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Contents

1 螳
2 襷貊 螻殊(markov process)
3 襷貊 覿
4 1: 蠏覯 ろ
5 2: 殊, 蠏, ′
6 3: 譬覲 豺襭 覲
7 4: 譬覲 豺襭 覲 - markovchain packages
8 5: 一危 襯襦 襷り鍵
9 6: ′螳 危
10 HMM(Hidden Markov Model)
11 msm package
12 襷 企 覲旧″蟆 螳?
13 谿瑚襭


[edit]

1 螳 #

  • 襷貊 覿 襯 蠍磯朱 蟆一 襯 覲企 螻牛. 讀,
  • 企 ろ 襯 覿 蠏 ろ 覩碁 襯 豸″.
  • 螳 襴 磯ジ 覲螳 襯朱 讌 .
  • 觚覈 蟲豌, 瑚規企, 語

[edit]

2 襷貊 螻殊(markov process) #

  • S1 S2襦 覲 襯 螻殊 '襯 螳(stochastic process)'手 .
  • S1 S2襦 覲 S2螳 S1 蟆一 襯 螳 '襷貊 螻殊(markov process)'手 .
  • S1 S2襦 覲 襯(transition probablility) 螳 讌 覲讌 朱 '襷貊 豌伎(markov chain)'企手 .
  • 螳 蟆所骸企 襯 覲螳 朱 '(steady-state, long-run, equilibrium probablilty)' 手 .
    • 豈 襯 螻壱り 磯暑逢 螻 蠏碁, 蠏碁蟆 企 蠏碁 100螻, 1000螻襦 襴覃 誤 .
[edit]

3 襷貊 覿 #

  • ろ 襯 螳讌.
  • ろ 蠍郁 譟伎.
  • 螳 蠍郁 ろ .
  • 螳 碁旭企.
  • 襯 螳 蟆所骸企 殊.
  • 轟 蠍郁 覦襦 危襯 譟危.
  • 覲 螳 蠍郁 覯襷 覦.
  • 螳 蠍郁 蠍語願 殊.
  • 襷貊 覿 豐 .

[edit]

4 1: 蠏覯 ろ #

  • B覯(蟆)襯 襦 ろ. 伎 蠏 覯 ろ 朱 螻螳 企 襯 譟一企瓦 れ螻 螳.
    • 蟲覯 -> 蟲覯: 0.9
    • 蟲覯 -> 覯: 0.1
    • 覯 -> 蟲覯: 0.3
    • 蟲覯 -> 蟲覯: 0.7
  • 豌 A覯 100覈 伎螻 . (朱 螻豺 蠏螳 り 螳)
  • 22殊姶 覃 螳 螻, 蟲覯 75覈, 覯 25覈 り 豸″ .

x1 <- c(0.9, 0.1)
x2 <- c(0.3, 0.7)
tp <- rbind(x1, x2) #危襯
ss <- rbind(c(100,0)) #豐

for(t in seq(1:30)){
  
  prev_tp <- ss%*%tp
  out <- paste(t, "殊姶: ", "蟲覯:", round(prev_tp[1,1], 3), "覯:", round(prev_tp[1,2], 3))
  ss <- prev_tp
  print (out)
}

