Load Julia packages (libraries) needed for the snippets in chapter 0
using StatisticalRethinking
using CmdStan, StanMCMCChain
gr(size=(500,800))Plots.GRBackend()CmdStan uses a tmp directory to store the output of cmdstan
ProjDir = rel_path("..", "chapters", "04")
cd(ProjDir)snippet 4.7
howell1 = CSV.read(joinpath(dirname(Base.pathof(StatisticalRethinking)), "..", "data", "Howell1.csv"), delim=';')
df = convert(DataFrame, howell1);Use only adults
df2 = filter(row -> row[:age] >= 18, df)| height | weight | age | male | |
|---|---|---|---|---|
| Float64⍰ | Float64⍰ | Float64⍰ | Int64⍰ | |
| 1 | 151.765 | 47.8256 | 63.0 | 1 |
| 2 | 139.7 | 36.4858 | 63.0 | 0 |
| 3 | 136.525 | 31.8648 | 65.0 | 0 |
| 4 | 156.845 | 53.0419 | 41.0 | 1 |
| 5 | 145.415 | 41.2769 | 51.0 | 0 |
| 6 | 163.83 | 62.9926 | 35.0 | 1 |
| 7 | 149.225 | 38.2435 | 32.0 | 0 |
| 8 | 168.91 | 55.48 | 27.0 | 1 |
| 9 | 147.955 | 34.8699 | 19.0 | 0 |
| 10 | 165.1 | 54.4877 | 54.0 | 1 |
| 11 | 154.305 | 49.8951 | 47.0 | 0 |
| 12 | 151.13 | 41.2202 | 66.0 | 1 |
| 13 | 144.78 | 36.0322 | 73.0 | 0 |
| 14 | 149.9 | 47.7 | 20.0 | 0 |
| 15 | 150.495 | 33.8493 | 65.3 | 0 |
| 16 | 163.195 | 48.5627 | 36.0 | 1 |
| 17 | 157.48 | 42.3258 | 44.0 | 1 |
| 18 | 143.942 | 38.3569 | 31.0 | 0 |
| 19 | 161.29 | 48.9879 | 39.0 | 1 |
| 20 | 156.21 | 42.7227 | 29.0 | 0 |
| 21 | 146.4 | 35.4936 | 56.0 | 1 |
| 22 | 148.59 | 37.9033 | 45.0 | 0 |
| 23 | 147.32 | 35.4652 | 19.0 | 0 |
| 24 | 147.955 | 40.313 | 29.0 | 1 |
| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
Define the Stan language model
weightsmodel = "
data {
int < lower = 1 > N; // Sample size
vector[N] height; // Predictor
vector[N] weight; // Outcome
}
parameters {
real alpha; // Intercept
real beta; // Slope (regression coefficients)
real < lower = 0 > sigma; // Error SD
}
transformed parameters {
vector[N] mu; // Intermediate mu
for (i in 1:N)
mu[i] = alpha + beta*weight[i];
}
model {
height ~ normal(mu , sigma);
}
generated quantities {
}
""\ndata {\n int < lower = 1 > N; // Sample size\n vector[N] height; // Predictor\n vector[N] weight; // Outcome\n}\n\nparameters {\n real alpha; // Intercept\n real beta; // Slope (regression coefficients)\n real < lower = 0 > sigma; // Error SD\n}\n\ntransformed parameters {\n vector[N] mu; // Intermediate mu\n for (i in 1:N)\n mu[i] = alpha + beta*weight[i];\n}\n\nmodel {\n height ~ normal(mu , sigma);\n}\n\ngenerated quantities {\n}\n"Define the Stanmodel and set the output format to :mcmcchain.
stanmodel = Stanmodel(name="weights", monitors = ["alpha", "beta", "sigma"],model=weightsmodel,
output_format=:mcmcchain)Input data for cmdstan
weightsdata = [
Dict("N" => length(df2[:height]), "height" => df2[:height], "weight" => df2[:weight])
]=====> /home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04
File /home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.stan will be updated.
1-element Array{Dict{String,Any},1}:
Dict("height"=>Union{Missing, Float64}[151.765, 139.7, 136.525, 156.845, 145.415, 163.83, 149.225, 168.91, 147.955, 165.1 … 156.21, 160.655, 146.05, 156.21, 152.4, 162.56, 142.875, 162.56, 156.21, 158.75],"weight"=>Union{Missing, Float64}[47.8256, 36.4858, 31.8648, 53.0419, 41.2769, 62.9926, 38.2435, 55.48, 34.8699, 54.4877 … 44.0268, 47.8823, 39.4058, 41.0501, 40.8233, 47.0318, 34.2462, 52.1631, 54.0625, 52.5316],"N"=>352)Sample using cmdstan
rc, chn, cnames = stan(stanmodel, weightsdata, ProjDir, diagnostics=false,
CmdStanDir=CMDSTAN_HOME)Describe the draws
describe(chn)
--- Translating Stan model to C++ code ---
bin/stanc /home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.stan --o=/home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.hpp
Model name=weights_model
Input file=/home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.stan
Output file=/home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.hpp
Compiling pre-compiled header
g++ -Wall -I . -isystem stan/lib/stan_math/lib/eigen_3.3.3 -isystem stan/lib/stan_math/lib/boost_1.66.0 -isystem stan/lib/stan_math/lib/sundials_3.1.0/include -std=c++1y -DBOOST_RESULT_OF_USE_TR1 -DBOOST_NO_DECLTYPE -DBOOST_DISABLE_ASSERTS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -Wno-unused-function -Wno-uninitialized -I src -isystem stan/src -isystem stan/lib/stan_math/ -DFUSION_MAX_VECTOR_SIZE=12 -Wno-unused-local-typedefs -DEIGEN_NO_DEBUG -DNO_FPRINTF_OUTPUT -pipe -c -O3 stan/src/stan/model/model_header.hpp -o stan/src/stan/model/model_header.hpp.gch
--- Linking C++ model ---
g++ -Wall -I . -isystem stan/lib/stan_math/lib/eigen_3.3.3 -isystem stan/lib/stan_math/lib/boost_1.66.0 -isystem stan/lib/stan_math/lib/sundials_3.1.0/include -std=c++1y -DBOOST_RESULT_OF_USE_TR1 -DBOOST_NO_DECLTYPE -DBOOST_DISABLE_ASSERTS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -Wno-unused-function -Wno-uninitialized -I src -isystem stan/src -isystem stan/lib/stan_math/ -DFUSION_MAX_VECTOR_SIZE=12 -Wno-unused-local-typedefs -DEIGEN_NO_DEBUG -DNO_FPRINTF_OUTPUT -pipe src/cmdstan/main.cpp -O3 -o /home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights -include /home/travis/build/StanJulia/StatisticalRethinking.jl/docs/build/04/tmp/weights.hpp stan/lib/stan_math/lib/sundials_3.1.0/lib/libsundials_nvecserial.a stan/lib/stan_math/lib/sundials_3.1.0/lib/libsundials_cvodes.a stan/lib/stan_math/lib/sundials_3.1.0/lib/libsundials_idas.a
Length of data array is not equal to nchains,
all chains will use the first data dictionary.
