 4.396525e-01
## [152,] 0.9991524 8.475813e-04
## [153,] 0.9926500 7.350005e-03
## [154,] 0.6827812 3.172188e-01
## [155,] 0.5846795 4.153205e-01
## [156,] 0.9929467 7.053347e-03
## [157,] 0.9638830 3.611698e-02
## [158,] 1.0000000 6.418381e-11
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## [160,] 0.6876666 3.123334e-01
## [161,] 0.8431880 1.568120e-01
## [162,] 0.9143547 8.564530e-02
## [163,] 1.0000000 2.716579e-12
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## [165,] 0.9093805 9.061950e-02
## [166,] 0.9999992 7.677395e-07
## [167,] 0.7725140 2.274860e-01
## [168,] 0.9999953 4.710955e-06
## [169,] 0.9998617 1.382705e-04
## [170,] 0.7924267 2.075733e-01
## [171,] 0.9999984 1.618886e-06
## [172,] 0.9997886 2.113798e-04
## [173,] 1.0000000 3.451454e-12
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## [175,] 0.7165976 2.834024e-01
## [176,] 0.5049364 4.950636e-01
## [177,] 0.9999826 1.737463e-05
## [178,] 0.9996974 3.025586e-04
## [179,] 0.8753202 1.246798e-01
## [180,] 1.0000000 2.351817e-28
## [181,] 0.3627759 6.372241e-01
## [182,] 0.9992064 7.936411e-04
## [183,] 0.7248286 2.751714e-01
## [184,] 1.0000000 2.582981e-09
## [185,] 0.9457722 5.422784e-02
## [186,] 0.6447717 3.552283e-01
## [187,] 1.0000000 2.920368e-26
## [188,] 0.9974917 2.508288e-03
## [189,] 0.7721384 2.278616e-01
## [190,] 0.5575681 4.424319e-01
## [191,] 0.7159696 2.840304e-01
## [192,] 0.9999886 1.139860e-05
## [193,] 0.9954224 4.577601e-03
## [194,] 0.9999992 7.529941e-07
## [195,] 0.6516910 3.483090e-01
## [196,] 1.0000000 1.576272e-12
## [197,] 0.9309025 6.909755e-02
## [198,] 0.9994235 5.765393e-04
## [199,] 1.0000000 2.183597e-13
## [200,] 1.0000000 9.503872e-15
## [201,] 0.9964038 3.596189e-03
## [202,] 1.0000000 1.091091e-10
## [203,] 0.5412363 4.587637e-01
## [204,] 0.6034654 3.965346e-01
## [205,] 0.9748107 2.518928e-02
## [206,] 1.0000000 2.981399e-22
## [207,] 0.9785776 2.142244e-02
## [208,] 0.9738108 2.618920e-02
## [209,] 0.9987028 1.297208e-03
## [210,] 1.0000000 4.951419e-23
## [211,] 1.0000000 2.690500e-08
## [212,] 0.9267270 7.327303e-02
## [213,] 0.9990532 9.467593e-04
## [214,] 0.5209290 4.790710e-01
## [215,] 0.9987517 1.248335e-03
## [216,] 1.0000000 1.563824e-10
## [217,] 0.9999405 5.952712e-05
## [218,] 0.8691642 1.308358e-01
## [219,] 0.9858276 1.417244e-02
## [220,] 0.4156180 5.843820e-01
## [221,] 1.0000000 1.919599e-08
## [222,] 0.9860014 1.399865e-02
## [223,] 0.3957023 6.042977e-01
## [224,] 0.9995325 4.675104e-04
## [225,] 1.0000000 1.393975e-12
## [226,] 1.0000000 3.835382e-10
## [227,] 0.5160902 4.839098e-01
## [228,] 0.5158144 4.841856e-01
## [229,] 0.6761446 3.238554e-01
## [230,] 0.9194183 8.058170e-02
## [231,] 0.9999999 6.635226e-08
## [232,] 