蟆郁骸
[1] "1 殊姶:  蟲覯: 90 覯: 10"
[1] "2 殊姶:  蟲覯: 84 覯: 16"
[1] "3 殊姶:  蟲覯: 80.4 覯: 19.6"
[1] "4 殊姶:  蟲覯: 78.24 覯: 21.76"
[1] "5 殊姶:  蟲覯: 76.944 覯: 23.056"
[1] "6 殊姶:  蟲覯: 76.166 覯: 23.834"
[1] "7 殊姶:  蟲覯: 75.7 覯: 24.3"
[1] "8 殊姶:  蟲覯: 75.42 覯: 24.58"
[1] "9 殊姶:  蟲覯: 75.252 覯: 24.748"
[1] "10 殊姶:  蟲覯: 75.151 覯: 24.849"
[1] "11 殊姶:  蟲覯: 75.091 覯: 24.909"
[1] "12 殊姶:  蟲覯: 75.054 覯: 24.946"
[1] "13 殊姶:  蟲覯: 75.033 覯: 24.967"
[1] "14 殊姶:  蟲覯: 75.02 覯: 24.98"
[1] "15 殊姶:  蟲覯: 75.012 覯: 24.988"
[1] "16 殊姶:  蟲覯: 75.007 覯: 24.993"
[1] "17 殊姶:  蟲覯: 75.004 覯: 24.996"
[1] "18 殊姶:  蟲覯: 75.003 覯: 24.997"
[1] "19 殊姶:  蟲覯: 75.002 覯: 24.998"
[1] "20 殊姶:  蟲覯: 75.001 覯: 24.999"
[1] "21 殊姶:  蟲覯: 75.001 覯: 24.999"
[1] "22 殊姶:  蟲覯: 75 覯: 25"
[1] "23 殊姶:  蟲覯: 75 覯: 25"
[1] "24 殊姶:  蟲覯: 75 覯: 25"
[1] "25 殊姶:  蟲覯: 75 覯: 25"
[1] "26 殊姶:  蟲覯: 75 覯: 25"
[1] "27 殊姶:  蟲覯: 75 覯: 25"
[1] "28 殊姶:  蟲覯: 75 覯: 25"
[1] "29 殊姶:  蟲覯: 75 覯: 25"
[1] "30 殊姶:  蟲覯: 75 覯: 25"

[edit]

5 2: 殊, 蠏, ′ #

襷 1 覯 蟲覯襦 企 り 螳覃, 116殊姶 . 讀, 蟲覯 覈 讌 蟆 り 豸 . 企 襯 '殊 (transient state)'手 . 殊 螳 1螻 螳 襯 '蠏 (recurrent state)'手 覃, 蠏 譴 襯 '′ (absorbing state)'手 . ′ ろ 蟠蠏轟朱 企襦 れ朱 譴 覩碁ゼ 螳 蟆曙郁 襷. (手 [http]蠍 蠏碁)

x1 <- c(0.9, 0.1)
x2 <- c(0.0, 1.0)
tp <- rbind(x1, x2) #危襯
ss <- rbind(c(100,0)) #豐

for(t in seq(1:120)){
  
  prev_tp <- ss%*%tp
  out <- paste(t, "殊姶: ", "蟲覯:", round(prev_tp[1,1], 3), "覯:", round(prev_tp[1,2], 3))
  ss <- prev_tp
  print (out)
}