Calling /home/travis/cmdstan/bin/stansummary to infer across chains.
Inference for Stan model: weights_model
4 chains: each with iter=(1000,1000,1000,1000); warmup=(0,0,0,0); thin=(1,1,1,1); 4000 iterations saved.
Warmup took (0.52, 0.58, 0.60, 0.59) seconds, 2.3 seconds total
Sampling took (0.98, 0.95, 0.93, 0.95) seconds, 3.8 seconds total
Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat
lp__ -747 3.6e-02 1.3e+00 -750 -747 -746 1.2e+03 3.2e+02 1.0e+00
accept_stat__ 0.93 1.5e-03 1.0e-01 0.73 0.97 1.00 4.3e+03 1.1e+03 1.0e+00
stepsize__ 0.10 4.0e-03 5.7e-03 0.100 0.10 0.11 2.0e+00 5.2e-01 3.7e+13
treedepth__ 4.0 1.9e-02 1.2e+00 2.0 4.0 5.0 3.8e+03 1.0e+03 1.0e+00
n_leapfrog__ 27 2.8e-01 1.7e+01 3.0 31 63 3.8e+03 9.9e+02 1.0e+00
divergent__ 0.00 -nan 0.0e+00 0.00 0.00 0.00 -nan -nan -nan
energy__ 749 4.9e-02 1.8e+00 747 749 752 1.3e+03 3.3e+02 1.0e+00
alpha 114 5.5e-02 1.9e+00 111 114 117 1.2e+03 3.2e+02 1.0e+00
beta 0.91 1.2e-03 4.3e-02 0.84 0.90 0.98 1.2e+03 3.2e+02 1.0e+00
sigma 5.1 5.4e-03 2.0e-01 4.8 5.1 5.4 1.3e+03 3.5e+02 1.0e+00
mu[1] 157 5.2e-03 3.0e-01 157 157 158 3.4e+03 8.8e+02 1.0e+00
mu[2] 147 1.2e-02 4.6e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[3] 143 1.7e-02 6.3e-01 142 143 144 1.4e+03 3.6e+02 1.0e+00
mu[4] 162 1.0e-02 4.4e-01 161 162 163 1.8e+03 4.8e+02 1.0e+00
mu[5] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.6e+02 1.0e+00
mu[6] 171 2.2e-02 8.1e-01 170 171 172 1.4e+03 3.6e+02 1.0e+00
mu[7] 148 9.6e-03 4.0e-01 148 148 149 1.7e+03 4.6e+02 1.0e+00
mu[8] 164 1.3e-02 5.2e-01 163 164 165 1.6e+03 4.2e+02 1.0e+00
mu[9] 145 1.3e-02 5.1e-01 145 145 146 1.5e+03 3.8e+02 1.0e+00
mu[10] 163 1.2e-02 4.9e-01 162 163 164 1.7e+03 4.4e+02 1.0e+00
mu[11] 159 6.9e-03 3.4e-01 158 159 160 2.5e+03 6.5e+02 1.0e+00
mu[12] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.5e+02 1.0e+00
mu[13] 146 1.2e-02 4.7e-01 146 146 147 1.5e+03 4.0e+02 1.0e+00
mu[14] 157 5.1e-03 3.0e-01 157 157 158 3.4e+03 9.0e+02 1.0e+00
mu[15] 145 1.5e-02 5.5e-01 144 145 145 1.4e+03 3.7e+02 1.0e+00
mu[16] 158 5.7e-03 3.1e-01 157 158 158 3.0e+03 7.9e+02 1.0e+00
mu[17] 152 5.4e-03 3.0e-01 152 152 153 3.0e+03 8.0e+02 1.0e+00
mu[18] 149 9.5e-03 4.0e-01 148 149 149 1.8e+03 4.6e+02 1.0e+00
mu[19] 158 6.0e-03 3.2e-01 158 158 159 2.8e+03 7.4e+02 1.0e+00
mu[20] 153 5.1e-03 2.9e-01 152 153 153 3.2e+03 8.5e+02 1.0e+00
mu[21] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[22] 148 1.0e-02 4.1e-01 147 148 149 1.7e+03 4.4e+02 1.0e+00
mu[23] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[24] 150 7.3e-03 3.4e-01 150 150 151 2.2e+03 5.7e+02 1.0e+00
mu[25] 164 1.3e-02 5.1e-01 163 164 165 1.6e+03 4.3e+02 1.0e+00
mu[26] 148 1.0e-02 4.2e-01 147 148 149 1.7e+03 4.3e+02 1.0e+00
mu[27] 149 9.3e-03 3.9e-01 148 149 149 1.8e+03 4.7e+02 1.0e+00
mu[28] 156 4.5e-03 2.8e-01 156 156 157 4.0e+03 1.0e+03 1.0e+00
mu[29] 149 8.9e-03 3.8e-01 148 149 150 1.8e+03 4.8e+02 1.0e+00
mu[30] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[31] 157 4.9e-03 2.9e-01 156 157 157 3.6e+03 9.4e+02 1.0e+00
mu[32] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.7e+02 1.0e+00
mu[33] 159 6.4e-03 3.3e-01 158 159 159 2.7e+03 7.0e+02 1.0e+00
mu[34] 159 6.4e-03 3.3e-01 158 159 159 2.7e+03 7.0e+02 1.0e+00
mu[35] 165 1.4e-02 5.6e-01 164 165 166 1.6e+03 4.1e+02 1.0e+00
mu[36] 149 8.6e-03 3.7e-01 149 149 150 1.9e+03 4.9e+02 1.0e+00
mu[37] 159 6.9e-03 3.4e-01 158 159 160 2.5e+03 6.5e+02 1.0e+00
mu[38] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.6e+02 1.0e+00
mu[39] 149 9.2e-03 3.9e-01 148 149 149 1.8e+03 4.7e+02 1.0e+00
mu[40] 152 5.4e-03 3.0e-01 152 152 153 3.1e+03 8.1e+02 1.0e+00
mu[41] 154 4.3e-03 2.8e-01 154 154 155 4.2e+03 1.1e+03 1.0e+00
mu[42] 167 1.7e-02 6.4e-01 166 167 168 1.5e+03 3.9e+02 1.0e+00
mu[43] 156 4.5e-03 2.8e-01 156 156 157 3.9e+03 1.0e+03 1.0e+00