0.5729533 4.270467e-01
## [233,] 0.6465974 3.534026e-01
## [234,] 0.4276206 5.723794e-01
## [235,] 0.9999329 6.709838e-05
## [236,] 0.9957173 4.282723e-03
## [237,] 0.9981359 1.864091e-03
## [238,] 0.9948598 5.140178e-03
## [239,] 0.9998638 1.361932e-04
## [240,] 0.8740790 1.259210e-01
## [241,] 1.0000000 1.898001e-20
## [242,] 1.0000000 3.773331e-10
## [243,] 0.6522527 3.477473e-01
## [244,] 0.9999968 3.176684e-06
## [245,] 0.4065797 5.934203e-01
## [246,] 0.4375626 5.624374e-01
## [247,] 0.9989185 1.081539e-03
## [248,] 0.9999904 9.554929e-06
## [249,] 1.0000000 7.187044e-57
## [250,] 0.9999998 1.903384e-07
## [251,] 0.9999627 3.726136e-05
## [252,] 0.9999070 9.304289e-05
## [253,] 1.0000000 4.942214e-08
## [254,] 0.9999737 2.630864e-05
## [255,] 0.5592034 4.407966e-01
## [256,] 0.9476336 5.236639e-02
## [257,] 0.7714190 2.285810e-01
## [258,] 1.0000000 5.549573e-16
## [259,] 0.3578593 6.421407e-01
## [260,] 0.3581136 6.418864e-01
## [261,] 0.9864669 1.353307e-02
## [262,] 0.9999997 3.076545e-07
## [263,] 0.6856109 3.143891e-01
## [264,] 0.9986249 1.375082e-03
## [265,] 0.5174639 4.825361e-01
## [266,] 0.9979517 2.048274e-03
## [267,] 0.9261242 7.387584e-02
## [268,] 0.9549601 4.503989e-02
## [269,] 0.9999999 1.465900e-07
## [270,] 0.8530333 1.469667e-01
## [271,] 0.9999925 7.536549e-06
## [272,] 1.0000000 8.322675e-10
## [273,] 1.0000000 2.389911e-17
## [274,] 0.9899891 1.001093e-02
## [275,] 0.8299387 1.700613e-01
## [276,] 1.0000000 2.097582e-11
## [277,] 0.4478617 5.521383e-01
## [278,] 0.4200617 5.799383e-01
## [279,] 1.0000000 1.778759e-11
## [280,] 1.0000000 3.259110e-16
## [281,] 0.9531086 4.689141e-02
## [282,] 1.0000000 1.121423e-10
## [283,] 0.7814427 2.185573e-01
## [284,] 0.5391352 4.608648e-01
## [285,] 0.8228862 1.771138e-01
## [286,] 0.9991581 8.418558e-04
## [287,] 0.9996395 3.604923e-04
## [288,] 0.7083215 2.916785e-01
## [289,] 1.0000000 1.834476e-08
## [290,] 1.0000000 1.092950e-26
## [291,] 0.5012747 4.987253e-01
## [292,] 0.6397328 3.602672e-01
## [293,] 0.9999511 4.893526e-05
## [294,] 1.0000000 3.120393e-18
## [295,] 0.9999339 6.605584e-05
## [296,] 1.0000000 6.777592e-10
## [297,] 1.0000000 3.389046e-26
## [298,] 0.8129709 1.870291e-01
## [299,] 0.6071779 3.928221e-01
## [300,] 0.5103754 4.896246e-01
## [301,] 0.9445025 5.549753e-02
## [302,] 0.9176125 8.238750e-02
## [303,] 1.0000000 1.274488e-17
## [304,] 0.9866532 1.334677e-02
## [305,] 0.9999939 6.061134e-06
## [306,] 0.5467504 4.532496e-01
## [307,] 0.9973158 2.684238e-03
## [308,] 0.7324128 2.675872e-01
## [309,] 0.9999960 3.976972e-06
## [310,] 0.9999501 4.987814e-05
## [311,] 0.9999962 3.751470e-06
## [312,] 0.9999999 9.082663e-08
## [313,] 1.0000000 7.922809e-09
## [314,] 0.6189410 3.810590e-01
## [315,] 0.9276013 7.239871e-02
## [316,] 0.7023033 2.976967e-01
## [317,] 0.5945467 4.054533e-01
## [318,] 1.0000000 3.539197e-12
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## [320,] 1.0000000 3.506396e-09
