STA1312: Bayesian Uniform-Binomial
Kusman Sadik, IPB University
2025-02-19
Ilustrasi: data menyebar Binomial dengan prior sebaran Uniform(0,1)
library(Bolstad)Data: menyebar Binomial(y=7, n=20), y adalah banyaknya sukses dari n percobaan
Sebaran prior bagi pi adalah Uniform(0, 1), pi adalah peluang sukses
Melakukan simulasi untuk memperoleh sebaran posterior bagi pi melalui MCMC
simulasi.post.pi <- binogcp(7, 20, density = "uniform", params = c(0, 1))
## hasil simulasi berdasarkan MCMC
simulasi.post.pi## $name
## [1] "pi"
##
## $param.x
## [1] 0.0005 0.0015 0.0025 0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095
## [11] 0.0105 0.0115 0.0125 0.0135 0.0145 0.0155 0.0165 0.0175 0.0185 0.0195
## [21] 0.0205 0.0215 0.0225 0.0235 0.0245 0.0255 0.0265 0.0275 0.0285 0.0295
## [31] 0.0305 0.0315 0.0325 0.0335 0.0345 0.0355 0.0365 0.0375 0.0385 0.0395
## [41] 0.0405 0.0415 0.0425 0.0435 0.0445 0.0455 0.0465 0.0475 0.0485 0.0495
## [51] 0.0505 0.0515 0.0525 0.0535 0.0545 0.0555 0.0565 0.0575 0.0585 0.0595
## [61] 0.0605 0.0615 0.0625 0.0635 0.0645 0.0655 0.0665 0.0675 0.0685 0.0695
## [71] 0.0705 0.0715 0.0725 0.0735 0.0745 0.0755 0.0765 0.0775 0.0785 0.0795
## [81] 0.0805 0.0815 0.0825 0.0835 0.0845 0.0855 0.0865 0.0875 0.0885 0.0895
## [91] 0.0905 0.0915 0.0925 0.0935 0.0945 0.0955 0.0965 0.0975 0.0985 0.0995
## [101] 0.1005 0.1015 0.1025 0.1035 0.1045 0.1055 0.1065 0.1075 0.1085 0.1095
## [111] 0.1105 0.1115 0.1125 0.1135 0.1145 0.1155 0.1165 0.1175 0.1185 0.1195
## [121] 0.1205 0.1215 0.1225 0.1235 0.1245 0.1255 0.1265 0.1275 0.1285 0.1295
## [131] 0.1305 0.1315 0.1325 0.1335 0.1345 0.1355 0.1365 0.1375 0.1385 0.1395
## [141] 0.1405 0.1415 0.1425 0.1435 0.1445 0.1455 0.1465 0.1475 0.1485 0.1495
## [151] 0.1505 0.1515 0.1525 0.1535 0.1545 0.1555 0.1565 0.1575 0.1585 0.1595
## [161] 0.1605 0.1615 0.1625 0.1635 0.1645 0.1655 0.1665 0.1675 0.1685 0.1695
## [171] 0.1705 0.1715 0.1725 0.1735 0.1745 0.1755 0.1765 0.1775 0.1785 0.1795
## [181] 0.1805 0.1815 0.1825 0.1835 0.1845 0.1855 0.1865 0.1875 0.1885 0.1895
## [191] 0.1905 0.1915 0.1925 0.1935 0.1945 0.1955 0.1965 0.1975 0.1985 0.1995
## [201] 0.2005 0.2015 0.2025 0.2035 0.2045 0.2055 0.2065 0.2075 0.2085 0.2095
## [211] 0.2105 0.2115 0.2125 0.2135 0.2145 0.2155 0.2165 0.2175 0.2185 0.2195
## [221] 0.2205 0.2215 0.2225 0.2235 0.2245 0.2255 0.2265 0.2275 0.2285 0.2295
## [231] 0.2305 0.2315 0.2325 0.2335 0.2345 0.2355 0.2365 0.2375 0.2385 0.2395
## [241] 0.2405 0.2415 0.2425 0.2435 0.2445 0.2455 0.2465 0.2475 0.2485 0.2495
## [251] 0.2505 0.2515 0.2525 0.2535 0.2545 0.2555 0.2565 0.2575 0.2585 0.2595
## [261] 0.2605 0.2615 0.2625 0.2635 0.2645 0.2655 0.2665 0.2675 0.2685 0.2695
## [271] 0.2705 0.2715 0.2725 0.2735 0.2745 0.2755 0.2765 0.2775 0.2785 0.2795
## [281] 0.2805 0.2815 0.2825 0.2835 0.2845 0.2855 0.2865 0.2875 0.2885 0.2895
## [291] 0.2905 0.2915 0.2925 0.2935 0.2945 0.2955 0.2965 0.2975 0.2985 0.2995
## [301] 0.3005 0.3015 0.3025 0.3035 0.3045 0.3055 0.3065 0.3075 0.3085 0.3095
## [311] 0.3105 0.3115 0.3125 0.3135 0.3145 0.3155 0.3165 0.3175 0.3185 0.3195
## [321] 0.3205 0.3215 0.3225 0.3235 0.3245 0.3255 0.3265 0.3275 0.3285 0.3295
## [331] 0.3305 0.3315 0.3325 0.3335 0.3345 0.3355 0.3365 0.3375 0.3385 0.3395
## [341] 0.3405 0.3415 0.3425 0.3435 0.3445 0.3455 0.3465 0.3475 0.3485 0.3495
## [351] 0.3505 0.3515 0.3525 0.3535 0.3545 0.3555 0.3565 0.3575 0.3585 0.3595
## [361] 0.3605 0.3615 0.3625 0.3635 0.3645 0.3655 0.3665 0.3675 0.3685 0.3695
## [371] 0.3705 0.3715 0.3725 0.3735 0.3745 0.3755 0.3765 0.3775 0.3785 0.3795
## [381] 0.3805 0.3815 0.3825 0.3835 0.3845 0.3855 0.3865 0.3875 0.3885 0.3895
## [391] 0.3905 0.3915 0.3925 0.3935 0.3945 0.3955 0.3965 0.3975 0.3985 0.3995
## [401] 0.4005 0.4015 0.4025 0.4035 0.4045 0.4055 0.4065 0.4075 0.4085 0.4095
## [411] 0.4105 0.4115 0.4125 0.4135 0.4145 0.4155 0.4165 0.4175 0.4185 0.4195
## [421] 0.4205 0.4215 0.4225 0.4235 0.4245 0.4255 0.4265 0.4275 0.4285 0.4295
## [431] 0.4305 0.4315 0.4325 0.4335 0.4345 0.4355 0.4365 0.4375 0.4385 0.4395
## [441] 0.4405 0.4415 0.4425 0.4435 0.4445 0.4455 0.4465 0.4475 0.4485 0.4495
## [451] 0.4505 0.4515 0.4525 0.4535 0.4545 0.4555 0.4565 0.4575 0.4585 0.4595
## [461] 0.4605 0.4615 0.4625 0.4635 0.4645 0.4655 0.4665 0.4675 0.4685 0.4695
## [471] 0.4705 0.4715 0.4725 0.4735 0.4745 0.4755 0.4765 0.4775 0.4785 0.4795
## [481] 0.4805 0.4815 0.4825 0.4835 0.4845 0.4855 0.4865 0.4875 0.4885 0.4895
## [491] 0.4905 0.4915 0.4925 0.4935 0.4945 0.4955 0.4965 0.4975 0.4985 0.4995
## [501] 0.5005 0.5015 0.5025 0.5035 0.5045 0.5055 0.5065 0.5075 0.5085 0.5095
## [511] 0.5105 0.5115 0.5125 0.5135 0.5145 0.5155 0.5165 0.5175 0.5185 0.5195
## [521] 0.5205 0.5215 0.5225 0.5235 0.5245 0.5255 0.5265 0.5275 0.5285 0.5295
## [531] 0.5305 0.5315 0.5325 0.5335 0.5345 0.5355 0.5365 0.5375 0.5385 0.5395
## [541] 0.5405 0.5415 0.5425 0.5435 0.5445 0.5455 0.5465 0.5475 0.5485 0.5495
## [551] 0.5505 0.5515 0.5525 0.5535 0.5545 0.5555 0.5565 0.5575 0.5585 0.5595
## [561] 0.5605 0.5615 0.5625 0.5635 0.5645 0.5655 0.5665 0.5675 0.5685 0.5695
## [571] 0.5705 0.5715 0.5725 0.5735 0.5745 0.5755 0.5765 0.5775 0.5785 0.5795
## [581] 0.5805 0.5815 0.5825 0.5835 0.5845 0.5855 0.5865 0.5875 0.5885 0.5895
## [591] 0.5905 0.5915 0.5925 0.5935 0.5945 0.5955 0.5965 0.5975 0.5985 0.5995
## [601] 0.6005 0.6015 0.6025 0.6035 0.6045 0.6055 0.6065 0.6075 0.6085 0.6095
## [611] 0.6105 0.6115 0.6125 0.6135 0.6145 0.6155 0.6165 0.6175 0.6185 0.6195
## [621] 0.6205 0.6215 0.6225 0.6235 0.6245 0.6255 0.6265 0.6275 0.6285 0.6295
## [631] 0.6305 0.6315 0.6325 0.6335 0.6345 0.6355 0.6365 0.6375 0.6385 0.6395
## [641] 0.6405 0.6415 0.6425 0.6435 0.6445 0.6455 0.6465 0.6475 0.6485 0.6495
## [651] 0.6505 0.6515 0.6525 0.6535 0.6545 0.6555 0.6565 0.6575 0.6585 0.6595
## [661] 0.6605 0.6615 0.6625 0.6635 0.6645 0.6655 0.6665 0.6675 0.6685 0.6695
## [671] 0.6705 