mu[44] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.1e+03 1.0e+00
mu[45] 160 7.9e-03 3.7e-01 159 160 161 2.2e+03 5.8e+02 1.0e+00
mu[46] 163 1.2e-02 4.8e-01 162 163 164 1.7e+03 4.5e+02 1.0e+00
mu[47] 155 4.3e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[48] 157 5.3e-03 3.0e-01 157 157 158 3.3e+03 8.6e+02 1.0e+00
mu[49] 161 9.3e-03 4.1e-01 160 161 162 1.9e+03 5.1e+02 1.0e+00
mu[50] 157 5.0e-03 3.0e-01 156 157 157 3.5e+03 9.1e+02 1.0e+00
mu[51] 155 4.2e-03 2.8e-01 155 155 156 4.3e+03 1.1e+03 1.0e+00
mu[52] 152 5.3e-03 3.0e-01 152 152 153 3.1e+03 8.1e+02 1.0e+00
mu[53] 147 1.2e-02 4.6e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[54] 165 1.4e-02 5.4e-01 164 164 165 1.6e+03 4.2e+02 1.0e+00
mu[55] 148 1.1e-02 4.3e-01 147 148 148 1.6e+03 4.3e+02 1.0e+00
mu[56] 158 5.5e-03 3.1e-01 157 158 158 3.1e+03 8.2e+02 1.0e+00
mu[57] 148 1.1e-02 4.3e-01 147 148 148 1.6e+03 4.3e+02 1.0e+00
mu[58] 157 4.8e-03 2.9e-01 156 157 157 3.7e+03 9.7e+02 1.0e+00
mu[59] 157 4.8e-03 2.9e-01 156 157 157 3.6e+03 9.5e+02 1.0e+00
mu[60] 166 1.5e-02 6.0e-01 165 166 167 1.5e+03 4.0e+02 1.0e+00
mu[61] 148 9.9e-03 4.1e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[62] 157 4.8e-03 2.9e-01 156 157 157 3.7e+03 9.6e+02 1.0e+00
mu[63] 153 4.8e-03 2.9e-01 153 153 153 3.5e+03 9.2e+02 1.0e+00
mu[64] 159 7.2e-03 3.5e-01 159 159 160 2.4e+03 6.2e+02 1.0e+00
mu[65] 150 8.3e-03 3.7e-01 149 150 150 1.9e+03 5.1e+02 1.0e+00
mu[66] 160 7.7e-03 3.6e-01 159 160 160 2.3e+03 5.9e+02 1.0e+00
mu[67] 150 8.3e-03 3.6e-01 149 150 150 1.9e+03 5.1e+02 1.0e+00
mu[68] 147 1.2e-02 4.6e-01 146 147 147 1.5e+03 4.1e+02 1.0e+00
mu[69] 156 4.4e-03 2.8e-01 155 156 156 4.1e+03 1.1e+03 1.0e+00
mu[70] 152 5.5e-03 3.0e-01 152 152 153 3.0e+03 7.9e+02 1.0e+00
mu[71] 157 5.0e-03 3.0e-01 156 157 157 3.5e+03 9.1e+02 1.0e+00
mu[72] 164 1.3e-02 5.3e-01 163 164 165 1.6e+03 4.2e+02 1.0e+00
mu[73] 158 5.7e-03 3.1e-01 157 158 158 3.0e+03 7.9e+02 1.0e+00
mu[74] 153 5.1e-03 2.9e-01 152 153 153 3.3e+03 8.6e+02 1.0e+00
mu[75] 146 1.3e-02 5.1e-01 145 146 146 1.5e+03 3.9e+02 1.0e+00
mu[76] 165 1.4e-02 5.7e-01 164 165 166 1.5e+03 4.1e+02 1.0e+00
mu[77] 160 8.3e-03 3.8e-01 160 160 161 2.1e+03 5.6e+02 1.0e+00
mu[78] 157 4.8e-03 2.9e-01 156 157 157 3.7e+03 9.6e+02 1.0e+00
mu[79] 151 6.7e-03 3.3e-01 150 151 151 2.4e+03 6.2e+02 1.0e+00
mu[80] 143 1.6e-02 5.9e-01 143 143 144 1.4e+03 3.6e+02 1.0e+00
mu[81] 166 1.5e-02 5.8e-01 165 166 167 1.5e+03 4.0e+02 1.0e+00
mu[82] 153 5.0e-03 2.9e-01 152 153 153 3.4e+03 8.9e+02 1.0e+00
mu[83] 150 7.7e-03 3.5e-01 149 150 151 2.1e+03 5.4e+02 1.0e+00
mu[84] 155 4.3e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[85] 151 6.5e-03 3.2e-01 151 151 152 2.4e+03 6.4e+02 1.0e+00
mu[86] 157 5.0e-03 3.0e-01 156 157 157 3.5e+03 9.1e+02 1.0e+00
mu[87] 148 1.0e-02 4.2e-01 147 148 149 1.7e+03 4.3e+02 1.0e+00
mu[88] 155 4.2e-03 2.7e-01 154 155 155 4.2e+03 1.1e+03 1.0e+00
mu[89] 152 5.5e-03 3.0e-01 152 152 153 3.0e+03 7.9e+02 1.0e+00
mu[90] 164 1.2e-02 5.0e-01 163 164 164 1.7e+03 4.3e+02 1.0e+00
mu[91] 162 1.1e-02 4.5e-01 162 162 163 1.8e+03 4.7e+02 1.0e+00
mu[92] 161 9.3e-03 4.1e-01 160 161 162 1.9e+03 5.1e+02 1.0e+00
mu[93] 152 5.3e-03 3.0e-01 152 152 153 3.1e+03 8.1e+02 1.0e+00
mu[94] 159 6.6e-03 3.4e-01 158 159 159 2.6e+03 6.8e+02 1.0e+00
mu[95] 152 5.9e-03 3.1e-01 151 152 152 2.7e+03 7.1e+02 1.0e+00
mu[96] 165 1.4e-02 5.4e-01 164 165 165 1.6e+03 4.1e+02 1.0e+00
mu[97] 152 5.6e-03 3.0e-01 152 152 153 2.9e+03 7.7e+02 1.0e+00
mu[98] 162 1.0e-02 4.4e-01 161 162 163 1.8e+03 4.8e+02 1.0e+00
mu[99] 159 7.2e-03 3.5e-01 159 159 160 2.4e+03 6.2e+02 1.0e+00
mu[100] 152 5.3e-03 3.0e-01 152 152 153 3.1e+03 8.3e+02 1.0e+00
mu[101] 158 6.1e-03 3.2e-01 158 158 159 2.8e+03 7.3e+02 1.0e+00
mu[102] 149 9.3e-03 3.9e-01 148 149 149 1.8e+03 4.7e+02 1.0e+00
mu[103] 159 6.8e-03 3.4e-01 158 159 160 2.5e+03 6.6e+02 1.0e+00