[1] "1 殊姶:  蟲覯: 90 覯: 10"
[1] "2 殊姶:  蟲覯: 81 覯: 19"
[1] "3 殊姶:  蟲覯: 72.9 覯: 27.1"
[1] "4 殊姶:  蟲覯: 65.61 覯: 34.39"
[1] "5 殊姶:  蟲覯: 59.049 覯: 40.951"
[1] "6 殊姶:  蟲覯: 53.144 覯: 46.856"
[1] "7 殊姶:  蟲覯: 47.83 覯: 52.17"
[1] "8 殊姶:  蟲覯: 43.047 覯: 56.953"
[1] "9 殊姶:  蟲覯: 38.742 覯: 61.258"
[1] "10 殊姶:  蟲覯: 34.868 覯: 65.132"
[1] "11 殊姶:  蟲覯: 31.381 覯: 68.619"
[1] "12 殊姶:  蟲覯: 28.243 覯: 71.757"
[1] "13 殊姶:  蟲覯: 25.419 覯: 74.581"
[1] "14 殊姶:  蟲覯: 22.877 覯: 77.123"
[1] "15 殊姶:  蟲覯: 20.589 覯: 79.411"
[1] "16 殊姶:  蟲覯: 18.53 覯: 81.47"
[1] "17 殊姶:  蟲覯: 16.677 覯: 83.323"
[1] "18 殊姶:  蟲覯: 15.009 覯: 84.991"
[1] "19 殊姶:  蟲覯: 13.509 覯: 86.491"
[1] "20 殊姶:  蟲覯: 12.158 覯: 87.842"
[1] "21 殊姶:  蟲覯: 10.942 覯: 89.058"
[1] "22 殊姶:  蟲覯: 9.848 覯: 90.152"
[1] "23 殊姶:  蟲覯: 8.863 覯: 91.137"
[1] "24 殊姶:  蟲覯: 7.977 覯: 92.023"
[1] "25 殊姶:  蟲覯: 7.179 覯: 92.821"
[1] "26 殊姶:  蟲覯: 6.461 覯: 93.539"
[1] "27 殊姶:  蟲覯: 5.815 覯: 94.185"
[1] "28 殊姶:  蟲覯: 5.233 覯: 94.767"
[1] "29 殊姶:  蟲覯: 4.71 覯: 95.29"
[1] "30 殊姶:  蟲覯: 4.239 覯: 95.761"
[1] "31 殊姶:  蟲覯: 3.815 覯: 96.185"
[1] "32 殊姶:  蟲覯: 3.434 覯: 96.566"
[1] "33 殊姶:  蟲覯: 3.09 覯: 96.91"
[1] "34 殊姶:  蟲覯: 2.781 覯: 97.219"
[1] "35 殊姶:  蟲覯: 2.503 覯: 97.497"
[1] "36 殊姶:  蟲覯: 2.253 覯: 97.747"
[1] "37 殊姶:  蟲覯: 2.028 覯: 97.972"
[1] "38 殊姶:  蟲覯: 1.825 覯: 98.175"
[1] "39 殊姶:  蟲覯: 1.642 覯: 98.358"
[1] "40 殊姶:  蟲覯: 1.478 覯: 98.522"
[1] "41 殊姶:  蟲覯: 1.33 覯: 98.67"
[1] "42 殊姶:  蟲覯: 1.197 覯: 98.803"
[1] "43 殊姶:  蟲覯: 1.078 覯: 98.922"
[1] "44 殊姶:  蟲覯: 0.97 覯: 99.03"
[1] "45 殊姶:  蟲覯: 0.873 覯: 99.127"
[1] "46 殊姶:  蟲覯: 0.786 覯: 99.214"
[1] "47 殊姶:  蟲覯: 0.707 覯: 99.293"
[1] "48 殊姶:  蟲覯: 0.636 覯: 99.364"
[1] "49 殊姶:  蟲覯: 0.573 覯: 99.427"
[1] "50 殊姶:  蟲覯: 0.515 覯: 99.485"
[1] "51 殊姶:  蟲覯: 0.464 覯: 99.536"
[1] "52 殊姶:  蟲覯: 0.417 覯: 99.583"
[1] "53 殊姶:  蟲覯: 0.376 覯: 99.624"
[1] "54 殊姶:  蟲覯: 0.338 覯: 99.662"
[1] "55 殊姶:  蟲覯: 0.304 覯: 99.696"
[1] "56 殊姶:  蟲覯: 0.274 覯: 99.726"
[1] "57 殊姶:  蟲覯: 0.247 覯: 99.753"
[1] "58 殊姶:  蟲覯: 0.222 覯: 99.778"
[1] "59 殊姶:  蟲覯: 0.2 覯: 99.8"
[1] "60 殊姶:  蟲覯: 0.18 覯: 99.82"
[1] "61 殊姶:  蟲覯: 0.162 覯: 99.838"
[1] "62 殊姶:  蟲覯: 0.146 覯: 99.854"
[1] "63 殊姶:  蟲覯: 0.131 覯: 99.869"