## [321,] 0.3864160 6.135840e-01
## [322,] 1.0000000 1.082627e-09
## [323,] 0.6459419 3.540581e-01
## [324,] 0.9057889 9.421107e-02
## [325,] 0.5896859 4.103141e-01
## [326,] 0.6841668 3.158332e-01
## [327,] 0.7256056 2.743944e-01
## [328,] 0.9999941 5.906899e-06
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## [330,] 0.5805301 4.194699e-01
## [331,] 1.0000000 2.609093e-22
## [332,] 0.5019820 4.980180e-01
## [333,] 1.0000000 5.190345e-10
## [334,] 0.9999992 8.014204e-07
## [335,] 1.0000000 1.027201e-09
## [336,] 0.9999999 6.578257e-08
## [337,] 1.0000000 5.092233e-10
## [338,] 1.0000000 4.411397e-10
## [339,] 0.9230731 7.692694e-02
## [340,] 0.9439503 5.604975e-02
## [341,] 0.9988148 1.185246e-03
## [342,] 0.9999219 7.810728e-05
## [343,] 1.0000000 1.020454e-22
## [344,] 0.9122391 8.776088e-02
## [345,] 0.8948667 1.051333e-01
## [346,] 0.6743678 3.256322e-01
## [347,] 1.0000000 3.934769e-10
## [348,] 0.9999837 1.633631e-05
## [349,] 1.0000000 2.067260e-09
## [350,] 0.7528187 2.471813e-01
## [351,] 0.8715425 1.284575e-01
## [352,] 0.5030270 4.969730e-01
## [353,] 0.9763280 2.367201e-02
## [354,] 0.9765262 2.347378e-02
## [355,] 0.9999959 4.109997e-06
## [356,] 0.8681978 1.318022e-01
## [357,] 0.9985676 1.432378e-03
## [358,] 0.9999999 9.137969e-08
## [359,] 1.0000000 2.536130e-08
## [360,] 0.9998152 1.848077e-04
## [361,] 0.9925742 7.425750e-03
## [362,] 0.9328060 6.719402e-02
## [363,] 0.3833718 6.166282e-01
## [364,] 1.0000000 9.925835e-25
## [365,] 0.4751426 5.248574e-01
## [366,] 1.0000000 2.172914e-14
## [367,] 0.9498562 5.014380e-02
## [368,] 0.7829663 2.170337e-01
## [369,] 0.7697594 2.302406e-01
## [370,] 0.9684467 3.155326e-02
## [371,] 0.8719304 1.280696e-01
## [372,] 1.0000000 1.292479e-10
## [373,] 0.9716488 2.835117e-02
## [374,] 0.9535598 4.644016e-02
## [375,] 1.0000000 1.088433e-13
## [376,] 0.9608680 3.913204e-02
## [377,] 1.0000000 2.638506e-19
## [378,] 0.5445262 4.554738e-01
## [379,] 0.3968941 6.031059e-01
## [380,] 0.9226855 7.731447e-02
## [381,] 0.9995412 4.587658e-04
## [382,] 0.6278625 3.721375e-01
## [383,] 0.6091698 3.908302e-01
## [384,] 0.3964490 6.035510e-01
## [385,] 0.9999405 5.951981e-05
## [386,] 0.9999999 1.336334e-07
## [387,] 0.9999780 2.195349e-05
## [388,] 0.9699070 3.009299e-02
## [389,] 0.9794649 2.053507e-02
## [390,] 0.4913191 5.086809e-01
## [391,] 0.9988451 1.154949e-03
## [392,] 0.9989791 1.020922e-03
## [393,] 0.9970642 2.935839e-03
## [394,] 0.9694194 3.058057e-02
## [395,] 0.9992302 7.698051e-04
## [396,] 