mu[104] 168 1.8e-02 6.8e-01 167 168 169 1.4e+03 3.8e+02 1.0e+00
mu[105] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.7e+02 1.0e+00
mu[106] 149 8.4e-03 3.7e-01 149 149 150 1.9e+03 5.0e+02 1.0e+00
mu[107] 147 1.1e-02 4.4e-01 147 147 148 1.6e+03 4.2e+02 1.0e+00
mu[108] 152 5.6e-03 3.0e-01 152 152 152 2.9e+03 7.7e+02 1.0e+00
mu[109] 154 4.3e-03 2.8e-01 154 154 155 4.1e+03 1.1e+03 1.0e+00
mu[110] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.8e+02 1.0e+00
mu[111] 164 1.3e-02 5.1e-01 163 164 165 1.6e+03 4.3e+02 1.0e+00
mu[112] 144 1.6e-02 5.8e-01 143 144 145 1.4e+03 3.6e+02 1.0e+00
mu[113] 151 6.7e-03 3.3e-01 150 151 151 2.4e+03 6.2e+02 1.0e+00
mu[114] 160 8.2e-03 3.8e-01 160 160 161 2.1e+03 5.6e+02 1.0e+00
mu[115] 158 6.1e-03 3.2e-01 158 158 159 2.8e+03 7.4e+02 1.0e+00
mu[116] 162 1.1e-02 4.5e-01 162 162 163 1.8e+03 4.7e+02 1.0e+00
mu[117] 163 1.1e-02 4.7e-01 162 163 164 1.7e+03 4.5e+02 1.0e+00
mu[118] 164 1.3e-02 5.2e-01 163 164 165 1.6e+03 4.3e+02 1.0e+00
mu[119] 152 5.5e-03 3.0e-01 152 152 153 3.0e+03 7.9e+02 1.0e+00
mu[120] 151 6.7e-03 3.3e-01 150 151 151 2.4e+03 6.2e+02 1.0e+00
mu[121] 159 6.7e-03 3.4e-01 158 159 159 2.6e+03 6.7e+02 1.0e+00
mu[122] 154 4.3e-03 2.8e-01 154 154 154 4.1e+03 1.1e+03 1.0e+00
mu[123] 155 4.3e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[124] 152 5.7e-03 3.1e-01 151 152 152 2.8e+03 7.4e+02 1.0e+00
mu[125] 160 8.5e-03 3.9e-01 160 160 161 2.1e+03 5.4e+02 1.0e+00
mu[126] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.0e+03 1.0e+00
mu[127] 143 1.7e-02 6.1e-01 142 143 144 1.4e+03 3.6e+02 1.0e+00
mu[128] 165 1.4e-02 5.7e-01 164 165 166 1.5e+03 4.1e+02 1.0e+00
mu[129] 162 9.8e-03 4.2e-01 161 162 162 1.9e+03 4.9e+02 1.0e+00
mu[130] 147 1.2e-02 4.6e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[131] 158 5.9e-03 3.2e-01 158 158 159 2.9e+03 7.6e+02 1.0e+00
mu[132] 165 1.5e-02 5.8e-01 165 165 166 1.5e+03 4.0e+02 1.0e+00
mu[133] 152 5.6e-03 3.0e-01 151 152 152 2.9e+03 7.6e+02 1.0e+00
mu[134] 159 7.2e-03 3.5e-01 159 159 160 2.4e+03 6.3e+02 1.0e+00
mu[135] 156 4.5e-03 2.8e-01 156 156 156 4.0e+03 1.0e+03 1.0e+00
mu[136] 170 2.0e-02 7.6e-01 169 170 171 1.4e+03 3.7e+02 1.0e+00
mu[137] 158 6.0e-03 3.2e-01 158 158 159 2.8e+03 7.4e+02 1.0e+00
mu[138] 142 1.7e-02 6.4e-01 141 142 143 1.4e+03 3.5e+02 1.0e+00
mu[139] 146 1.3e-02 5.0e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[140] 155 4.2e-03 2.8e-01 155 155 156 4.3e+03 1.1e+03 1.0e+00
mu[141] 154 4.5e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[142] 155 4.2e-03 2.8e-01 155 155 156 4.3e+03 1.1e+03 1.0e+00
mu[143] 149 8.7e-03 3.8e-01 149 149 150 1.9e+03 4.9e+02 1.0e+00
mu[144] 151 6.5e-03 3.2e-01 151 151 152 2.5e+03 6.5e+02 1.0e+00
mu[145] 155 4.2e-03 2.8e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[146] 162 1.1e-02 4.6e-01 162 162 163 1.8e+03 4.6e+02 1.0e+00
mu[147] 161 9.4e-03 4.1e-01 161 161 162 1.9e+03 5.1e+02 1.0e+00
mu[148] 149 8.6e-03 3.7e-01 149 149 150 1.9e+03 4.9e+02 1.0e+00
mu[149] 155 4.2e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[150] 150 7.2e-03 3.4e-01 150 150 151 2.2e+03 5.8e+02 1.0e+00
mu[151] 160 8.5e-03 3.9e-01 160 160 161 2.1e+03 5.4e+02 1.0e+00
mu[152] 149 9.1e-03 3.9e-01 148 149 149 1.8e+03 4.7e+02 1.0e+00
mu[153] 149 8.5e-03 3.7e-01 149 149 150 1.9e+03 5.0e+02 1.0e+00
mu[154] 154 4.3e-03 2.8e-01 154 154 154 4.1e+03 1.1e+03 1.0e+00
mu[155] 150 8.2e-03 3.6e-01 149 150 150 2.0e+03 5.2e+02 1.0e+00
mu[156] 142 1.8e-02 6.6e-01 141 142 143 1.3e+03 3.5e+02 1.0e+00
mu[157] 156 4.6e-03 2.8e-01 156 156 157 3.9e+03 1.0e+03 1.0e+00
mu[158] 151 7.0e-03 3.3e-01 150 151 151 2.3e+03 6.0e+02 1.0e+00
mu[159] 159 7.2e-03 3.5e-01 159 159 160 2.4e+03 6.3e+02 1.0e+00
mu[160] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.6e+02 1.0e+00
mu[161] 163 1.2e-02 4.9e-01 163 163 164 1.7e+03 4.4e+02 1.0e+00
mu[162] 155 4.2e-03 2.7e-01 154 155 155 4.2e+03 1.1e+03 1.0e+00