[1] "64 殊姶:  蟲覯: 0.118 覯: 99.882"
[1] "65 殊姶:  蟲覯: 0.106 覯: 99.894"
[1] "66 殊姶:  蟲覯: 0.096 覯: 99.904"
[1] "67 殊姶:  蟲覯: 0.086 覯: 99.914"
[1] "68 殊姶:  蟲覯: 0.077 覯: 99.923"
[1] "69 殊姶:  蟲覯: 0.07 覯: 99.93"
[1] "70 殊姶:  蟲覯: 0.063 覯: 99.937"
[1] "71 殊姶:  蟲覯: 0.056 覯: 99.944"
[1] "72 殊姶:  蟲覯: 0.051 覯: 99.949"
[1] "73 殊姶:  蟲覯: 0.046 覯: 99.954"
[1] "74 殊姶:  蟲覯: 0.041 覯: 99.959"
[1] "75 殊姶:  蟲覯: 0.037 覯: 99.963"
[1] "76 殊姶:  蟲覯: 0.033 覯: 99.967"
[1] "77 殊姶:  蟲覯: 0.03 覯: 99.97"
[1] "78 殊姶:  蟲覯: 0.027 覯: 99.973"
[1] "79 殊姶:  蟲覯: 0.024 覯: 99.976"
[1] "80 殊姶:  蟲覯: 0.022 覯: 99.978"
[1] "81 殊姶:  蟲覯: 0.02 覯: 99.98"
[1] "82 殊姶:  蟲覯: 0.018 覯: 99.982"
[1] "83 殊姶:  蟲覯: 0.016 覯: 99.984"
[1] "84 殊姶:  蟲覯: 0.014 覯: 99.986"
[1] "85 殊姶:  蟲覯: 0.013 覯: 99.987"
[1] "86 殊姶:  蟲覯: 0.012 覯: 99.988"
[1] "87 殊姶:  蟲覯: 0.01 覯: 99.99"
[1] "88 殊姶:  蟲覯: 0.009 覯: 99.991"
[1] "89 殊姶:  蟲覯: 0.008 覯: 99.992"
[1] "90 殊姶:  蟲覯: 0.008 覯: 99.992"
[1] "91 殊姶:  蟲覯: 0.007 覯: 99.993"
[1] "92 殊姶:  蟲覯: 0.006 覯: 99.994"
[1] "93 殊姶:  蟲覯: 0.006 覯: 99.994"
[1] "94 殊姶:  蟲覯: 0.005 覯: 99.995"
[1] "95 殊姶:  蟲覯: 0.004 覯: 99.996"
[1] "96 殊姶:  蟲覯: 0.004 覯: 99.996"
[1] "97 殊姶:  蟲覯: 0.004 覯: 99.996"
[1] "98 殊姶:  蟲覯: 0.003 覯: 99.997"
[1] "99 殊姶:  蟲覯: 0.003 覯: 99.997"
[1] "100 殊姶:  蟲覯: 0.003 覯: 99.997"
[1] "101 殊姶:  蟲覯: 0.002 覯: 99.998"
[1] "102 殊姶:  蟲覯: 0.002 覯: 99.998"
[1] "103 殊姶:  蟲覯: 0.002 覯: 99.998"
[1] "104 殊姶:  蟲覯: 0.002 覯: 99.998"
[1] "105 殊姶:  蟲覯: 0.002 覯: 99.998"
[1] "106 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "107 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "108 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "109 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "110 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "111 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "112 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "113 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "114 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "115 殊姶:  蟲覯: 0.001 覯: 99.999"
[1] "116 殊姶:  蟲覯: 0 覯: 100"
[1] "117 殊姶:  蟲覯: 0 覯: 100"
[1] "118 殊姶:  蟲覯: 0 覯: 100"
[1] "119 殊姶:  蟲覯: 0 覯: 100"
[1] "120 殊姶:  蟲覯: 0 覯: 100"