0.6715 0.6725 0.6735 0.6745 0.6755 0.6765 0.6775 0.6785 0.6795
## [681] 0.6805 0.6815 0.6825 0.6835 0.6845 0.6855 0.6865 0.6875 0.6885 0.6895
## [691] 0.6905 0.6915 0.6925 0.6935 0.6945 0.6955 0.6965 0.6975 0.6985 0.6995
## [701] 0.7005 0.7015 0.7025 0.7035 0.7045 0.7055 0.7065 0.7075 0.7085 0.7095
## [711] 0.7105 0.7115 0.7125 0.7135 0.7145 0.7155 0.7165 0.7175 0.7185 0.7195
## [721] 0.7205 0.7215 0.7225 0.7235 0.7245 0.7255 0.7265 0.7275 0.7285 0.7295
## [731] 0.7305 0.7315 0.7325 0.7335 0.7345 0.7355 0.7365 0.7375 0.7385 0.7395
## [741] 0.7405 0.7415 0.7425 0.7435 0.7445 0.7455 0.7465 0.7475 0.7485 0.7495
## [751] 0.7505 0.7515 0.7525 0.7535 0.7545 0.7555 0.7565 0.7575 0.7585 0.7595
## [761] 0.7605 0.7615 0.7625 0.7635 0.7645 0.7655 0.7665 0.7675 0.7685 0.7695
## [771] 0.7705 0.7715 0.7725 0.7735 0.7745 0.7755 0.7765 0.7775 0.7785 0.7795
## [781] 0.7805 0.7815 0.7825 0.7835 0.7845 0.7855 0.7865 0.7875 0.7885 0.7895
## [791] 0.7905 0.7915 0.7925 0.7935 0.7945 0.7955 0.7965 0.7975 0.7985 0.7995
## [801] 0.8005 0.8015 0.8025 0.8035 0.8045 0.8055 0.8065 0.8075 0.8085 0.8095
## [811] 0.8105 0.8115 0.8125 0.8135 0.8145 0.8155 0.8165 0.8175 0.8185 0.8195
## [821] 0.8205 0.8215 0.8225 0.8235 0.8245 0.8255 0.8265 0.8275 0.8285 0.8295
## [831] 0.8305 0.8315 0.8325 0.8335 0.8345 0.8355 0.8365 0.8375 0.8385 0.8395
## [841] 0.8405 0.8415 0.8425 0.8435 0.8445 0.8455 0.8465 0.8475 0.8485 0.8495
## [851] 0.8505 0.8515 0.8525 0.8535 0.8545 0.8555 0.8565 0.8575 0.8585 0.8595
## [861] 0.8605 0.8615 0.8625 0.8635 0.8645 0.8655 0.8665 0.8675 0.8685 0.8695
## [871] 0.8705 0.8715 0.8725 0.8735 0.8745 0.8755 0.8765 0.8775 0.8785 0.8795
## [881] 0.8805 0.8815 0.8825 0.8835 0.8845 0.8855 0.8865 0.8875 0.8885 0.8895
## [891] 0.8905 0.8915 0.8925 0.8935 0.8945 0.8955 0.8965 0.8975 0.8985 0.8995
## [901] 0.9005 0.9015 0.9025 0.9035 0.9045 0.9055 0.9065 0.9075 0.9085 0.9095
## [911] 0.9105 0.9115 0.9125 0.9135 0.9145 0.9155 0.9165 0.9175 0.9185 0.9195
## [921] 0.9205 0.9215 0.9225 0.9235 0.9245 0.9255 0.9265 0.9275 0.9285 0.9295
## [931] 0.9305 0.9315 0.9325 0.9335 0.9345 0.9355 0.9365 0.9375 0.9385 0.9395
## [941] 0.9405 0.9415 0.9425 0.9435 0.9445 0.9455 0.9465 0.9475 0.9485 0.9495
## [951] 0.9505 0.9515 0.9525 0.9535 0.9545 0.9555 0.9565 0.9575 0.9585 0.9595
## [961] 0.9605 0.9615 0.9625 0.9635 0.9645 0.9655 0.9665 0.9675 0.9685 0.9695
## [971] 0.9705 0.9715 0.9725 0.9735 0.9745 0.9755 0.9765 0.9775 0.9785 0.9795
## [981] 0.9805 0.9815 0.9825 0.9835 0.9845 0.9855 0.9865 0.9875 0.9885 0.9895
## [991] 0.9905 0.9915 0.9925 0.9935 0.9945 0.9955 0.9965 0.9975 0.9985 0.9995
##
## $prior
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1000] 1
##
## $likelihood
## [1] 7.761871e-24 1.675574e-20 5.908100e-19 6.147255e-18 3.523904e-17
## [6] 1.417102e-16 4.503766e-16 1.210391e-15 2.869048e-15 6.168413e-15
## [11] 1.226678e-14 2.288662e-14 4.049044e-14 6.848549e-14 1.114582e-13
## [16] 1.754390e-13 2.681973e-13 3.995670e-13 5.818031e-13 8.299674e-13
## [21] 1.162344e-12 1.600885e-12 2.171679e-12 2.905456e-12 3.838108e-12
## [26] 5.011240e-12 6.472746e-12 8.277397e-12 1.048746e-11 1.317335e-11
## [31] 1.641423e-11 2.029874e-11 2.492563e-11 3.040450e-11 3.685643e-11
## [36] 4.441478e-11 5.322582e-11 6.344954e-11 7.526028e-11 8.884755e-11
## [41] 1.044167e-10 1.221896e-10 1.424055e-10 1.653215e-10 1.912137e-10
## [46] 2.203773e-10 2.531277e-10 2.898011e-10 3.307550e-10 3.763691e-10
## [51] 4.270456e-10 4.832101e-10 5.453119e-10 6.138249e-10 6.892479e-10
## [56] 7.721050e-10 8.629465e-10 9.623490e-10 1.070916e-09 1.189277e-09
## [61] 1.318092e-09 1.458047e-09 1.609855e-09 1.774260e-09 1.952034e-09
## [66] 2.143977e-09 2.350919e-09 2.573720e-09 2.813268e-09 3.070482e-09
## [71] 3.346308e-09 3.641725e-09 3.957737e-09 4.295383e-09 4.655726e-09
## [76] 5.039861e-09 5.448911e-09 5.884029e-09 6.346394e-09 6.837215e-09
## [81] 7.357727e-09 7.909196e-09 8.492911e-09 9.110190e-09 9.762375e-09
## [86] 1.045084e-08 1.117697e-08 1.194218e-08 1.274793e-08 1.359567e-08
## [91] 1.448689e-08 1.542310e-08 1.640584e-08 1.743664e-08 1.851708e-08
## [96] 1.964875e-08 2.083326e-08 2.207222e-08 2.336728e-08 2.472008e-08
## [101] 2.613230e-08 2.760561e-08 2.914171e-08 3.074229e-08 3.240908e-08
## [106] 3.414379e-08 3.594815e-08 3.782389e-08 3.977276e-08 4.179649e-08
## [111] 4.389685e-08 4.607557e-08 4.833440e-08 5.067510e-08 5.309942e-08
## [116] 5.560909e-08 5.820586e-08 6.089145e-08 6.366761e-08 6.653605e-08
## [121] 6.949848e-08 7.255660e-08 7.571209e-08 7.896664e-08 8.232191e-08
## [126] 8.577953e-08 8.934114e-08 9.300835e-08 9.678276e-08 1.006659e-07
## [131] 1.046594e-07 1.087647e-07 1.129833e-07 1.173168e-07 1.217665e-07
## [136] 1.263339e-07 1.310204e-07 1.358274e-07 1.407561e-07 1.458078e-07
## [141] 1.509839e-07 1.562856e-07 1.617140e-07 1.672704e-07 1.729558e-07
## [146] 1.787713e-07 1.847180e-07 1.907968e-07 1.970088e-07 2.033548e-07
## [151] 2.098357e-07 2.164524e-07 2.232056e-07 2.300961e-07 2.371245e-07
## [156] 2.442914e-07 2.515976e-07 2.590435e-07 2.666296e-07 2.743564e-07
## [161] 2.822243e-07 2.902335e-07 2.983844e-07 3.066773e-07 3.151122e-07
## [166] 3.236894e-07 3.324088e-07 3.412706e-07 3.502746e-07 3.594208e-07
## [171] 3.687090e-07 3.781391e-07 3.877106e-07 3.974235e-07 4.072771e-07
## [176] 4.172712e-07 4.274052e-07 4.376786e-07 4.480907e-07 4.586409e-07
## [181] 4.693285e-07 4.801526e-07 4.911125e-07 5.022072e-07 5.134358e-07
## [186] 5.247972e-07 5.362905e-07 5.479144e-07 5.596678e-07 5.715494e-07
## [191] 5.835579e-07 5.956920e-07 6.079502e-07 6.203312e-07 6.328333e-07
## [196] 6.454550e-07 6.581946e-07 6.710505e-07 6.840210e-07 6.971042e-07
## [201] 7.102982e-07 7.236013e-07 7.370114e-07 7.505265e-07 7.641447e-07
## [206] 7.778637e-07 7.916815e-07 8.055959e-07 8.196046e-07 8.337053e-07
## [211] 8.478957e-07 8.621735e-07 8.765362e-07 8.909813e-07 9.055064e-07