1.0000000 1.711602e-11
## [397,] 1.0000000 9.929747e-10
## [398,] 0.9637284 3.627161e-02
## [399,] 1.0000000 7.830469e-13
## [400,] 0.8014019 1.985981e-01
## [401,] 0.6550534 3.449466e-01
## [402,] 0.9035319 9.646805e-02
## [403,] 1.0000000 6.855750e-10
## [404,] 0.9424454 5.755464e-02
## [405,] 1.0000000 3.846581e-12
## [406,] 1.0000000 1.268050e-13
## [407,] 1.0000000 1.078898e-15
## [408,] 0.9978245 2.175543e-03
## [409,] 0.7901164 2.098836e-01
## [410,] 1.0000000 1.333294e-08
## [411,] 1.0000000 1.202508e-12
## [412,] 1.0000000 1.103050e-12
## [413,] 0.9966279 3.372053e-03
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## [415,] 0.6290828 3.709172e-01
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## [417,] 1.0000000 6.764281e-11
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## [421,] 1.0000000 1.799187e-16
## [422,] 1.0000000 3.524948e-12
## [423,] 0.8044075 1.955925e-01
## [424,] 0.9159464 8.405359e-02
## [425,] 1.0000000 3.705608e-17
## [426,] 1.0000000 4.328425e-16
## [427,] 0.5655923 4.344077e-01
## [428,] 1.0000000 8.166844e-14
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## [430,] 1.0000000 3.255161e-11
## [431,] 1.0000000 2.444135e-09
## [432,] 0.9999934 6.593000e-06
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## [434,] 0.9999998 1.825241e-07
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## [436,] 0.5971848 4.028152e-01
## [437,] 1.0000000 2.312995e-13
## [438,] 1.0000000 8.157671e-11
## [439,] 1.0000000 2.073581e-13
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## [441,] 1.0000000 3.002994e-10
## [442,] 0.8272040 1.727960e-01
## [443,] 1.0000000 4.951222e-19
## [444,] 1.0000000 2.696095e-26
## [445,] 0.8036692 1.963308e-01
## [446,] 0.9277302 7.226980e-02
## [447,] 0.9428652 5.713478e-02
## [448,] 0.9998516 1.483846e-04
## [449,] 1.0000000 4.376314e-12
## [450,] 1.0000000 9.673972e-12
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## [452,] 1.0000000 3.426188e-18
## [453,] 1.0000000 1.377992e-08
## [454,] 1.0000000 5.465340e-11
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## [456,] 1.0000000 4.291128e-10
## [457,] 0.9998835 1.165253e-04
## [458,] 0.9998507 1.493202e-04
## [459,] 0.9344622 6.553784e-02
## [460,] 0.9999503 4.970417e-05
## [461,] 1.0000000 6.530294e-17
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## [463,] 1.0000000 1.225962e-09
## [464,] 0.9999810 1.896065e-05
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## [468,] 0.5246095 4.753905e-01
## [469,] 0.9247853 7.521466e-02
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## [473,] 0.6438370 3.561630e-01