[edit]

6 3: 譬覲 豺襭 覲 #

豢豌: http://secom.hanbat.ac.kr/or/chapter1/right04.html
企 譬覲 ル 豺襭 轟覲 譴 磯 朱覲朱 企蟇磯 伎, 伎 蟆曙 譴 85% 豺襭 伎覃 15% 襷 蟆曙一企. 豺襭 伎 譴 朱 襦 襦 れ 蠍磯 覃 豺襭 ル 螳 殊螻, 1 危襯 螳り .

chapter1-17.gif

x1 <- c(0.7, 0.2, 0.1)
x2 <- c(0.1, 0.7, 0.2)
x3 <- c(0.02, 0.01, 0.97)
tp <- rbind(x1, x2, x3) #危襯
ss <- rbind(c(1,0,0)) #豐

for(t in seq(1:50)){
  
  prev_tp <- ss%*%tp
  out <- paste(t, "殊姶: ", 
               "轟覲:", round(prev_tp[1,1], 3), 
               "朱覲:", round(prev_tp[1,2], 3),
               "伎/襷:", round(prev_tp[1,3], 3)
               )
  ss <- prev_tp
  print (out)
}

蟆郁骸
[1] "1 殊姶:  轟覲: 0.7 朱覲: 0.2 伎/襷: 0.1"
[1] "2 殊姶:  轟覲: 0.512 朱覲: 0.281 伎/襷: 0.207"
[1] "3 殊姶:  轟覲: 0.391 朱覲: 0.301 伎/襷: 0.308"
[1] "4 殊姶:  轟覲: 0.31 朱覲: 0.292 伎/襷: 0.398"
[1] "5 殊姶:  轟覲: 0.254 朱覲: 0.27 伎/襷: 0.476"
[1] "6 殊姶:  轟覲: 0.214 朱覲: 0.245 伎/襷: 0.541"
[1] "7 殊姶:  轟覲: 0.185 朱覲: 0.22 伎/襷: 0.595"
[1] "8 殊姶:  轟覲: 0.164 朱覲: 0.197 伎/襷: 0.64"
[1] "9 殊姶:  轟覲: 0.147 朱覲: 0.177 伎/襷: 0.676"
[1] "10 殊姶:  轟覲: 0.134 朱覲: 0.16 伎/襷: 0.706"
[1] "11 殊姶:  轟覲: 0.124 朱覲: 0.146 伎/襷: 0.73"
[1] "12 殊姶:  轟覲: 0.116 朱覲: 0.134 伎/襷: 0.75"
[1] "13 殊姶:  轟覲: 0.11 朱覲: 0.125 伎/襷: 0.766"
[1] "14 殊姶:  轟覲: 0.104 朱覲: 0.117 伎/襷: 0.779"
[1] "15 殊姶:  轟覲: 0.1 朱覲: 0.11 伎/襷: 0.789"
[1] "16 殊姶:  轟覲: 0.097 朱覲: 0.105 伎/襷: 0.798"
[1] "17 殊姶:  轟覲: 0.094 朱覲: 0.101 伎/襷: 0.804"
[1] "18 殊姶:  轟覲: 0.092 朱覲: 0.098 伎/襷: 0.81"
[1] "19 殊姶:  轟覲: 0.091 朱覲: 0.095 伎/襷: 0.814"
[1] "20 殊姶:  轟覲: 0.089 朱覲: 0.093 伎/襷: 0.818"
[1] "21 殊姶:  轟覲: 0.088 朱覲: 0.091 伎/襷: 0.821"
[1] "22 殊姶:  轟覲: 0.087 朱覲: 0.089 伎/襷: 0.823"
[1] "23 殊姶:  轟覲: 0.086 朱覲: 0.088 伎/襷: 0.825"
[1] "24 殊姶:  轟覲: 0.086 朱覲: 0.087 伎/襷: 0.827"
[1] "25 殊姶:  轟覲: 0.085 朱覲: 0.087 伎/襷: 0.828"
[1] "26 殊姶:  轟覲: 0.085 朱覲: 0.086 伎/襷: 0.829"
[1] "27 殊姶:  轟覲: 0.085 朱覲: 0.085 伎/襷: 0.83"
[1] "28 殊姶:  轟覲: 0.084 朱覲: 0.085 伎/襷: 0.831"
[1] "29 殊姶:  轟覲: 0.084 朱覲: 0.085 伎/襷: 0.831"
[1] "30 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.832"
[1] "31 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.832"
[1] "32 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.832"
[1] "33 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.832"
[1] "34 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.833"
[1] "35 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.833"
[1] "36 殊姶:  轟覲: 0.084 朱覲: 0.084 伎/襷: 0.833"
[1] "37 殊姶:  轟覲: 0.083 朱覲: 0.084 伎/襷: 0.833"
[1] "38 殊姶:  轟覲: 0.083 朱覲: 0.084 伎/襷: 0.833"
[1] "39 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "40 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "41 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "42 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "43 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "44 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "45 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "46 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "47 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "48 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "49 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
[1] "50 殊姶:  轟覲: 0.083 朱覲: 0.083 伎/襷: 0.833"
ル 8.3% 螳螳 轟覲螻 朱覲 豺襭譴企 83.34% 襷蟇磯 豺襭 伎 手 豢 .