mu[163] 146 1.2e-02 4.8e-01 145 146 147 1.5e+03 4.0e+02 1.0e+00
mu[164] 155 4.2e-03 2.8e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[165] 157 5.4e-03 3.0e-01 157 157 158 3.2e+03 8.4e+02 1.0e+00
mu[166] 155 4.2e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[167] 158 5.6e-03 3.1e-01 157 158 158 3.1e+03 8.1e+02 1.0e+00
mu[168] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.5e+02 1.0e+00
mu[169] 149 9.4e-03 3.9e-01 148 149 149 1.8e+03 4.6e+02 1.0e+00
mu[170] 152 5.6e-03 3.0e-01 152 152 152 2.9e+03 7.7e+02 1.0e+00
mu[171] 148 9.6e-03 4.0e-01 148 148 149 1.7e+03 4.6e+02 1.0e+00
mu[172] 158 5.5e-03 3.1e-01 157 158 158 3.1e+03 8.2e+02 1.0e+00
mu[173] 149 8.8e-03 3.8e-01 148 149 150 1.8e+03 4.8e+02 1.0e+00
mu[174] 150 7.6e-03 3.5e-01 150 150 151 2.1e+03 5.5e+02 1.0e+00
mu[175] 159 7.2e-03 3.5e-01 159 159 160 2.4e+03 6.3e+02 1.0e+00
mu[176] 163 1.2e-02 4.8e-01 162 163 164 1.7e+03 4.5e+02 1.0e+00
mu[177] 155 4.2e-03 2.8e-01 155 155 156 4.3e+03 1.1e+03 1.0e+00
mu[178] 150 8.3e-03 3.6e-01 149 150 150 1.9e+03 5.1e+02 1.0e+00
mu[179] 153 4.8e-03 2.9e-01 153 153 153 3.5e+03 9.2e+02 1.0e+00
mu[180] 143 1.7e-02 6.3e-01 142 143 144 1.4e+03 3.6e+02 1.0e+00
mu[181] 155 4.2e-03 2.8e-01 155 155 155 4.3e+03 1.1e+03 1.0e+00
mu[182] 148 9.8e-03 4.1e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[183] 147 1.2e-02 4.7e-01 146 147 147 1.5e+03 4.0e+02 1.0e+00
mu[184] 151 6.7e-03 3.3e-01 150 151 151 2.4e+03 6.2e+02 1.0e+00
mu[185] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.7e+02 1.0e+00
mu[186] 157 5.1e-03 3.0e-01 157 157 158 3.4e+03 9.0e+02 1.0e+00
mu[187] 156 4.4e-03 2.8e-01 155 156 156 4.1e+03 1.1e+03 1.0e+00
mu[188] 151 6.5e-03 3.2e-01 151 151 152 2.5e+03 6.5e+02 1.0e+00
mu[189] 147 1.1e-02 4.5e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[190] 157 5.4e-03 3.0e-01 157 157 158 3.2e+03 8.4e+02 1.0e+00
mu[191] 147 1.1e-02 4.5e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[192] 165 1.4e-02 5.6e-01 164 165 166 1.6e+03 4.1e+02 1.0e+00
mu[193] 149 9.1e-03 3.9e-01 148 149 150 1.8e+03 4.7e+02 1.0e+00
mu[194] 157 4.9e-03 2.9e-01 156 157 157 3.5e+03 9.3e+02 1.0e+00
mu[195] 147 1.2e-02 4.7e-01 146 147 147 1.5e+03 4.0e+02 1.0e+00
mu[196] 151 6.4e-03 3.2e-01 151 151 152 2.5e+03 6.6e+02 1.0e+00
mu[197] 154 4.2e-03 2.8e-01 154 154 155 4.2e+03 1.1e+03 1.0e+00
mu[198] 160 7.4e-03 3.6e-01 159 160 160 2.3e+03 6.1e+02 1.0e+00
mu[199] 164 1.3e-02 5.1e-01 163 164 165 1.6e+03 4.3e+02 1.0e+00
mu[200] 148 9.9e-03 4.1e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[201] 167 1.6e-02 6.3e-01 166 167 168 1.5e+03 3.9e+02 1.0e+00
mu[202] 154 4.3e-03 2.8e-01 154 154 155 4.1e+03 1.1e+03 1.0e+00
mu[203] 154 4.3e-03 2.8e-01 154 154 155 4.1e+03 1.1e+03 1.0e+00
mu[204] 154 4.3e-03 2.8e-01 154 154 155 4.1e+03 1.1e+03 1.0e+00
mu[205] 154 4.3e-03 2.8e-01 154 154 155 4.2e+03 1.1e+03 1.0e+00
mu[206] 151 7.1e-03 3.4e-01 150 151 151 2.2e+03 5.8e+02 1.0e+00
mu[207] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.0e+03 1.0e+00
mu[208] 145 1.4e-02 5.3e-01 144 145 146 1.4e+03 3.8e+02 1.0e+00
mu[209] 144 1.6e-02 5.9e-01 143 144 144 1.4e+03 3.6e+02 1.0e+00
mu[210] 146 1.2e-02 4.8e-01 146 146 147 1.5e+03 4.0e+02 1.0e+00
mu[211] 159 6.5e-03 3.3e-01 158 159 159 2.6e+03 6.9e+02 1.0e+00
mu[212] 162 1.0e-02 4.4e-01 161 162 163 1.8e+03 4.8e+02 1.0e+00
mu[213] 147 1.1e-02 4.4e-01 147 147 148 1.6e+03 4.2e+02 1.0e+00
mu[214] 151 7.1e-03 3.4e-01 150 151 151 2.2e+03 5.9e+02 1.0e+00
mu[215] 160 7.6e-03 3.6e-01 159 160 160 2.3e+03 6.0e+02 1.0e+00
mu[216] 154 4.5e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[217] 159 6.9e-03 3.4e-01 158 159 160 2.5e+03 6.5e+02 1.0e+00
mu[218] 144 1.5e-02 5.6e-01 143 144 145 1.4e+03 3.7e+02 1.0e+00
mu[219] 154 4.5e-03 2.8e-01 153 154 154 3.8e+03 1.0e+03 1.0e+00
mu[220] 157 5.4e-03 3.0e-01 157 157 158 3.2e+03 8.4e+02 1.0e+00