## [216] 9.201089e-07 9.347862e-07 9.495358e-07 9.643548e-07 9.792407e-07
## [221] 9.941907e-07 1.009202e-06 1.024272e-06 1.039398e-06 1.054576e-06
## [226] 1.069804e-06 1.085080e-06 1.100399e-06 1.115759e-06 1.131158e-06
## [231] 1.146591e-06 1.162057e-06 1.177551e-06 1.193071e-06 1.208614e-06
## [236] 1.224176e-06 1.239754e-06 1.255346e-06 1.270947e-06 1.286555e-06
## [241] 1.302167e-06 1.317779e-06 1.333388e-06 1.348990e-06 1.364584e-06
## [246] 1.380164e-06 1.395728e-06 1.411273e-06 1.426795e-06 1.442291e-06
## [251] 1.457758e-06 1.473192e-06 1.488590e-06 1.503950e-06 1.519266e-06
## [256] 1.534537e-06 1.549759e-06 1.564929e-06 1.580043e-06 1.595098e-06
## [261] 1.610091e-06 1.625019e-06 1.639878e-06 1.654665e-06 1.669377e-06
## [266] 1.684012e-06 1.698564e-06 1.713033e-06 1.727414e-06 1.741704e-06
## [271] 1.755900e-06 1.769999e-06 1.783999e-06 1.797895e-06 1.811686e-06
## [276] 1.825367e-06 1.838937e-06 1.852392e-06 1.865730e-06 1.878947e-06
## [281] 1.892041e-06 1.905008e-06 1.917847e-06 1.930554e-06 1.943127e-06
## [286] 1.955563e-06 1.967860e-06 1.980014e-06 1.992024e-06 2.003886e-06
## [291] 2.015599e-06 2.027160e-06 2.038566e-06 2.049816e-06 2.060907e-06
## [296] 2.071836e-06 2.082602e-06 2.093202e-06 2.103634e-06 2.113896e-06
## [301] 2.123986e-06 2.133902e-06 2.143643e-06 2.153205e-06 2.162588e-06
## [306] 2.171790e-06 2.180808e-06 2.189641e-06 2.198288e-06 2.206747e-06
## [311] 2.215015e-06 2.223093e-06 2.230978e-06 2.238669e-06 2.246164e-06
## [316] 2.253463e-06 2.260564e-06 2.267465e-06 2.274166e-06 2.280666e-06
## [321] 2.286963e-06 2.293057e-06 2.298947e-06 2.304631e-06 2.310109e-06
## [326] 2.315380e-06 2.320444e-06 2.325299e-06 2.329946e-06 2.334383e-06
## [331] 2.338610e-06 2.342627e-06 2.346432e-06 2.350027e-06 2.353410e-06
## [336] 2.356582e-06 2.359541e-06 2.362288e-06 2.364824e-06 2.367146e-06
## [341] 2.369257e-06 2.371156e-06 2.372842e-06 2.374317e-06 2.375580e-06
## [346] 2.376631e-06 2.377472e-06 2.378101e-06 2.378521e-06 2.378730e-06
## [351] 2.378730e-06 2.378521e-06 2.378104e-06 2.377480e-06 2.376648e-06
## [356] 2.375610e-06 2.374367e-06 2.372920e-06 2.371268e-06 2.369414e-06
## [361] 2.367358e-06 2.365102e-06 2.362645e-06 2.359990e-06 2.357138e-06
## [366] 2.354089e-06 2.350844e-06 2.347406e-06 2.343776e-06 2.339954e-06
## [371] 2.335942e-06 2.331741e-06 2.327354e-06 2.322781e-06 2.318024e-06
## [376] 2.313084e-06 2.307963e-06 2.302663e-06 2.297185e-06 2.291531e-06
## [381] 2.285702e-06 2.279701e-06 2.273529e-06 2.267189e-06 2.260680e-06
## [386] 2.254007e-06 2.247170e-06 2.240171e-06 2.233013e-06 2.225696e-06
## [391] 2.218224e-06 2.210599e-06 2.202821e-06 2.194894e-06 2.186820e-06
## [396] 2.178599e-06 2.170236e-06 2.161731e-06 2.153087e-06 2.144305e-06
## [401] 2.135389e-06 2.126341e-06 2.117162e-06 2.107854e-06 2.098421e-06
## [406] 2.088864e-06 2.079186e-06 2.069388e-06 2.059473e-06 2.049444e-06
## [411] 2.039303e-06 2.029051e-06 2.018692e-06 2.008227e-06 1.997659e-06
## [416] 1.986991e-06 1.976224e-06 1.965362e-06 1.954405e-06 1.943357e-06
## [421] 1.932221e-06 1.920997e-06 1.909690e-06 1.898300e-06 1.886832e-06
## [426] 1.875285e-06 1.863665e-06 1.851971e-06 1.840208e-06 1.828376e-06
## [431] 1.816480e-06 1.804520e-06 1.792499e-06 1.780421e-06 1.768286e-06
## [436] 1.756097e-06 1.743856e-06 1.731567e-06 1.719230e-06 1.706849e-06
## [441] 1.694426e-06 1.681962e-06 1.669461e-06 1.656924e-06 1.644353e-06
## [446] 1.631752e-06 1.619121e-06 1.606464e-06 1.593782e-06 1.581077e-06
## [451] 1.568352e-06 1.555609e-06 1.542850e-06 1.530077e-06 1.517292e-06
## [456] 1.504496e-06 1.491694e-06 1.478885e-06 1.466072e-06 1.453258e-06
## [461] 1.440444e-06 1.427632e-06 1.414823e-06 1.402021e-06 1.389227e-06
## [466] 1.376442e-06 1.363669e-06 1.350910e-06 1.338165e-06 1.325437e-06
## [471] 1.312729e-06 1.300040e-06 1.287374e-06 1.274732e-06 1.262115e-06
## [476] 1.249525e-06 1.236965e-06 1.224434e-06 1.211936e-06 1.199471e-06
## [481] 1.187042e-06 1.174649e-06 1.162294e-06 1.149978e-06 1.137704e-06
## [486] 1.125472e-06 1.113283e-06 1.101140e-06 1.089044e-06 1.076995e-06
## [491] 1.064995e-06 1.053045e-06 1.041147e-06 1.029302e-06 1.017511e-06
## [496] 1.005775e-06 9.940951e-07 9.824726e-07 9.709085e-07 9.594040e-07
## [501] 9.479599e-07 9.365774e-07 9.252574e-07 9.140009e-07 9.028087e-07
## [506] 8.916819e-07 8.806213e-07 8.696277e-07 8.587020e-07 8.478450e-07
## [511] 8.370575e-07 8.263401e-07 8.156938e-07 8.051191e-07 7.946167e-07
## [516] 7.841874e-07 7.738317e-07 7.635502e-07 7.533436e-07 7.432124e-07
## [521] 7.331572e-07 7.231784e-07 7.132766e-07 7.034522e-07 6.937056e-07
## [526] 6.840374e-07 6.744479e-07 6.649375e-07 6.555065e-07 6.461553e-07
## [531] 6.368842e-07 6.276935e-07 6.185834e-07 6.095543e-07 6.006063e-07
## [536] 5.917396e-07 5.829545e-07 5.742511e-07 5.656296e-07 5.570900e-07
## [541] 5.486326e-07 5.402573e-07 5.319643e-07 5.237536e-07 5.156252e-07
## [546] 5.075792e-07 4.996156e-07 4.917342e-07 4.839352e-07 4.762184e-07
## [551] 4.685838e-07 4.610313e-07 4.535608e-07 4.461721e-07 4.388651e-07
## [556] 4.316397e-07 4.244957e-07 4.174329e-07 4.104511e-07 4.035501e-07
## [561] 3.967297e-07 3.899897e-07 3.833297e-07 3.767495e-07 3.702488e-07
## [566] 3.638274e-07 3.574849e-07 3.512210e-07 3.450354e-07 3.389277e-07
## [571] 3.328976e-07 3.269448e-07 3.210687e-07 3.152691e-07 3.095456e-07
## [576] 3.038976e-07 2.983249e-07 2.928271e-07 2.874035e-07 2.820539e-07
## [581] 2.767777e-07 2.715745e-07 2.664439e-07 2.613853e-07 2.563982e-07
## [586] 2.514822e-07 2.466368e-07 2.418614e-07 2.371555e-07 2.325186e-07
## [591] 2.279503e-07 2.234498e-07 2.190168e-07 2.146507e-07 2.103508e-07
## [596] 2.061167e-07 2.019478e-07 1.978435e-07 1.938033e-07 1.898266e-07
## [601] 1.859128e-07 1.820613e-07 1.782716e-07 1.745430e-07 1.708750e-07
## [606] 1.672669e-07 1.637183e-07 1.602284e-07 1.567967e-07 1.534226e-07
## [611] 