[edit]

7 4: 譬覲 豺襭 覲 - markovchain packages #

http://cran.r-project.org/web/packages/markovchain/markovchain.pdf
install.packages("markovchain")
library("markovchain")

statesNames=c("轟覲","朱覲", "伎/襷")
mt <- matrix(c(0.7,0.2,0.1,0.1,0.7,0.2,0.02,0.01,0.97), byrow=TRUE, nrow=3)
mc<-new("markovchain", transitionMatrix=mt, states=statesNames)
mc^2 #2覯讌 螻
steadyStates(mc)

蟆郁骸
> mc^2
A Markov chain^2 
 A  3 - dimensional discrete Markov Chain with following states 
 轟覲 朱覲 伎/襷 
 The transition matrix   (by rows)  is defined as follows 
          轟覲 朱覲 伎/襷
轟覲    0.5120   0.2810    0.2070
朱覲    0.1440   0.5120    0.3440
伎/襷   0.0344   0.0207    0.9449

> steadyStates(mcA)
       轟覲   朱覲 伎/襷
[1,] 0.08333333 0.08333333 0.8333333
[edit]

8 5: 一危 襯襦 襷り鍵 #

raw <- data.frame(name=c("f1","f1","f1","f1","f2","f2","f2","f2"),
                  year=c(83,   84,  85,  86,  83,  84,  85,  86),
                  state=sample(1:3, 8, replace=TRUE)
                  )

transition.probabilities <- function(D, timevar="year",
                                     idvar="name", statevar="state") {
  merged <- merge(D, cbind(nextt=D[,timevar] + 1, D),
    by.x = c(timevar, idvar), by.y = c("nextt", idvar))
  t(table(merged[, grep(statevar, names(merged), value = TRUE)]))
}

transition.probabilities(raw, timevar="year", idvar="name",statevar="state")


install.packages("markovchain")
library("markovchain")

sequence<-c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a", "b", "a", "a", "b", "b", "b", "a")
mcFitMLE<-markovchainFit(data=sequence)
#str(mcFitMLE)
#mcFitMLE$estimate@transitionMatrix
#mcFitMLE$estimate@states
markov<-new("markovchain", states=mcFitMLE$estimate@states, transitionMatrix=mcFitMLE$estimate@transitionMatrix)
plotMc(markov)

[edit]

9 6: ′螳 危 #

D覦燕 1,000螻螳 螻 (http://secom.hanbat.ac.kr/or/chapter1/right04.html)
1.png
R <- matrix(c(0.2,0, 0.3,0,0.5,0.5), byrow=TRUE, nrow=3)
Q <- matrix(c(0,0.8,0,0,0,0.7,0,0,0), byrow=TRUE, nrow=3)
IQ <- diag(rep(1,3)) - Q
IQ
iIQ<-ginv(IQ)
iIQ %*% R
rowSums(iIQ)

[edit]

10 HMM(Hidden Markov Model) #

  • 襷貊 覈語 ''企朱 螳 豢螳
  • れ梗 & 伎 伎伎 .