mu[221] 153 5.1e-03 2.9e-01 152 153 153 3.3e+03 8.6e+02 1.0e+00
mu[222] 145 1.5e-02 5.5e-01 144 145 145 1.4e+03 3.7e+02 1.0e+00
mu[223] 150 8.0e-03 3.6e-01 149 150 150 2.0e+03 5.3e+02 1.0e+00
mu[224] 146 1.2e-02 4.8e-01 146 146 147 1.5e+03 4.0e+02 1.0e+00
mu[225] 160 7.9e-03 3.7e-01 159 160 161 2.2e+03 5.8e+02 1.0e+00
mu[226] 155 4.3e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[227] 158 6.2e-03 3.3e-01 158 158 159 2.8e+03 7.2e+02 1.0e+00
mu[228] 167 1.7e-02 6.5e-01 166 167 168 1.5e+03 3.9e+02 1.0e+00
mu[229] 153 4.7e-03 2.8e-01 153 153 154 3.6e+03 9.5e+02 1.0e+00
mu[230] 161 9.0e-03 4.0e-01 160 161 162 2.0e+03 5.2e+02 1.0e+00
mu[231] 160 7.7e-03 3.6e-01 159 160 160 2.3e+03 5.9e+02 1.0e+00
mu[232] 145 1.4e-02 5.4e-01 144 145 146 1.4e+03 3.8e+02 1.0e+00
mu[233] 150 8.3e-03 3.7e-01 149 150 150 1.9e+03 5.1e+02 1.0e+00
mu[234] 168 1.8e-02 6.8e-01 167 168 169 1.4e+03 3.8e+02 1.0e+00
mu[235] 161 9.2e-03 4.1e-01 160 161 162 2.0e+03 5.1e+02 1.0e+00
mu[236] 150 7.7e-03 3.5e-01 149 150 151 2.1e+03 5.4e+02 1.0e+00
mu[237] 154 4.5e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[238] 163 1.2e-02 4.9e-01 163 163 164 1.7e+03 4.4e+02 1.0e+00
mu[239] 155 4.2e-03 2.7e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[240] 151 6.3e-03 3.2e-01 151 151 152 2.5e+03 6.6e+02 1.0e+00
mu[241] 152 5.8e-03 3.1e-01 151 152 152 2.8e+03 7.3e+02 1.0e+00
mu[242] 152 5.3e-03 3.0e-01 152 152 153 3.1e+03 8.3e+02 1.0e+00
mu[243] 153 4.9e-03 2.9e-01 152 153 153 3.5e+03 9.1e+02 1.0e+00
mu[244] 151 6.8e-03 3.3e-01 150 151 151 2.3e+03 6.1e+02 1.0e+00
mu[245] 153 5.0e-03 2.9e-01 152 153 153 3.3e+03 8.7e+02 1.0e+00
mu[246] 156 4.4e-03 2.8e-01 155 156 156 4.1e+03 1.1e+03 1.0e+00
mu[247] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.8e+02 1.0e+00
mu[248] 152 5.3e-03 3.0e-01 152 152 153 3.1e+03 8.3e+02 1.0e+00
mu[249] 158 5.7e-03 3.1e-01 157 158 158 3.0e+03 8.0e+02 1.0e+00
mu[250] 155 4.3e-03 2.8e-01 155 155 156 4.2e+03 1.1e+03 1.0e+00
mu[251] 162 1.0e-02 4.3e-01 161 162 162 1.8e+03 4.8e+02 1.0e+00
mu[252] 157 5.0e-03 2.9e-01 156 157 157 3.5e+03 9.1e+02 1.0e+00
mu[253] 153 4.7e-03 2.8e-01 153 153 154 3.7e+03 9.7e+02 1.0e+00
mu[254] 153 4.7e-03 2.8e-01 153 153 154 3.6e+03 9.5e+02 1.0e+00
mu[255] 162 1.0e-02 4.4e-01 161 162 163 1.8e+03 4.7e+02 1.0e+00
mu[256] 154 4.3e-03 2.8e-01 154 154 155 4.2e+03 1.1e+03 1.0e+00
mu[257] 157 4.8e-03 2.9e-01 156 157 157 3.7e+03 9.6e+02 1.0e+00
mu[258] 143 1.7e-02 6.3e-01 141 143 144 1.4e+03 3.6e+02 1.0e+00
mu[259] 165 1.4e-02 5.6e-01 164 165 166 1.6e+03 4.1e+02 1.0e+00
mu[260] 164 1.3e-02 5.3e-01 164 164 165 1.6e+03 4.2e+02 1.0e+00
mu[261] 157 4.9e-03 2.9e-01 156 157 157 3.5e+03 9.3e+02 1.0e+00
mu[262] 155 4.2e-03 2.7e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[263] 155 4.2e-03 2.8e-01 155 155 156 4.3e+03 1.1e+03 1.0e+00
mu[264] 158 5.9e-03 3.2e-01 158 158 159 2.9e+03 7.6e+02 1.0e+00
mu[265] 156 4.5e-03 2.8e-01 156 156 156 4.0e+03 1.0e+03 1.0e+00
mu[266] 154 4.5e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[267] 165 1.4e-02 5.4e-01 164 165 166 1.6e+03 4.1e+02 1.0e+00
mu[268] 150 7.6e-03 3.5e-01 150 150 151 2.1e+03 5.5e+02 1.0e+00
mu[269] 160 7.8e-03 3.7e-01 159 160 160 2.2e+03 5.8e+02 1.0e+00
mu[270] 156 4.4e-03 2.8e-01 155 156 156 4.1e+03 1.1e+03 1.0e+00
mu[271] 159 6.4e-03 3.3e-01 158 159 159 2.7e+03 7.1e+02 1.0e+00
mu[272] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.0e+03 1.0e+00
mu[273] 160 8.0e-03 3.7e-01 159 160 161 2.2e+03 5.7e+02 1.0e+00
mu[274] 151 6.9e-03 3.3e-01 150 151 151 2.3e+03 6.1e+02 1.0e+00
mu[275] 148 1.0e-02 4.2e-01 147 148 149 1.7e+03 4.3e+02 1.0e+00
mu[276] 161 8.6e-03 3.9e-01 160 161 161 2.1e+03 5.4e+02 1.0e+00
mu[277] 154 4.2e-03 2.8e-01 154 154 155 4.2e+03 1.1e+03 1.0e+00
mu[278] 153 4.7e-03 2.8e-01 153 153 154 3.6e+03 9.5e+02 1.0e+00
mu[279] 156 4.5e-03 2.8e-01 156 156 157 3.9e+03 1.0e+03 1.0e+00
