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author cristian
date Thu, 07 Sep 2017 10:21:45 -0400
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1 ### Auxiliary functions ###
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2
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3 # Finds the peak
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4 peaks <- function(x,partial=TRUE){
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5 if (partial){ #includes the first and the last element
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6 which(diff(c(TRUE,diff(x)>=0,FALSE))<0)
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7 }else {
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8 which(diff(diff(x)>=0)<0)+1
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9 }
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10 }
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11
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12
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13 #Function that finds the valleys
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14 valleys <- function(x,partial=TRUE){
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15 if (partial){ #includes the first and the last element
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16 which(diff(c(FALSE,diff(x)>0,TRUE))>0)
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17 }else {
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18 which(diff(diff(x)>0)>0)+1
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19 }
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20 }
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21
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22
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23 #Function that calculates the probability masses
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24 #ker: kernel density
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25 #v: valleys
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26 probability_mass <- function(ker,v){
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27 require(sfsmisc, quietly = TRUE)
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28 ker$y[which(ker$x<0)] = 0
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29 pm = c()
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30 for(j in 1:(length(v)-1)){
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31 pm[j] = integrate.xy(ker$x,ker$y,ker$x[v[j]],ker$x[v[j+1]], use.spline = FALSE)
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32 }
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33 pm = pm/sum(pm)
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34 return(pm)
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35 }
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36
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37
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38 #Function that tests if pm < value
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39 #pm: probability masses
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40 test_pm <- function(pm,value){
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41 p = c()
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42 num_pm = length(pm)
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43 for(j in 1:num_pm){
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44 if(pm[j]<value){
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45 p = c(p,j)
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46 }
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47 }
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48 return(p)
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49 }
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50
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51
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52
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53 ### Main functions ###
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54
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55 # Estimate the kernel density and calculate the probability masses
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56 # obs : data set
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57 # num.points : number of points for the estimation of the kernel density
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58 density_pm <- function(obs, num.points, p.bw = p.bw, threshold.modes = threshold.modes){
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59
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60 # fit model
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61 ker = density(obs, bw = p.bw, n = num.points)
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62
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63 # find peaks
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64 p = peaks(ker$y)
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65
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66 # find valleys
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67 v = valleys(ker$y)
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68
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69 # probability masses
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70 pm = probability_mass(ker,v)
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71 num_pm = length(pm)
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72
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73 # number of pm < threshold.modes
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74 p.del = test_pm(pm,threshold.modes)
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75
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76 # delete modes with probability masses < threshold.modes
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77 for(j in 1:num_pm){
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78 if(j %in% p.del){
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79 p[j] = NA
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80 v[j+1] = NA
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81 }
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82 }
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83 p = p[!is.na(p)]
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84 v = v[!is.na(v)]
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85
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86 # probability masses (without the ones < threshold.modes)
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87 pm = probability_mass(ker,v)
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88 num_pm = length(pm)
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89
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90 # number of pm<0.05
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91 p5 = test_pm(pm,0.05)
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92
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93 # number of pm<0.10
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94 p10 = test_pm(pm,0.10)
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95
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96 estimate = list(ker=ker,peaks=p,valleys=v,pm=pm,p5=p5,p10=p10)
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97
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98 return(estimate)
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99 }
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100
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101
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102
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103 # Estimate the kernel density and calculate the probability masses, and do bootstrap
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104 # obs : data set
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105 # num.points : number of points for the estimation of the kernel density
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106 density_pm_boot <- function(obs, num.points, p.bw = p.bw, threshold.modes = threshold.modes){
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107
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108 # fit model
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109 ker = density(obs,bw = p.bw, n = num.points)
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110
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111 # find peaks
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112 p = peaks(ker$y)
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113
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114 # find valleys
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115 v = valleys(ker$y)
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116
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117 # probability masses
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118 pm = probability_mass(ker, v)
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119 num_pm = length(pm)
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120
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121 # number of pm < threshold.modes
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122 p.del = test_pm(pm,threshold.modes)
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123
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124 # delete modes with probability masses < threshold.modes
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125 for(j in 1:num_pm){
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126 if(j %in% p.del){
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127 p[j] = 0
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128 v[j+1] = 0
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129 }
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130 }
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131 p = p[! p == 0]
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132 v = v[! v == 0]
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133
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134 # probability masses (without the ones < threshold.modes)
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135 pm = probability_mass(ker,v)
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136 num_pm = length(pm)
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137
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138 estimate = list(ker=ker,peaks=p,valleys=v,pm=pm)
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139
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140 return(estimate)
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141 }