: 伎語 p.244, れ殊
れ螻 螳.
觜
觜0.70.3
0.40.6

豐蠍 襯
  • 觜 = 0.6
  • = 0.4

磯
  • 觜
    • 一 = 0.1
    • 狩 = 0.4
    • 豌 = 0.5

    • 一 = 0.6
    • 狩 = 0.3
    • 豌 = 0.1

'一->一->豌->狩' る 螳螳 豸° ?
#install.packages("RHmm")
library("RHmm")

weatherTransitions <- 
  rbind(
    c(0.7, 0.3),
    c(0.4, 0.6)
  )

s1 <- c(0.1, 0.4, 0.5)
s2 <- c(0.6, 0.3, 0.1)
dist <- distributionSet(dis="DISCRETE", proba=list(s1, s2), labels =c("一", "狩", "豌"))
dist

weatherHmm <- HMMSet(initProb=c(0.6, 0.4), transMat=weatherTransitions, distribution=dist)
weatherPath <- viterbi(HMM=weatherHmm, obs=c("一", "一", "豌", "狩"))
weatherPath

蟆郁骸
> weatherPath
$states
[1] 2 2 1 1

$logViterbiScore
[1] -5.331171

$logProbSeq
[1] -0.8306799

attr(,"class")
[1] "viterbiClass"
>
  • states螳 2 2 1 1襦 '->->觜->觜' 螳レ煙 .
  • '一->一->豌->狩' 豕 伎 螳(viterbi score) 0.0048384. (exp(weatherPath$logViterbiScore))
  • '一->一->豌->狩' 覦 襯 0.4357529 (exp(weatherPath$logProbSeq)) --> 襷??

讌覓碁
  • 蠏碁螳 殊殊 一朱 狩襷 襯?
  • '一->一->豌'襯 蟆曙 3手 ?
  • 讌 3 '一->一->豌'襯 , る螻 伎殊 覓伎 蟆朱 豸°?

谿瑚:viterbi 螻襴讀
viterbi.gif

[edit]

11 msm package #

library("msm")
data("cav")
str(cav)
cav <- cav[!is.na(cav$pdiag),]
cav[1:11,]

m <- statetable.msm(state, PTNUM, data = cav)
class(m)

twoway4.q <- rbind(c(0, 0.25, 0, 0.25), 
                    c(0.166, 0, 0.166, 0.166), 
                    c(0, 0.25, 0, 0.25), 
                    c(0, 0, 0, 0))
rownames(twoway4.q) <- colnames(twoway4.q) <- c("Well", "Mild", "Severe", "Death")

cav.msm <- msm(state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q, death = 4)
#pmatrix.msm(cav.msm, t = 1, ci = "normal")
pmatrix.msm(cav.msm, t = 1, ci = "none")


> pmatrix.msm(cav.msm, t = 1, ci = "none")
              Well       Mild     Severe      Death
Well   0.853040629 0.08916579 0.01486643 0.04292715
Mild   0.156269251 0.56585635 0.20550354 0.07237086
Severe 0.009996569 0.07884756 0.66057662 0.25057925
Death  0.000000000 0.00000000 0.00000000 1.00000000

[edit]

12 襷 企 覲旧″蟆 螳? #

螻螳 100襷 覈 . 螻螳れ 螳,蟲襷,危 豢 覺れ朱, れ螻 螳 伎 覲伎.

觜
螳50%
螳->危30%
螳->蟲襷->蟲襷->危10%
螳->蟲襷5%
螳->蟲襷->危3%
螳->蟲襷->蟲襷->蟲襷2%

'螳->蟲襷->?' 覓殊(?) 覓伎願螳? 轟壱 '蟲襷' 襯 讌 蟆螳?
..一危 覿 襷貊 覈語 讌 蟆.


鏤
蠍 蠍郁鍵..
企: : るジ讓曙 襦螻豺 企Ν 譯殊語. 襦螻豺
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螳 蟆 蠍 螻 豺伎 蟆企.