mu[280] 150 8.1e-03 3.6e-01 149 150 150 2.0e+03 5.2e+02 1.0e+00
mu[281] 145 1.4e-02 5.2e-01 145 145 146 1.5e+03 3.8e+02 1.0e+00
mu[282] 149 8.4e-03 3.7e-01 149 149 150 1.9e+03 5.0e+02 1.0e+00
mu[283] 148 1.0e-02 4.2e-01 147 148 148 1.6e+03 4.3e+02 1.0e+00
mu[284] 158 5.8e-03 3.2e-01 157 158 158 3.0e+03 7.8e+02 1.0e+00
mu[285] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[286] 153 4.6e-03 2.8e-01 153 153 154 3.8e+03 9.9e+02 1.0e+00
mu[287] 157 5.4e-03 3.1e-01 157 157 158 3.2e+03 8.3e+02 1.0e+00
mu[288] 160 8.0e-03 3.7e-01 159 160 161 2.2e+03 5.7e+02 1.0e+00
mu[289] 154 4.5e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[290] 157 5.4e-03 3.1e-01 157 157 158 3.2e+03 8.3e+02 1.0e+00
mu[291] 156 4.5e-03 2.8e-01 156 156 157 3.9e+03 1.0e+03 1.0e+00
mu[292] 165 1.4e-02 5.6e-01 164 165 166 1.6e+03 4.1e+02 1.0e+00
mu[293] 158 5.7e-03 3.1e-01 157 158 158 3.0e+03 7.9e+02 1.0e+00
mu[294] 158 5.4e-03 3.1e-01 157 158 158 3.2e+03 8.3e+02 1.0e+00
mu[295] 157 4.9e-03 2.9e-01 156 157 157 3.5e+03 9.3e+02 1.0e+00
mu[296] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[297] 147 1.1e-02 4.5e-01 146 147 148 1.6e+03 4.1e+02 1.0e+00
mu[298] 158 6.0e-03 3.2e-01 158 158 159 2.8e+03 7.5e+02 1.0e+00
mu[299] 160 8.3e-03 3.8e-01 160 160 161 2.1e+03 5.6e+02 1.0e+00
mu[300] 156 4.5e-03 2.8e-01 156 156 156 4.0e+03 1.0e+03 1.0e+00
mu[301] 147 1.1e-02 4.4e-01 147 147 148 1.6e+03 4.2e+02 1.0e+00
mu[302] 158 5.8e-03 3.1e-01 157 158 158 3.0e+03 7.8e+02 1.0e+00
mu[303] 148 9.8e-03 4.1e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[304] 157 4.8e-03 2.9e-01 156 157 157 3.6e+03 9.5e+02 1.0e+00
mu[305] 164 1.3e-02 5.2e-01 163 164 165 1.6e+03 4.2e+02 1.0e+00
mu[306] 163 1.2e-02 4.8e-01 162 163 164 1.7e+03 4.5e+02 1.0e+00
mu[307] 158 5.6e-03 3.1e-01 157 158 158 3.0e+03 8.0e+02 1.0e+00
mu[308] 153 4.9e-03 2.9e-01 152 153 153 3.4e+03 9.0e+02 1.0e+00
mu[309] 145 1.4e-02 5.4e-01 144 145 146 1.4e+03 3.8e+02 1.0e+00
mu[310] 159 6.9e-03 3.4e-01 159 159 160 2.5e+03 6.5e+02 1.0e+00
mu[311] 154 4.3e-03 2.8e-01 154 154 154 4.1e+03 1.1e+03 1.0e+00
mu[312] 144 1.5e-02 5.7e-01 143 144 145 1.4e+03 3.7e+02 1.0e+00
mu[313] 157 4.8e-03 2.9e-01 156 157 157 3.6e+03 9.5e+02 1.0e+00
mu[314] 156 4.3e-03 2.8e-01 155 156 156 4.1e+03 1.1e+03 1.0e+00
mu[315] 157 4.9e-03 2.9e-01 156 157 157 3.6e+03 9.4e+02 1.0e+00
mu[316] 151 6.8e-03 3.3e-01 150 151 151 2.3e+03 6.2e+02 1.0e+00
mu[317] 159 7.3e-03 3.6e-01 159 159 160 2.3e+03 6.2e+02 1.0e+00
mu[318] 155 4.2e-03 2.7e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[319] 152 5.5e-03 3.0e-01 152 152 153 3.0e+03 7.9e+02 1.0e+00
mu[320] 152 6.0e-03 3.1e-01 151 152 152 2.7e+03 7.0e+02 1.0e+00
mu[321] 155 4.2e-03 2.8e-01 154 155 155 4.3e+03 1.1e+03 1.0e+00
mu[322] 160 8.3e-03 3.8e-01 160 160 161 2.1e+03 5.6e+02 1.0e+00
mu[323] 158 6.3e-03 3.3e-01 158 158 159 2.7e+03 7.2e+02 1.0e+00
mu[324] 160 8.2e-03 3.8e-01 160 160 161 2.1e+03 5.6e+02 1.0e+00
mu[325] 154 4.5e-03 2.8e-01 153 154 154 3.8e+03 1.0e+03 1.0e+00
mu[326] 146 1.3e-02 4.9e-01 145 146 147 1.5e+03 3.9e+02 1.0e+00
mu[327] 153 5.0e-03 2.9e-01 152 153 153 3.3e+03 8.7e+02 1.0e+00
mu[328] 156 4.6e-03 2.8e-01 156 156 157 3.9e+03 1.0e+03 1.0e+00
mu[329] 152 5.8e-03 3.1e-01 151 152 152 2.8e+03 7.3e+02 1.0e+00
mu[330] 148 9.6e-03 4.0e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[331] 153 4.8e-03 2.9e-01 153 153 154 3.6e+03 9.3e+02 1.0e+00
mu[332] 162 1.1e-02 4.6e-01 162 162 163 1.8e+03 4.6e+02 1.0e+00
mu[333] 153 5.0e-03 2.9e-01 152 153 153 3.4e+03 8.9e+02 1.0e+00
mu[334] 150 7.9e-03 3.6e-01 149 150 150 2.0e+03 5.3e+02 1.0e+00
mu[335] 153 4.8e-03 2.8e-01 153 153 154 3.6e+03 9.4e+02 1.0e+00
mu[336] 162 9.8e-03 4.2e-01 161 162 162 1.9e+03 4.9e+02 1.0e+00
mu[337] 149 9.4e-03 3.9e-01 148 149 149 1.8e+03 4.6e+02 1.0e+00
mu[338] 153 5.1e-03 2.9e-01 152 153 153 3.3e+03 8.6e+02 1.0e+00