1.501055e-07 1.468448e-07 1.436398e-07 1.404900e-07 1.373948e-07
## [616] 1.343535e-07 1.313655e-07 1.284303e-07 1.255472e-07 1.227156e-07
## [621] 1.199349e-07 1.172045e-07 1.145238e-07 1.118922e-07 1.093091e-07
## [626] 1.067738e-07 1.042859e-07 1.018445e-07 9.944927e-08 9.709948e-08
## [631] 9.479455e-08 9.253390e-08 9.031693e-08 8.814305e-08 8.601166e-08
## [636] 8.392219e-08 8.187405e-08 7.986665e-08 7.789942e-08 7.597179e-08
## [641] 7.408317e-08 7.223301e-08 7.042073e-08 6.864577e-08 6.690758e-08
## [646] 6.520559e-08 6.353926e-08 6.190803e-08 6.031136e-08 5.874872e-08
## [651] 5.721955e-08 5.572334e-08 5.425954e-08 5.282764e-08 5.142712e-08
## [656] 5.005746e-08 4.871815e-08 4.740867e-08 4.612853e-08 4.487724e-08
## [661] 4.365428e-08 4.245919e-08 4.129146e-08 4.015063e-08 3.903622e-08
## [666] 3.794775e-08 3.688476e-08 3.584680e-08 3.483340e-08 3.384411e-08
## [671] 3.287849e-08 3.193611e-08 3.101651e-08 3.011928e-08 2.924399e-08
## [676] 2.839021e-08 2.755753e-08 2.674554e-08 2.595384e-08 2.518203e-08
## [681] 2.442970e-08 2.369647e-08 2.298196e-08 2.228578e-08 2.160757e-08
## [686] 2.094694e-08 2.030355e-08 1.967701e-08 1.906700e-08 1.847314e-08
## [691] 1.789511e-08 1.733255e-08 1.678514e-08 1.625255e-08 1.573445e-08
## [696] 1.523052e-08 1.474045e-08 1.426394e-08 1.380066e-08 1.335034e-08
## [701] 1.291266e-08 1.248734e-08 1.207410e-08 1.167266e-08 1.128273e-08
## [706] 1.090405e-08 1.053636e-08 1.017938e-08 9.832869e-09 9.496566e-09
## [711] 9.170224e-09 8.853601e-09 8.546457e-09 8.248557e-09 7.959671e-09
## [716] 7.679571e-09 7.408038e-09 7.144852e-09 6.889800e-09 6.642672e-09
## [721] 6.403265e-09 6.171375e-09 5.946806e-09 5.729365e-09 5.518862e-09
## [726] 5.315112e-09 5.117933e-09 4.927148e-09 4.742581e-09 4.564062e-09
## [731] 4.391426e-09 4.224507e-09 4.063148e-09 3.907191e-09 3.756483e-09
## [736] 3.610876e-09 3.470222e-09 3.334381e-09 3.203211e-09 3.076576e-09
## [741] 2.954345e-09 2.836385e-09 2.722571e-09 2.612779e-09 2.506887e-09
## [746] 2.404777e-09 2.306334e-09 2.211446e-09 2.120003e-09 2.031898e-09
## [751] 1.947027e-09 1.865288e-09 1.786583e-09 1.710814e-09 1.637888e-09
## [756] 1.567713e-09 1.500200e-09 1.435262e-09 1.372814e-09 1.312776e-09
## [761] 1.255065e-09 1.199605e-09 1.146320e-09 1.095136e-09 1.045982e-09
## [766] 9.987881e-10 9.534867e-10 9.100120e-10 8.683005e-10 8.282901e-10
## [771] 7.899207e-10 7.531339e-10 7.178730e-10 6.840832e-10 6.517110e-10
## [776] 6.207048e-10 5.910144e-10 5.625913e-10 5.353882e-10 5.093597e-10
## [781] 4.844614e-10 4.606506e-10 4.378858e-10 4.161268e-10 3.953349e-10
## [786] 3.754725e-10 3.565033e-10 3.383920e-10 3.211047e-10 3.046087e-10
## [791] 2.888720e-10 2.738642e-10 2.595555e-10 2.459174e-10 2.329223e-10
## [796] 2.205435e-10 2.087555e-10 1.975332e-10 1.868530e-10 1.766917e-10
## [801] 1.670271e-10 1.578379e-10 1.491034e-10 1.408038e-10 1.329200e-10
## [806] 1.254335e-10 1.183268e-10 1.115828e-10 1.051851e-10 9.911804e-11
## [811] 9.336647e-11 8.791587e-11 8.275231e-11 7.786240e-11 7.323328e-11
## [816] 6.885264e-11 6.470863e-11 6.078993e-11 5.708565e-11 5.358539e-11
## [821] 5.027916e-11 4.715740e-11 4.421096e-11 4.143110e-11 3.880942e-11
## [826] 3.633793e-11 3.400895e-11 3.181517e-11 2.974961e-11 2.780556e-11
## [831] 2.597668e-11 2.425686e-11 2.264030e-11 2.112148e-11 1.969511e-11
## [836] 1.835616e-11 1.709986e-11 1.592163e-11 1.481714e-11 1.378226e-11
## [841] 1.281306e-11 1.190582e-11 1.105698e-11 1.026318e-11 9.521222e-12
## [846] 8.828066e-12 8.180836e-12 7.576802e-12 7.013376e-12 6.488110e-12
## [851] 5.998680e-12 5.542893e-12 5.118668e-12 4.724043e-12 4.357159e-12
## [856] 4.016263e-12 3.699698e-12 3.405902e-12 3.133400e-12 2.880802e-12
## [861] 2.646798e-12 2.430155e-12 2.229712e-12 2.044376e-12 1.873121e-12
## [866] 1.714981e-12 1.569049e-12 1.434474e-12 1.310459e-12 1.196255e-12
## [871] 1.091160e-12 9.945174e-13 9.057127e-13 8.241707e-13 7.493542e-13
## [876] 6.807609e-13 6.179223e-13 5.604012e-13 5.077898e-13 4.597085e-13
## [881] 4.158036e-13 3.757464e-13 3.392308e-13 3.059729e-13 2.757088e-13
## [886] 2.481940e-13 2.232016e-13 2.005217e-13 1.799597e-13 1.613360e-13
## [891] 1.444844e-13 1.292516e-13 1.154962e-13 1.030877e-13 9.190611e-14
## [896] 8.184100e-14 7.279082e-14 6.466235e-14 5.737004e-14 5.083549e-14
## [901] 4.498690e-14 3.975860e-14 3.509057e-14 3.092802e-14 2.722098e-14
## [906] 2.392394e-14 2.099547e-14 1.839793e-14 1.609714e-14 1.406211e-14
## [911] 1.226476e-14 1.067970e-14 9.283993e-15 8.056924e-15 6.979840e-15
## [916] 6.035950e-15 5.210165e-15 4.488940e-15 3.860140e-15 3.312902e-15
## [921] 2.837522e-15 2.425342e-15 2.068649e-15 1.760585e-15 1.495061e-15
## [926] 1.266679e-15 1.070664e-15 9.027999e-16 7.593673e-16 6.370951e-16
## [931] 5.331103e-16 4.448949e-16 3.702465e-16 3.072428e-16 2.542097e-16
## [936] 2.096925e-16 1.724300e-16 1.413316e-16 1.154560e-16 9.399340e-17
## [941] 7.624865e-17 6.162665e-17 4.961940e-17 3.979451e-17 3.178502e-17
## [946] 2.528048e-17 2.001905e-17 1.578067e-17 1.238099e-17 9.666131e-18
## [951] 7.508141e-18 5.801017e-18 4.457299e-18 3.405127e-18 2.585709e-18
## [956] 1.951169e-18 1.462700e-18 1.088999e-18 8.049522e-19 5.905139e-19
## [961] 4.297777e-19 3.101948e-19 2.219278e-19 1.573147e-19 1.104293e-19
## [966] 7.672099e-20 5.272244e-20 3.581298e-20 2.402894e-20 1.591229e-20
## [971] 1.039094e-20 6.684714e-21 4.232065e-21 2.633589e-21 1.608775e-21
## [976] 9.632744e-22 5.644012e-22 3.229908e-22 1.801465e-22 9.768576e-23
## [981] 5.135505e-23 2.608943e-23 1.275917e-23 5.980147e-24 2.671912e-24
## [986] 1.130786e-24 4.497991e-25 1.665674e-25 5.674252e-26 1.751344e-26
## [991] 4.801625e-27 1.138925e-27 2.253772e-28 3.532228e-29 4.054604e-30
## [996] 3.006433e-31 1.154053e-32 1.464234e-34 1.925852e-37 1.216437e-43
##
## $posterior
## [1] 1.263570e-17 2.727701e-14 9.617914e-13 1.000724e-11 5.736633e-11