## [474,] 0.9935835 6.416510e-03
## [475,] 0.6195354 3.804646e-01
## [476,] 0.3854133 6.145867e-01
## [477,] 0.7640044 2.359956e-01
## [478,] 1.0000000 4.181668e-09
## [479,] 0.9999986 1.416236e-06
## [480,] 0.9280527 7.194731e-02
## [481,] 0.8227053 1.772947e-01
## [482,] 0.9999991 9.448901e-07
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## [484,] 0.7956134 2.043866e-01
## [485,] 0.8297798 1.702202e-01
## [486,] 1.0000000 5.849668e-09
## [487,] 0.6523252 3.476748e-01
## [488,] 1.0000000 1.721593e-11
## [489,] 0.9943796 5.620398e-03
## [490,] 0.9989022 1.097799e-03
## [491,] 0.7430280 2.569720e-01
## [492,] 0.9905373 9.462712e-03
## [493,] 1.0000000 2.497606e-19
## [494,] 0.6520767 3.479233e-01
## [495,] 0.9999980 1.972320e-06
## [496,] 1.0000000 1.002141e-08
## [497,] 0.9999999 1.241595e-07
## [498,] 0.4723408 5.276592e-01
## [499,] 0.9999446 5.537497e-05
## [500,] 0.9654356 3.456443e-02
## [501,] 0.9987625 1.237528e-03
## [502,] 1.0000000 5.930589e-10
## [503,] 0.6624727 3.375273e-01
## [504,] 0.9157071 8.429294e-02
## [505,] 0.9943543 5.645711e-03
## [506,] 0.7746187 2.253813e-01
## [507,] 0.9999998 2.067028e-07
## [508,] 0.6003786 3.996214e-01
## [509,] 1.0000000 3.391778e-18
## [510,] 1.0000000 9.666179e-10
## [511,] 0.7369340 2.630660e-01
## [512,] 0.5599483 4.400517e-01
## [513,] 0.9922834 7.716619e-03
## [514,] 1.0000000 4.798048e-13
## [515,] 0.7691459 2.308541e-01
## [516,] 0.9994276 5.724066e-04
## [517,] 0.9999611 3.894260e-05
## [518,] 1.0000000 1.871561e-21
## [519,] 0.9281023 7.189769e-02
## [520,] 1.0000000 1.177348e-09
## [521,] 0.9625993 3.740071e-02
## [522,] 0.9200536 7.994643e-02
## [523,] 0.7909727 2.090273e-01
## [524,] 1.0000000 1.292839e-09
## [525,] 0.3955828 6.044172e-01
## [526,] 0.5169640 4.830360e-01
## [527,] 0.6550112 3.449888e-01
## [528,] 0.6332652 3.667348e-01
## [529,] 1.0000000 2.922153e-25
## [530,] 0.4574305 5.425695e-01
## [531,] 0.9969278 3.072170e-03
## [532,] 0.9999999 5.402776e-08
## [533,] 1.0000000 9.637069e-14
## [534,] 0.9994655 5.344605e-04
## [535,] 0.3871034 6.128966e-01
## [536,] 0.9999539 4.606179e-05
## [537,] 0.5127810 4.872190e-01
## [538,] 0.9965335 3.466547e-03
## [539,] 0.9300968 6.990319e-02
## [540,] 0.8613909 1.386091e-01
## [541,] 0.9302977 6.970229e-02
## [542,] 1.0000000 1.532602e-15
## [543,] 1.0000000 1.830760e-14
## [544,] 0.9256671 7.433293e-02
## [545,] 0.5997790 4.002210e-01
## [546,] 0.9999999 1.022505e-07
## [547,] 0.9482021 5.179789e-02
## [548,] 0.9999999 9.984802e-08
## [549,] 0.9755971 2.440288e-02
## [550,] 0.9227712 7.722881e-02
## [551,] 1.0000000 2.365517e-12
## [552,] 1.0000000 1.069760e-10
## [553,] 1.0000000 1.762153e-09
## [554,] 0.4313684 5.686316e-01
## [555,] 0.7307796 2.692204e-01
## [556,] 0.9956786 4.321383e-03
## [557,] 1.0000000 4.798570e-12
## [558,] 0.9211309 7.886915e-02
## [559,] 