mu[339] 146 1.2e-02 4.8e-01 146 146 147 1.5e+03 4.0e+02 1.0e+00
mu[340] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.1e+03 1.0e+00
mu[341] 148 9.8e-03 4.1e-01 148 148 149 1.7e+03 4.5e+02 1.0e+00
mu[342] 154 4.4e-03 2.8e-01 153 154 154 4.0e+03 1.0e+03 1.0e+00
mu[343] 154 4.4e-03 2.8e-01 153 154 154 3.9e+03 1.0e+03 1.0e+00
mu[344] 157 5.2e-03 3.0e-01 157 157 158 3.3e+03 8.7e+02 1.0e+00
mu[345] 150 8.3e-03 3.7e-01 149 150 150 1.9e+03 5.1e+02 1.0e+00
mu[346] 151 6.6e-03 3.2e-01 150 151 152 2.4e+03 6.3e+02 1.0e+00
mu[347] 151 6.8e-03 3.3e-01 150 151 151 2.3e+03 6.1e+02 1.0e+00
mu[348] 156 4.7e-03 2.9e-01 156 156 157 3.8e+03 9.9e+02 1.0e+00
mu[349] 145 1.4e-02 5.4e-01 144 145 146 1.4e+03 3.8e+02 1.0e+00
mu[350] 161 9.2e-03 4.1e-01 160 161 162 2.0e+03 5.1e+02 1.0e+00
mu[351] 163 1.1e-02 4.7e-01 162 163 164 1.7e+03 4.5e+02 1.0e+00
mu[352] 161 9.7e-03 4.2e-01 161 161 162 1.9e+03 5.0e+02 1.0e+00
Samples were drawn using hmc with nuts.
For each parameter, N_Eff is a crude measure of effective sample size,
and R_hat is the potential scale reduction factor on split chains (at
convergence, R_hat=1).
Iterations = 1:1000
Thinning interval = 1
Chains = 1,2,3,4
Samples per chain = 1000
Empirical Posterior Estimates:
Mean SD Naive SE MCSE ESS
alpha 113.84662700 1.93744094 0.0306336310 0.0490944240 1000
beta 0.90577455 0.04255897 0.0006729164 0.0010797076 1000
sigma 5.10538214 0.19832238 0.0031357521 0.0055810858 1000
Quantiles:
2.5% 25.0% 50.0% 75.0% 97.5%
alpha 110.1015750 112.50975000 113.896500 115.1565000 117.5120500
beta 0.8238506 0.87694575 0.904653 0.9342925 0.9896207
sigma 4.7219000 4.97362500 5.105230 5.2339925 5.5106255Compare with a previous result
clip_38s_example_output = "
Samples were drawn using hmc with nuts.
For each parameter, N_Eff is a crude measure of effective sample size,
and R_hat is the potential scale reduction factor on split chains (at
convergence, R_hat=1).
Iterations = 1:1000
Thinning interval = 1
Chains = 1,2,3,4
Samples per chain = 1000
Empirical Posterior Estimates:
Mean SD Naive SE MCSE ESS
alpha 113.82267275 1.89871177 0.0300212691 0.053895503 1000
beta 0.90629952 0.04155225 0.0006569987 0.001184630 1000
sigma 5.10334279 0.19755211 0.0031235731 0.004830464 1000
Quantiles:
2.5% 25.0% 50.0% 75.0% 97.5%
alpha 110.1927000 112.4910000 113.7905000 115.1322500 117.5689750
beta 0.8257932 0.8775302 0.9069425 0.9357115 0.9862574
sigma 4.7308260 4.9644050 5.0958800 5.2331875 5.5133417
sigma 3.9447100 4.1530675 4.254755 4.36483000 4.5871028
""\n\nSamples were drawn using hmc with nuts.\nFor each parameter, N_Eff is a crude measure of effective sample size,\nand R_hat is the potential scale reduction factor on split chains (at\nconvergence, R_hat=1).\n\nIterations = 1:1000\nThinning interval = 1\nChains = 1,2,3,4\nSamples per chain = 1000\n\nEmpirical Posterior Estimates:\n Mean SD Naive SE MCSE ESS\nalpha 113.82267275 1.89871177 0.0300212691 0.053895503 1000\n beta 0.90629952 0.04155225 0.0006569987 0.001184630 1000\nsigma 5.10334279 0.19755211 0.0031235731 0.004830464 1000\n\nQuantiles:\n 2.5% 25.0% 50.0% 75.0% 97.5%\nalpha 110.1927000 112.4910000 113.7905000 115.1322500 117.5689750\n beta 0.8257932 0.8775302 0.9069425 0.9357115 0.9862574\nsigma 4.7308260 4.9644050 5.0958800 5.2331875 5.5133417\nsigma 3.9447100 4.1530675 4.254755 4.36483000 4.5871028\n\n"Plot the density of posterior draws
plot(chn)Plot regression line using means and observations
xi = 30.0:0.1:65.0
rws, vars, chns = size(chn[:, 1, :])
alpha_vals = convert(Vector{Float64}, reshape(chn.value[:, 1, :], (rws*chns)))
beta_vals = convert(Vector{Float64}, reshape(chn.value[:, 2, :], (rws*chns)))
yi = mean(alpha_vals) .+ mean(beta_vals)*xi
scatter(df2[:weight], df2[:height], lab="Observations")
plot!(xi, yi, lab="Regression line")End of clip_38.1s.jl
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