## [6] 2.306928e-10 7.331771e-10 1.970419e-09 4.670581e-09 1.004168e-08
## [11] 1.996933e-08 3.725758e-08 6.591519e-08 1.114889e-07 1.814451e-07
## [16] 2.856007e-07 4.366037e-07 6.504631e-07 9.471289e-07 1.351121e-06
## [21] 1.892203e-06 2.606112e-06 3.535319e-06 4.729849e-06 6.248132e-06
## [26] 8.157898e-06 1.053711e-05 1.347494e-05 1.707275e-05 2.144515e-05
## [31] 2.672105e-05 3.304472e-05 4.057694e-05 4.949609e-05 5.999932e-05
## [36] 7.230370e-05 8.664738e-05 1.032908e-04 1.225177e-04 1.446367e-04
## [41] 1.699820e-04 1.989149e-04 2.318247e-04 2.691303e-04 3.112806e-04
## [46] 3.587567e-04 4.120717e-04 4.717730e-04 5.384427e-04 6.126988e-04
## [51] 6.951961e-04 7.866273e-04 8.877241e-04 9.992579e-04 1.122040e-03
## [56] 1.256925e-03 1.404808e-03 1.566627e-03 1.743365e-03 1.936048e-03
## [61] 2.145749e-03 2.373583e-03 2.620715e-03 2.888353e-03 3.177755e-03
## [66] 3.490223e-03 3.827108e-03 4.189811e-03 4.579776e-03 4.998499e-03
## [71] 5.447522e-03 5.928436e-03 6.442880e-03 6.992540e-03 7.579149e-03
## [76] 8.204491e-03 8.870392e-03 9.578728e-03 1.033142e-02 1.113044e-02
## [81] 1.197779e-02 1.287554e-02 1.382578e-02 1.483066e-02 1.589237e-02
## [86] 1.701312e-02 1.819521e-02 1.944092e-02 2.075261e-02 2.213266e-02
## [91] 2.358350e-02 2.510758e-02 2.670739e-02 2.838545e-02 3.014433e-02
## [96] 3.198660e-02 3.391488e-02 3.593181e-02 3.804006e-02 4.024231e-02
## [101] 4.254129e-02 4.493973e-02 4.744037e-02 5.004599e-02 5.275939e-02
## [106] 5.558336e-02 5.852071e-02 6.157426e-02 6.474686e-02 6.804135e-02
## [111] 7.146056e-02 7.500734e-02 7.868454e-02 8.249502e-02 8.644160e-02
## [116] 9.052715e-02 9.475448e-02 9.912642e-02 1.036458e-01 1.083154e-01
## [121] 1.131380e-01 1.181163e-01 1.232532e-01 1.285514e-01 1.340135e-01
## [126] 1.396422e-01 1.454402e-01 1.514102e-01 1.575546e-01 1.638761e-01
## [131] 1.703771e-01 1.770602e-01 1.839278e-01 1.909824e-01 1.982262e-01
## [136] 2.056615e-01 2.132908e-01 2.211161e-01 2.291396e-01 2.373635e-01
## [141] 2.457898e-01 2.544205e-01 2.632575e-01 2.723028e-01 2.815582e-01
## [146] 2.910254e-01 3.007061e-01 3.106020e-01 3.207146e-01 3.310454e-01
## [151] 3.415958e-01 3.523672e-01 3.633609e-01 3.745780e-01 3.860196e-01
## [156] 3.976869e-01 4.095808e-01 4.217021e-01 4.340517e-01 4.466303e-01
## [161] 4.594385e-01 4.724769e-01 4.857460e-01 4.992461e-01 5.129775e-01
## [166] 5.269404e-01 5.411349e-01 5.555612e-01 5.702190e-01 5.851083e-01
## [171] 6.002288e-01 6.155801e-01 6.311619e-01 6.469736e-01 6.630146e-01
## [176] 6.792842e-01 6.957815e-01 7.125057e-01 7.294558e-01 7.466307e-01
## [181] 7.640292e-01 7.816500e-01 7.994918e-01 8.175532e-01 8.358324e-01
## [186] 8.543279e-01 8.730380e-01 8.919608e-01 9.110944e-01 9.304366e-01
## [191] 9.499856e-01 9.697389e-01 9.896944e-01 1.009850e+00 1.030202e+00
## [196] 1.050749e+00 1.071488e+00 1.092417e+00 1.113531e+00 1.134830e+00
## [201] 1.156309e+00 1.177965e+00 1.199796e+00 1.221797e+00 1.243966e+00
## [206] 1.266300e+00 1.288794e+00 1.311446e+00 1.334251e+00 1.357206e+00
## [211] 1.380306e+00 1.403549e+00 1.426931e+00 1.450446e+00 1.474092e+00
## [216] 1.497864e+00 1.521757e+00 1.545768e+00 1.569893e+00 1.594126e+00
## [221] 1.618463e+00 1.642900e+00 1.667433e+00 1.692056e+00 1.716765e+00
## [226] 1.741556e+00 1.766423e+00 1.791361e+00 1.816367e+00 1.841434e+00
## [231] 1.866559e+00 1.891735e+00 1.916959e+00 1.942224e+00 1.967526e+00
## [236] 1.992860e+00 2.018220e+00 2.043602e+00 2.069000e+00 2.094409e+00
## [241] 2.119824e+00 2.145239e+00 2.170649e+00 2.196049e+00 2.221433e+00
## [246] 2.246796e+00 2.272134e+00 2.297439e+00 2.322708e+00 2.347934e+00
## [251] 2.373113e+00 2.398239e+00 2.423306e+00 2.448310e+00 2.473244e+00
## [256] 2.498104e+00 2.522884e+00 2.547579e+00 2.572183e+00 2.596692e+00
## [261] 2.621099e+00 2.645400e+00 2.669590e+00 2.693662e+00 2.717613e+00
## [266] 2.741436e+00 2.765127e+00 2.788680e+00 2.812091e+00 2.835354e+00
## [271] 2.858464e+00 2.881417e+00 2.904207e+00 2.926829e+00 2.949279e+00
## [276] 2.971552e+00 2.993643e+00 3.015547e+00 3.037259e+00 3.058775e+00
## [281] 3.080091e+00 3.101201e+00 3.122101e+00 3.142788e+00 3.163255e+00
## [286] 3.183500e+00 3.203518e+00 3.223304e+00 3.242855e+00 3.262166e+00
## [291] 3.281234e+00 3.300054e+00 3.318623e+00 3.336937e+00 3.354991e+00
## [296] 3.372783e+00 3.390309e+00 3.407565e+00 3.424547e+00 3.441253e+00
## [301] 3.457680e+00 3.473822e+00 3.489679e+00 3.505246e+00 3.520521e+00
## [306] 3.535500e+00 3.550181e+00 3.564561e+00 3.578637e+00 3.592407e+00
## [311] 3.605868e+00 3.619018e+00 3.631854e+00 3.644374e+00 3.656576e+00
## [316] 3.668457e+00 3.680017e+00 3.691252e+00 3.702161e+00 3.712742e+00
## [321] 3.722994e+00 3.732914e+00 3.742502e+00 3.751755e+00 3.760673e+00
## [326] 3.769254e+00 3.777497e+00 3.785401e+00 3.792966e+00 3.800189e+00
## [331] 3.807070e+00 3.813609e+00 3.819804e+00 3.825656e+00 3.831164e+00
## [336] 3.836326e+00 3.841144e+00 3.845617e+00 3.849744e+00 3.853525e+00
## [341] 3.856961e+00 3.860052e+00 3.862797e+00 3.865198e+00 3.867254e+00
## [346] 3.868966e+00 3.870334e+00 3.871359e+00 3.872041e+00 3.872382e+00
## [351] 3.872382e+00 3.872042e+00 3.871364e+00 3.870347e+00 3.868993e+00
## [356] 3.867304e+00 3.865280e+00 3.862923e+00 3.860235e+00 3.857217e+00
## [361] 3.853870e+00 3.850196e+00 3.846198e+00 3.841875e+00 3.837232e+00
## [366] 3.832268e+00 3.826987e+00 3.821390e+00 3.815479e+00 3.809258e+00
## [371] 3.802727e+00 3.795889e+00 3.788746e+00 3.781301e+00 3.773557e+00
## [376] 3.765515e+00 3.757179e+00 3.748551e+00 3.739633e+00 3.730429e+00
## [381] 3.720941e+00 3.711171e+00 3.701124e+00 3.690802e+00 3.680207e+00
## [386] 3.669343e+00 3.658212e+00 3.646819e+00 3.635166e+00 3.623256e+00
## [391] 3.611092e+00 3.598678e+00 3.586017e+00 3.573112e+00 3.559967e+00
## [396] 3.546586e+00 3.532970e+00 3.519125e+00 3.505053e+00 3.490758e+00
## [401] 3.476243e+00 