clip_38t
using StatisticalRethinking
gr(size=(300,300))

Turing.setadbackend(:reverse_diff)

ProjDir = @__DIR__
cd(ProjDir)
loaded


┌ Warning: Package Turing does not have CmdStan in its dependencies:
│ - If you have Turing checked out for development and have
│   added CmdStan as a dependency but haven't updated your primary
│   environment's manifest file, try `Pkg.resolve()`.
│ - Otherwise you may need to report an issue with Turing
│ Loading CmdStan into Turing from project dependency, future warnings for Turing are suppressed.
└ @ nothing nothing:840
WARNING: using CmdStan.Sample in module Turing conflicts with an existing identifier.

snippet 4.38

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);
y = df2[:height];
x = df2[:weight];

Define the regression model

@model line(y, x) = begin
    #priors
    alpha ~ Normal(178.0, 100.0)
    beta ~ Normal(0.0, 10.0)
    s ~ Uniform(0, 50)

    #model
    mu = alpha .+ beta*x
    for i in 1:length(y)
      y[i] ~ Normal(mu[i], s)
    end
end;

Draw the samples

chn = sample(line(y, x), Turing.NUTS(1000, 0.65));
┌ Info: [Turing] looking for good initial eps...
└ @ Turing /Users/rob/.julia/packages/Turing/orJH9/src/samplers/support/hmc_core.jl:246
[NUTS{Any}] found initial ϵ: 0.05
└ @ Turing /Users/rob/.julia/packages/Turing/orJH9/src/samplers/support/hmc_core.jl:291
[NUTS] Sampling...  0%  ETA: 2:23:28
  ϵ:         0.05
  α:         0.5958469110979258
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  1%  ETA: 0:16:09
  ϵ:         0.025127276843784265
  α:         0.8255173439569742
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  2%  ETA: 0:08:07
  ϵ:         0.00851550348406546
  α:         0.9973471187140496
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  3%  ETA: 0:07:31
  ϵ:         0.007488854283617242
  α:         0.9966676932439508
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  3%  ETA: 0:07:10
  ϵ:         0.023359709956663345
  α:         0.8317960966270578
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  4%  ETA: 0:05:45
  ϵ:         0.016127966083582905
  α:         0.9751874958408335
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  5%  ETA: 0:05:42
  ϵ:         0.008813589454963862
  α:         0.9971288119295713
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  5%  ETA: 0:05:34
  ϵ:         0.03248192025884401
  α:         0.5864150451907146
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  6%  ETA: 0:05:04
  ϵ:         0.00901519552162794
  α:         0.9986803229850687
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  6%  ETA: 0:05:07
  ϵ:         0.014747236072985486
  α:         0.9800664253311455
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  7%  ETA: 0:05:06
  ϵ:         0.00965336217165113
  α:         0.9999581189235383
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  8%  ETA: 0:04:46
  ϵ:         0.010015851061809845
  α:         0.9999594826344835
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  8%  ETA: 0:04:32
  ϵ:         0.01578501722592339
  α:         1.0
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling...  9%  ETA: 0:04:19
  ϵ:         0.015513521070662171
  α:         0.8919170400899573
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 10%  ETA: 0:04:17
  ϵ:         0.014195283529381653
  α:         0.9571669004122665
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 10%  ETA: 0:04:24
  ϵ:         0.025364058061337482
  α:         0.6381469302922957
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 10%  ETA: 0:04:14
  ϵ:         0.005982454027802865
  α:         0.9979231791309169
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 11%  ETA: 0:04:16
  ϵ:         0.00718218178908927
  α:         0.9961240637045707
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 11%  ETA: 0:04:13
  ϵ:         0.006107587796129112
  α:         0.9984288567948547
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 12%  ETA: 0:04:12
  ϵ:         0.022109631240016605
  α:         0.925978903393585
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 12%  ETA: 0:04:05
  ϵ:         0.02388426012906928
  α:         0.9581414677634983
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 13%  ETA: 0:04:04
  ϵ:         0.00944682419634701
  α:         0.9915755233512149
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 13%  ETA: 0:04:06
  ϵ:         0.00837661029851762
  α:         0.9924702125479083
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 14%  ETA: 0:03:54
  ϵ:         0.01237312839968317
  α:         0.9997010022111945
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 15%  ETA: 0:03:45
  ϵ:         0.044838771724791754
  α:         0.0007231584721505598
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 16%  ETA: 0:03:41
  ϵ:         0.012431219772575601
  α:         0.9952663597442306
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 16%  ETA: 0:03:40
  ϵ:         0.005447763563671964
  α:         0.9994970086239011
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 16%  ETA: 0:03:40
  ϵ:         0.008870583180892622
  α:         0.9919721043756654
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 17%  ETA: 0:03:38
  ϵ:         0.011775209144808263
  α:         0.9744507378011469
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 18%  ETA: 0:03:36
  ϵ:         0.005711891175352187
  α:         0.9997494461488865
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 18%  ETA: 0:03:34
  ϵ:         0.0423801744416322
  α:         0.3092761809051894
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 19%  ETA: 0:03:22
  ϵ:         0.02060721236115353
  α:         0.9964768235583681
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 20%  ETA: 0:03:16
  ϵ:         0.010156350403491325
  α:         0.9754111069770062
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 21%  ETA: 0:03:06
  ϵ:         0.027614545232751843
  α:         0.8246540434075277
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 22%  ETA: 0:03:06
  ϵ:         0.017259084247298623
  α:         0.9131699260862771
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 22%  ETA: 0:03:05
  ϵ:         0.013431284897113937
  α:         0.9925283447313975
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 23%  ETA: 0:03:05
  ϵ:         0.011832113733028594
  α:         0.999057355500345
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 24%  ETA: 0:03:04
  ϵ:         0.026442553991805062