0.9999721 2.787492e-05
## [560,] 0.9892624 1.073764e-02
## [561,] 0.5833401 4.166599e-01
## [562,] 0.9919856 8.014440e-03
## [563,] 0.6061515 3.938485e-01
## [564,] 0.9953035 4.696501e-03
## [565,] 0.9999660 3.402114e-05
## [566,] 1.0000000 5.573192e-10
## [567,] 0.5010586 4.989414e-01
## [568,] 1.0000000 2.186679e-10
## [569,] 0.9999663 3.366452e-05
## [570,] 1.0000000 3.015047e-17
## [571,] 1.0000000 2.404062e-17
## [572,] 0.9965720 3.427989e-03
## [573,] 0.5190617 4.809383e-01
## [574,] 0.9998305 1.694543e-04
## [575,] 0.4063815 5.936185e-01
## [576,] 0.9948877 5.112305e-03
## [577,] 0.8783345 1.216655e-01
## [578,] 1.0000000 7.702418e-13
## [579,] 1.0000000 4.048244e-48
## [580,] 0.9467945 5.320551e-02
## [581,] 0.8983295 1.016705e-01
## [582,] 0.9533405 4.665953e-02
## [583,] 0.5750919 4.249081e-01
## [584,] 0.5754639 4.245361e-01
## [585,] 0.9978580 2.142019e-03
## [586,] 0.7826965 2.173035e-01
## [587,] 0.9999999 9.829544e-08
## [588,] 0.5166051 4.833949e-01
## [589,] 0.8513832 1.486168e-01
## [590,] 0.9417674 5.823258e-02
## [591,] 0.4572075 5.427925e-01
## [592,] 0.9660247 3.397527e-02
## [593,] 1.0000000 7.725052e-19
## [594,] 0.5009618 4.990382e-01
## [595,] 0.9251078 7.489225e-02
## [596,] 0.9996375 3.625390e-04
## [597,] 0.5199136 4.800864e-01
## [598,] 1.0000000 1.154884e-08
## [599,] 0.9994669 5.330783e-04
## [600,] 0.9988344 1.165563e-03
## [601,] 1.0000000 1.744362e-09
## [602,] 0.5001879 4.998121e-01
## [603,] 0.7202776 2.797224e-01
## [604,] 1.0000000 3.053647e-21
## [605,] 1.0000000 4.873058e-08
## [606,] 0.5881975 4.118025e-01
## [607,] 0.3588104 6.411896e-01
## [608,] 0.9916396 8.360441e-03
## [609,] 0.9359912 6.400876e-02
## [610,] 0.9137421 8.625794e-02
## [611,] 0.5451142 4.548858e-01
## [612,] 1.0000000 3.024875e-08
## [613,] 0.3595166 6.404834e-01
## [614,] 0.5329781 4.670219e-01
## [615,] 1.0000000 2.025515e-11
## [616,] 1.0000000 6.991321e-15
## [617,] 0.9926337 7.366307e-03
## [618,] 0.9999874 1.263232e-05
## [619,] 1.0000000 1.797584e-13
## [620,] 0.9330624 6.693764e-02
## [621,] 1.0000000 3.730702e-32
## [622,] 0.9420443 5.795567e-02
## [623,] 0.9999438 5.619307e-05
## [624,] 1.0000000 2.730247e-15
## [625,] 0.9953146 4.685428e-03
## [626,] 0.7458792 2.541208e-01
## [627,] 0.5215032 4.784968e-01
## [628,] 0.9965786 3.421415e-03
## [629,] 1.0000000 3.033075e-39
## [630,] 0.4927155 5.072845e-01
## [631,] 0.9999999 8.624630e-08
## [632,] 1.0000000 1.766560e-10
## [633,] 0.9246830 7.531695e-02
## [634,] 0.8375946 1.624054e-01
## [635,] 0.9195681 8.043189e-02
## [636,] 0.8391572 1.608428e-01
## [637,] 0.7663198 2.336802e-01
## [638,] 1.0000000 4.837358e-16
## [639,] 1.0000000 3.677942e-13
## [640,] 0.6089291 3.910709e-01
## [641,] 0.9995946 4.054188e-04