3.461513e+00 3.446570e+00 3.431418e+00 3.416062e+00
## [406] 3.400504e+00 3.384748e+00 3.368798e+00 3.352658e+00 3.336331e+00
## [411] 3.319821e+00 3.303133e+00 3.286269e+00 3.269233e+00 3.252030e+00
## [416] 3.234662e+00 3.217135e+00 3.199451e+00 3.181615e+00 3.163630e+00
## [421] 3.145501e+00 3.127230e+00 3.108822e+00 3.090281e+00 3.071611e+00
## [426] 3.052815e+00 3.033897e+00 3.014861e+00 2.995711e+00 2.976451e+00
## [431] 2.957084e+00 2.937614e+00 2.918046e+00 2.898382e+00 2.878627e+00
## [436] 2.858785e+00 2.838859e+00 2.818852e+00 2.798769e+00 2.778614e+00
## [441] 2.758390e+00 2.738100e+00 2.717749e+00 2.697340e+00 2.676876e+00
## [446] 2.656361e+00 2.635800e+00 2.615195e+00 2.594549e+00 2.573867e+00
## [451] 2.553152e+00 2.532407e+00 2.511636e+00 2.490842e+00 2.470029e+00
## [456] 2.449200e+00 2.428358e+00 2.407506e+00 2.386648e+00 2.365788e+00
## [461] 2.344927e+00 2.324070e+00 2.303219e+00 2.282379e+00 2.261550e+00
## [466] 2.240738e+00 2.219944e+00 2.199173e+00 2.178426e+00 2.157706e+00
## [471] 2.137017e+00 2.116361e+00 2.095742e+00 2.075161e+00 2.054622e+00
## [476] 2.034127e+00 2.013679e+00 1.993281e+00 1.972935e+00 1.952643e+00
## [481] 1.932409e+00 1.912234e+00 1.892121e+00 1.872072e+00 1.852091e+00
## [486] 1.832178e+00 1.812336e+00 1.792568e+00 1.772876e+00 1.753261e+00
## [491] 1.733727e+00 1.714274e+00 1.694905e+00 1.675622e+00 1.656427e+00
## [496] 1.637321e+00 1.618307e+00 1.599387e+00 1.580561e+00 1.561833e+00
## [501] 1.543203e+00 1.524673e+00 1.506245e+00 1.487920e+00 1.469700e+00
## [506] 1.451587e+00 1.433581e+00 1.415684e+00 1.397898e+00 1.380224e+00
## [511] 1.362663e+00 1.345216e+00 1.327884e+00 1.310669e+00 1.293572e+00
## [516] 1.276594e+00 1.259736e+00 1.242999e+00 1.226383e+00 1.209890e+00
## [521] 1.193521e+00 1.177277e+00 1.161157e+00 1.145164e+00 1.129297e+00
## [526] 1.113558e+00 1.097947e+00 1.082465e+00 1.067112e+00 1.051889e+00
## [531] 1.036797e+00 1.021835e+00 1.007004e+00 9.923056e-01 9.777390e-01
## [536] 9.633048e-01 9.490033e-01 9.348349e-01 9.207997e-01 9.068980e-01
## [541] 8.931299e-01 8.794957e-01 8.659953e-01 8.526289e-01 8.393966e-01
## [546] 8.262983e-01 8.133342e-01 8.005040e-01 7.878078e-01 7.752455e-01
## [551] 7.628170e-01 7.505221e-01 7.383607e-01 7.263325e-01 7.144373e-01
## [556] 7.026749e-01 6.910450e-01 6.795474e-01 6.681816e-01 6.569473e-01
## [561] 6.458443e-01 6.348720e-01 6.240300e-01 6.133180e-01 6.027355e-01
## [566] 5.922819e-01 5.819568e-01 5.717597e-01 5.616901e-01 5.517473e-01
## [571] 5.419307e-01 5.322399e-01 5.226742e-01 5.132329e-01 5.039154e-01
## [576] 4.947210e-01 4.856491e-01 4.766990e-01 4.678699e-01 4.591612e-01
## [581] 4.505720e-01 4.421016e-01 4.337493e-01 4.255143e-01 4.173958e-01
## [586] 4.093929e-01 4.015049e-01 3.937309e-01 3.860702e-01 3.785217e-01
## [591] 3.710848e-01 3.637585e-01 3.565418e-01 3.494341e-01 3.424343e-01
## [596] 3.355415e-01 3.287549e-01 3.220735e-01 3.154963e-01 3.090225e-01
## [601] 3.026512e-01 2.963812e-01 2.902119e-01 2.841420e-01 2.781708e-01
## [606] 2.722972e-01 2.665203e-01 2.608391e-01 2.552526e-01 2.497598e-01
## [611] 2.443598e-01 2.390516e-01 2.338341e-01 2.287065e-01 2.236677e-01
## [616] 2.187167e-01 2.138525e-01 2.090742e-01 2.043808e-01 1.997712e-01
## [621] 1.952445e-01 1.907996e-01 1.864357e-01 1.821516e-01 1.779465e-01
## [626] 1.738193e-01 1.697690e-01 1.657947e-01 1.618955e-01 1.580702e-01
## [631] 1.543180e-01 1.506378e-01 1.470287e-01 1.434898e-01 1.400201e-01
## [636] 1.366186e-01 1.332844e-01 1.300165e-01 1.268140e-01 1.236760e-01
## [641] 1.206015e-01 1.175896e-01 1.146393e-01 1.117498e-01 1.089202e-01
## [646] 1.061495e-01 1.034368e-01 1.007813e-01 9.818207e-02 9.563821e-02
## [651] 9.314885e-02 9.071313e-02 8.833019e-02 8.599918e-02 8.371924e-02
## [656] 8.148954e-02 7.930924e-02 7.717752e-02 7.509356e-02 7.305655e-02
## [661] 7.106568e-02 6.912016e-02 6.721920e-02 6.536202e-02 6.354784e-02
## [666] 6.177590e-02 6.004544e-02 5.835571e-02 5.670598e-02 5.509550e-02
## [671] 5.352356e-02 5.198943e-02 5.049240e-02 4.903178e-02 4.760687e-02
## [676] 4.621699e-02 4.486146e-02 4.353961e-02 4.225078e-02 4.099432e-02
## [681] 3.976960e-02 3.857596e-02 3.741279e-02 3.627947e-02 3.517539e-02
## [686] 3.409995e-02 3.305255e-02 3.203260e-02 3.103954e-02 3.007280e-02
## [691] 2.913180e-02 2.821601e-02 2.732487e-02 2.645785e-02 2.561442e-02
## [696] 2.479407e-02 2.399628e-02 2.322055e-02 2.246638e-02 2.173328e-02
## [701] 2.102078e-02 2.032840e-02 1.965568e-02 1.900215e-02 1.836739e-02
## [706] 1.775093e-02 1.715235e-02 1.657122e-02 1.600712e-02 1.545965e-02
## [711] 1.492839e-02 1.441295e-02 1.391295e-02 1.342799e-02 1.295771e-02
## [716] 1.250173e-02 1.205969e-02 1.163125e-02 1.121604e-02 1.081374e-02
## [721] 1.042400e-02 1.004650e-02 9.680925e-03 9.326948e-03 8.984267e-03
## [726] 8.652578e-03 8.331586e-03 8.021002e-03 7.720542e-03 7.429929e-03
## [731] 7.148890e-03 6.877160e-03 6.614480e-03 6.360594e-03 6.115254e-03
## [736] 5.878217e-03 5.649244e-03 5.428105e-03 5.214571e-03 5.008420e-03
## [741] 4.809437e-03 4.617408e-03 4.432128e-03 4.253395e-03 4.081011e-03
## [746] 3.914784e-03 3.754527e-03 3.600057e-03 3.451195e-03 3.307768e-03
## [751] 3.169605e-03 3.036540e-03 2.908414e-03 2.785068e-03 2.666350e-03
## [756] 2.552111e-03 2.442205e-03 2.336491e-03 2.234832e-03 2.137094e-03
## [761] 2.043146e-03 1.952861e-03 1.866117e-03 1.782794e-03 1.702775e-03
## [766] 1.625947e-03 1.552200e-03 1.481427e-03 1.413524e-03 1.348390e-03
## [771] 1.285928e-03 1.226042e-03 1.168640e-03 1.113633e-03 1.060933e-03
## [776] 1.010458e-03 9.621242e-04 9.158536e-04 8.715692e-04 8.291968e-04
## [781] 7.886644e-04 7.499023e-04 7.128430e-04 6.774212e-04 6.435737e-04
## [786] 6.112393e-04 5.803588e-04 5.508751e-04 5.227328e-04 4.958785e-04
## [791] 4.702605e-04 4.458289e-04 4.225356e-04 4.003338e-04 3.791789e-04
## [796] 3.590272e-04 3.398372e-04 3.215683e-04 3.041818e-04 2.876400e-04
## [801] 2.719068e-04 2.569475e-04 2.427284e-04 2.292173e-04 2.163831e-04
## [806] 2.041958e-04 1.926266e-04 1.816479e-04 1.712330e-04 1.613562e-04
## [811] 1.519931e-04 1.431200e-04 1.347141e-04 1.267538e-04 1.192179e-04
## [816] 1.120866e-04 1.053405e-04 9.896114e-05 9.293088e-05 8.723273e-05
## [821] 8.185044e-05 7.676847e-05 7.197191e-05 6.744651e-05 6.317864e-05
## [826] 5.915524e-05 5.536385e-05 5.179256e-05 4.842998e-05 4.526523e-05
## [831] 4.228795e-05 3.948822e-05 3.685660e-05 3.438408e-05 3.206206e-05
## [836] 2.988237e-05 2.783720e-05 2.591914e-05 2.412111e-05 2.243641e-05
## [841] 2.085864e-05 1.938172e-05 1.799988e-05 1.670764e-05 1.549979e-05
## [846] 1.437139e-05 1.331775e-05 1.233443e-05 1.141722e-05 1.056212e-05
## [851] 9.765372e-06 9.023386e-06 8.332782e-06 7.690363e-06 7.093106e-06
## [856] 6.538154e-06 6.022813e-06 5.544536e-06 5.100924e-06 4.689715e-06
## [861] 4.308776e-06 3.956098e-06 3.629793e-06 3.328081e-06 3.049291e-06
## [866] 2.791851e-06 2.554286e-06 2.335210e-06 2.133323e-06 1.947407e-06
## [871] 1.776321e-06 1.618995e-06 1.474428e-06 1.341684e-06 1.219889e-06
## [876] 1.108224e-06 1.005928e-06 9.122883e-07 8.266412e-07 7.483686e-07
## [881] 6.768951e-07 6.116850e-07 5.522406e-07 4.980993e-07 4.488319e-07
## [886] 4.040400e-07 3.633544e-07 3.264332e-07 2.929600e-07 2.626421e-07
## [891] 2.352091e-07 2.104113e-07 1.880185e-07 1.678185e-07 1.496158e-07
## [896] 1.332306e-07 1.184976e-07 1.052651e-07 9.339383e-08 8.275610e-08
## [901] 7.323507e-08 6.472382e-08 5.712465e-08 5.034835e-08 4.431359e-08
## [906] 3.894626e-08 3.417895e-08 2.995036e-08 2.620486e-08 2.289199e-08
## [911] 1.996605e-08 1.738570e-08 1.511360e-08 1.311603e-08 1.136262e-08
## [916] 9.826044e-09 8.481732e-09 7.307636e-09 6.283999e-09 5.393139e-09
## [921] 4.619259e-09 3.948262e-09 3.367595e-09 2.866091e-09 2.433839e-09
## [926] 2.062052e-09 1.742956e-09 1.469686e-09 1.236189e-09 1.037140e-09
## [931] 8.678610e-10 7.242533e-10 6.027316e-10 5.001666e-10 4.138330e-10
## [936] 3.413626e-10 2.807023e-10 2.300765e-10 1.879531e-10 1.530137e-10
## [941] 1.241267e-10 1.003232e-10 8.077641e-11 6.478228e-11 5.174347e-11
## [946] 4.115459e-11 3.258941e-11 2.568967e-11 2.015526e-11 1.573569e-11
## [951] 1.222265e-11 9.443592e-12 7.256127e-12 5.543274e-12 4.209328e-12
## [956] 3.176348e-12 2.381158e-12 1.772804e-12 1.310398e-12 9.613095e-13
## [961] 6.996436e-13 5.049723e-13 3.612807e-13 2.560957e-13 1.797700e-13
## [966] 1.248956e-13 8.582791e-14 5.830067e-14 3.911719e-14 2.590393e-14
## [971] 1.691562e-14 1.088218e-14 6.889463e-15 4.287273e-15 2.618957e-15
## [976] 1.568134e-15 9.188000e-16 5.258031e-16 2.932641e-16 1.590246e-16
## [981] 8.360191e-17 4.247151e-17 2.077091e-17 9.735200e-18 4.349659e-18
## [986] 1.840829e-18 7.322370e-19 2.711583e-19 9.237229e-20 2.851048e-20
## [991] 7.816661e-21 1.854079e-21 3.668961e-22 5.750185e-23 6.600571e-24
## [996] 4.894232e-25 1.878706e-26 2.383656e-28 3.135133e-31 1.980262e-37
##
## $pi
## [1] 0.0005 0.0015 0.0025 0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095
## [11] 0.0105 0.0115 0.0125 0.0135 0.0145 0.0155 0.0165 0.0175 0.0185 0.0195
## [21] 0.0205 0.0215 0.0225 0.0235 0.0245 0.0255 0.0265 0.0275 0.0285 0.0295
## [31] 0.0305 0.0315 0.0325 0.0335 0.0345 0.0355 0.0365 0.0375 0.0385 0.0395
## [41] 0.0405 0.0415 0.0425 0.0435 0.0445 0.0455 0.0465 0.0475 0.0485 0.0495
## [51] 0.0505 0.0515 0.0525 0.0535 0.0545 0.0555 0.0565 0.0575 0.0585 0.0595
## [61] 0.0605 0.0615 0.0625 0.0635 0.0645 0.0655 0.0665 0.0675 0.0685 0.0695
## [71] 0.0705 0.0715 0.0725 0.0735 0.0745 0.0755 0.0765 0.0775 0.0785 0.0795
## [81] 0.0805 0.0815 0.0825 0.0835 0.0845 0.0855 0.0865 0.0875 0.0885 0.0895
## [91] 0.0905 0.0915 0.0925 0.0935 0.0945 0.0955 0.0965 0.0975 0.0985 0.0995
## [101] 0.1005 0.1015 0.1025 0.1035 0.1045 0.1055 0.1065 0.1075 0.1085 0.1095
## [111] 0.1105 0.1115 0.1125 0.1135 0.1145 0.1155 0.1165 0.1175 0.1185 0.1195
## [121] 0.1205 0.1215 0.1225 0.1235 0.1245 0.1255 0.1265 0.1275 0.1285 0.1295
## [131] 0.1305 0.1315 0.1325 0.1335 0.1345 0.1355 0.1365 0.1375 0.1385 0.1395
## [141] 0.1405 0.1415 0.1425 0.1435 0.1445 0.1455 0.1465 0.1475 0.1485 0.1495
## [151] 0.1505 0.1515 0.1525 0.1535 0.1545 0.1555 0.1565 0.1575 0.1585 0.1595
## [161] 0.1605 0.1615 0.1625 0.1635 0.1645 0.1655 0.1665 0.1675 0.1685 0.1695
## [171] 0.1705 0.1715 0.1725 0.1735 0.1745 0.1755 0.1765 0.1775 0.1785 0.1795
## [181] 0.1805 0.1815 0.1825 0.1835 0.1845 0.1855 0.1865 0.1875 0.1885 0.1895
## [191] 0.1905 0.1915 0.1925 0.1935 0.1945 0.1955 0.1965 0.1975 0.1985 0.1995
## [201] 0.2005 0.2015 0.2025 0.2035 0.2045 0.2055 0.2065 0.2075 0.2085 0.2095
## [211] 0.2105 0.2115 0.2125 0.2135 0.2145 0.2155 0.2165 0.2175 0.2185 0.2195
## [221] 0.2205 0.2215 0.2225 0.2235 0.2245 0.2255 0.2265 0.2275 0.2285 0.2295
## [231] 0.2305 0.2315 0.2325 0.2335 0.2345 0.2355 0.2365 0.2375 0.2385 0.2395
## [241] 0.2405 0.2415 0.2425 0.2435 0.2445 0.2455 0.2465 0.2475 0.2485 0.2495
## [251] 0.2505 0.2515 0.2525 0.2535 0.2545 0.2555 0.2565 0.2575 0.2585 0.2595
## [261] 0.2605 0.2615 0.2625 0.2635 0.2645 0.2655 0.2665 0.2675 0.2685 0.2695
## [271] 0.2705 0.2715 0.2725 0.2735 0.2745 0.2755 0.2765 0.2775 0.2785 0.2795
## [281] 0.2805 0.2815 0.2825 0.2835 0.2845 0.2855 0.2865 0.2875 0.2885 0.2895
## [291] 0.2905 0.2915 0.2925 0.2935 0.2945 0.2955 0.2965 0.2975 0.2985 0.2995
## [301] 0.3005 0.3015 0.3025 0.3035 0.3045 0.3055 0.3065 0.3075 0.3085 0.3095
## [311] 0.3105 0.3115 0.3125 0.3135 0.3145 0.3155 0.3165 0.3175 0.3185 0.3195
## [321] 0.3205 0.3215 0.3225 0.3235 0.3245 0.3255 0.3265 0.3275 0.3285 0.3295
## [331] 0.3305 0.3315 0.3325 0.3335 0.3345 0.3355 0.3365 0.3375 0.3385 0.3395
## [341] 0.3405 0.3415 0.3425 0.3435 0.3445 0.3455 0.3465 0.3475 0.3485 0.3495
## [351] 0.3505 0.3515 0.3525 0.3535 0.3545 0.3555 0.3565 0.3575 0.3585 0.3595
## [361] 0.3605 0.3615 0.3625 0.3635 0.3645 0.3655 0.3665 0.3675 0.3685 0.3695
## [371] 0.3705 0.3715 0.3725 0.3735 0.3745 0.3755 0.3765 0.3775 0.3785 0.3795
## [381] 0.3805 0.3815 0.3825 0.3835 0.3845 0.3855 0.3865 0.3875 0.3885 0.3895
## [391] 0.3905 0.3915 0.3925 0.3935 0.3945 0.3955 0.3965 0.3975 0.3985 0.3995
## [401] 0.4005 0.4015 0.4025 0.4035 0.4045 0.4055 0.4065 0.4075 0.4085 0.4095
## [411] 0.4105 0.4115 0.4125 0.4135 0.4145 0.4155 0.4165 0.4175 0.4185 0.4195
## [421] 0.4205 0.4215 0.4225 0.4235 0.4245 0.4255 0.4265 0.4275 0.4285 0.4295
## [431] 0.4305 0.4315 0.4325 0.4335 0.4345 0.4355 0.4365 0.4375 0.4385 0.4395
## [441] 0.4405 0.4415 0.4425 0.4435 0.4445 0.4455 0.4465 0.4475 0.4485 0.4495
## [451] 0.4505 0.4515 0.4525 0.4535 0.4545 0.4555 0.4565 0.4575 0.4585 0.4595
## [461] 0.4605 0.4615 0.4625 0.4635 0.4645 0.4655 0.4665 0.4675 0.4685 0.4695
## [471] 0.4705 0.4715 0.4725 0.4735 0.4745 0.4755 0.4765 0.4775 0.4785 0.4795
## [481] 0.4805 0.4815 0.4825 0.4835 0.4845 0.4855 0.4865 0.4875 0.4885 0.4895
## [491] 0.4905 0.4915 0.4925 0.4935 0.4945 0.4955 0.4965 0.4975 0.4985 0.4995
## [501] 0.5005 0.5015 0.5025 0.5035 0.5045 0.5055 0.5065 0.5075 0.5085 0.5095
## [511] 0.5105 0.5115 0.5125 0.5135 0.5145 0.5155 0.5165 0.5175 0.5185 0.5195
## [521] 0.5205 0.5215 0.5225 0.5235 0.5245 0.5255 0.5265 0.5275 0.5285 0.5295
## [531] 0.5305 0.5315 0.5325 0.5335 0.5345 0.5355 0.5365 0.5375 0.5385 0.5395
## [541] 0.5405 0.5415 0.5425 0.5435 0.5445 0.5455 0.5465 0.5475 0.5485 0.5495
## [551] 0.5505 0.5515 0.5525 0.5535 0.5545 0.5555 0.5565 0.5575 0.5585 0.5595
## [561] 0.5605 0.5615 0.5625 0.5635 0.5645 0.5655 0.5665 0.5675 0.5685 0.5695
## [571] 0.5705 0.5715 0.5725 0.5735 0.5745 0.5755 0.5765 0.5775 0.5785 0.5795
## [581] 0.5805 0.5815 0.5825 0.5835 0.5845 0.5855 0.5865 0.5875 0.5885 0.5895
## [591] 0.5905 0.5915 0.5925 0.5935 0.5945 0.5955 0.5965 0.5975 0.5985 0.5995
## [601] 0.6005 0.6015 0.6025 0.6035 0.6045 0.6055 0.6065 0.6075 0.6085 0.6095
## [611] 0.6105 0.6115 0.6125 0.6135 0.6145 0.6155 0.6165 0.6175 0.6185 0.6195
## [621] 0.6205 0.6215 0.6225 0.6235 0.6245 0.6255 0.6265 0.6275 0.6285 0.6295
## [631] 0.6305 0.6315 0.6325 0.6335 0.6345 0.6355 0.6365 0.6375 0.6385 0.6395
## [641] 0.6405 0.6415 0.6425 0.6435 0.6445 0.6455 0.6465 0.6475 0.6485 0.6495
## [651] 0.6505 0.6515 0.6525 0.6535 0.6545 0.6555 0.6565 0.6575 0.6585 0.6595
## [661] 0.6605 0.6615 0.6625 0.6635 0.6645 0.6655 0.6665 0.6675 0.6685 0.6695
## [671] 0.6705 0.6715 0.6725 0.6735 0.6745 0.6755 0.6765 0.6775 0.6785 0.6795
## [681] 0.6805 0.6815 0.6825 0.6835 0.6845 0.6855 0.6865 0.6875 0.6885 0.6895
## [691] 0.6905 0.6915 0.6925 0.6935 0.6945 0.6955 0.6965 0.6975 0.6985 0.6995
## [701] 0.7005 0.7015 0.7025 0.7035 0.7045 0.7055 0.7065 0.7075 0.7085 0.7095
## [711] 0.7105 0.7115 0.7125 0.7135 0.7145 0.7155 0.7165 0.7175 0.7185 0.7195
## [721] 0.7205 0.7215 0.7225 0.7235 0.7245 0.7255 0.7265 0.7275 0.7285 0.7295
## [731] 0.7305 0.7315 0.7325 0.7335 0.7345 0.7355 0.7365 0.7375 0.7385 0.7395
## [741] 0.7405 0.7415 0.7425 0.7435 0.7445 0.7455 0.7465 0.7475 0.7485 0.7495
## [751] 0.7505 0.7515 0.7525 0.7535 0.7545 0.7555 0.7565 0.7575 0.7585 0.7595
## [761] 0.7605 0.7615 0.7625 0.7635 0.7645 0.7655 0.7665 0.7675 0.7685 0.7695
## [771] 0.7705 0.7715 0.7725 0.7735 0.7745 0.7755 0.7765 0.7775 0.7785 0.7795
## [781] 0.7805 0.7815 0.7825 0.7835 0.7845 0.7855 0.7865 0.7875 0.7885 0.7895
## [791] 0.7905 0.7915 0.7925 0.7935 0.7945 0.7955 0.7965 0.7975 0.7985 0.7995
## [801] 0.8005 0.8015 0.8025 0.8035 0.8045 0.8055 0.8065 0.8075 0.8085 0.8095
## [811] 0.8105 0.8115 0.8125 0.8135 0.8145 0.8155 0.8165 0.8175 0.8185 0.8195
## [821] 0.8205 0.8215 0.8225 0.8235 0.8245 0.8255 0.8265 0.8275 0.8285 0.8295
## [831] 0.8305 0.8315 0.8325 0.8335 0.8345 0.8355 0.8365 0.8375 0.8385 0.8395
## [841] 0.8405 0.8415 0.8425 0.8435 0.8445 0.8455 0.8465 0.8475 0.8485 0.8495
## [851] 0.8505 0.8515 0.8525 0.8535 0.8545 0.8555 0.8565 0.8575 0.8585 0.8595
## [861] 0.8605 0.8615 0.8625 0.8635 0.8645 0.8655 0.8665 0.8675 0.8685 0.8695
## [871] 0.8705 0.8715 0.8725 0.8735 0.8745 0.8755 0.8765 0.8775 0.8785 0.8795
## [881] 0.8805 0.8815 0.8825 0.8835 0.8845 0.8855 0.8865 0.8875 0.8885 0.8895
## [891] 0.8905 0.8915 0.8925 0.8935 0.8945 0.8955 0.8965 0.8975 0.8985 0.8995
## [901] 0.9005 0.9015 0.9025 0.9035 0.9045 0.9055 0.9065 0.9075 0.9085 0.9095
## [911] 0.9105 0.9115 0.9125 0.9135 0.9145 0.9155 0.9165 0.9175 0.9185 0.9195
## [921] 0.9205 0.9215 0.9225 0.9235 0.9245 0.9255 0.9265 0.9275 0.9285 0.9295
## [931] 0.9305 0.9315 0.9325 0.9335 0.9345 0.9355 0.9365 0.9375 0.9385 0.9395
## [941] 0.9405 0.9415 0.9425 0.9435 0.9445 0.9455 0.9465 0.9475 0.9485 0.9495
## [951] 0.9505 0.9515 0.9525 0.9535 0.9545 0.9555 0.9565 0.9575 0.9585 0.9595
## [961] 0.9605 0.9615 0.9625 0.9635 0.9645 0.9655 0.9665 0.9675 0.9685 0.9695
## [971] 0.9705 0.9715 0.9725 0.9735 0.9745 0.9755 0.9765 0.9775 0.9785 0.9795
## [981] 0.9805 0.9815 0.9825 0.9835 0.9845 0.9855 0.9865 0.9875 0.9885 0.9895
## [991] 0.9905 0.9915 0.9925 0.9935 0.9945 0.9955 0.9965 0.9975 0.9985 0.9995
##
## $pi.prior
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1000] 1
##
## attr(,"class")
## [1] "Bolstad"Mencari sebaran kumulatif posterior (CDF) menggunakan Simpson’s rule
cdf.post = cdf(simulasi.post.pi)
plot(cdf.post, type = "l", xlab = expression(pi[0]),
ylab = expression(Pr(pi <= pi[0])))
Inferensi Bayesian dari posterior: nilai harapan dan ragam
round(mean(simulasi.post.pi),5)## [1] 0.36364round(var(simulasi.post.pi),5)## [1] 0.01006Menggunakan fungsi quantile untuk menentukan 95% credible interval
nilai.kuantil <- quantile(simulasi.post.pi, probs = c(0.025, 0.975))
cat(paste("Approximate 95% credible interval : ["
, round(nilai.kuantil[1], 5), " ", round(nilai.kuantil[2], 5), "]\n", sep = ""))## Approximate 95% credible interval : [0.18057 0.56918].