  α:         0.2999838223674451
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 24%  ETA: 0:03:05
  ϵ:         0.012420069797388657
  α:         0.9988159535773793
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 24%  ETA: 0:03:02
  ϵ:         0.011121126232923783
  α:         0.9980320890961634
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 25%  ETA: 0:02:57
  ϵ:         0.007438132895977654
  α:         0.9859047364680493
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 26%  ETA: 0:02:56
  ϵ:         0.003711814549519056
  α:         0.9963716573087572
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 27%  ETA: 0:02:50
  ϵ:         0.0064845521097339235
  α:         0.9959111036797161
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 28%  ETA: 0:02:41
  ϵ:         0.006280622649199679
  α:         0.995970956132406
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 29%  ETA: 0:02:43
  ϵ:         0.0055866317162223764
  α:         0.9862155395387813
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 30%  ETA: 0:02:38
  ϵ:         0.007989524811837085
  α:         0.9980620201108341
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 30%  ETA: 0:02:36
  ϵ:         0.02288244260922675
  α:         0.9709808183913866
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 31%  ETA: 0:02:33
  ϵ:         0.049833761001675886
  α:         0.00021626650148486005
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 32%  ETA: 0:02:32
  ϵ:         0.008130603376851358
  α:         0.9999866856263872
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 33%  ETA: 0:02:28
  ϵ:         0.011526240381501615
  α:         0.9762554272657571
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 33%  ETA: 0:02:27
  ϵ:         0.014809127007086708
  α:         0.9961294496213143
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 34%  ETA: 0:02:29
  ϵ:         0.02430631072586857
  α:         0.88222840441524
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 34%  ETA: 0:02:25
  ϵ:         0.018503950588776907
  α:         0.5285285429091524
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 35%  ETA: 0:02:21
  ϵ:         0.01168814609138677
  α:         0.999012469594811
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 36%  ETA: 0:02:19
  ϵ:         0.0083580419493583
  α:         0.9999448725220954
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 36%  ETA: 0:02:19
  ϵ:         0.02296627218528175
  α:         0.8944536670612164
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 37%  ETA: 0:02:18
  ϵ:         0.012706497376307585
  α:         0.9997151695133639
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 37%  ETA: 0:02:18
  ϵ:         0.009736744091032557
  α:         0.9656672953525859
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 38%  ETA: 0:02:14
  ϵ:         0.017033446395948625
  α:         0.9770735216512014
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 39%  ETA: 0:02:14
  ϵ:         0.017666697060456694
  α:         0.866679299855932
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 39%  ETA: 0:02:14
  ϵ:         0.00858769698153709
  α:         0.9994702592427223
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 40%  ETA: 0:02:12
  ϵ:         0.014057363097769292
  α:         0.8490202220469975
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 40%  ETA: 0:02:11
  ϵ:         0.02145759541761293
  α:         0.8199068739473638
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 41%  ETA: 0:02:10
  ϵ:         0.018608749628827092
  α:         0.8809014950504805
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 42%  ETA: 0:02:08
  ϵ:         0.021735064118511976
  α:         0.9691183537837947
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 42%  ETA: 0:02:06
  ϵ:         0.009740403144477425
  α:         0.9965050055471739
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 43%  ETA: 0:02:06
  ϵ:         0.00958401510251089
  α:         0.9992534320583438
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 43%  ETA: 0:02:03
  ϵ:         0.020289144083874375
  α:         0.9974608969276128
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 45%  ETA: 0:01:57
  ϵ:         0.016929543920738904
  α:         0.996790222381062
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 46%  ETA: 0:01:55
  ϵ:         0.011369066950758733
  α:         0.9175607380726664
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 46%  ETA: 0:01:55
  ϵ:         0.013748553979606972
  α:         0.9922036049745192
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 46%  ETA: 0:01:55
  ϵ:         0.01505310103160407
  α:         0.9460578992302959
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 47%  ETA: 0:01:54
  ϵ:         0.016537030255606662
  α:         0.307105133962934
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 47%  ETA: 0:01:54
  ϵ:         0.007284604307140954
  α:         0.9999221534585019
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 48%  ETA: 0:01:54
  ϵ:         0.009895001230105213
  α:         0.9903640209158069
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 48%  ETA: 0:01:52
  ϵ:         0.012928841627830139
  α:         0.6619275397588733
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 49%  ETA: 0:01:52
  ϵ:         0.014912282984068234
  α:         0.8851879627352994
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 49%  ETA: 0:01:50
  ϵ:         0.01710482163093238
  α:         0.8219743102766803
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 50%  ETA: 0:01:48
  ϵ:         0.006799765104485656
  α:         0.9847463768263129
┌ Info:  Adapted ϵ = 0.013109170393989088, std = [1.0, 1.0, 1.0]; 500 iterations is used for adaption.
└ @ Turing /Users/rob/.julia/packages/Turing/orJH9/src/samplers/adapt/adapt.jl:91



[NUTS] Sampling... 51%  ETA: 0:01:47
  ϵ:         0.013109170393989088
  α:         0.9971886146479594
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 51%  ETA: 0:01:45
  ϵ:         0.013109170393989088
  α:         0.9923066813797669
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 52%  ETA: 0:01:44
  ϵ:         0.013109170393989088
  α:         0.9537974050410385
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 52%  ETA: 0:01:45
  ϵ:         0.013109170393989088
  α:         0.9202979426650503
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 52%  ETA: 0:01:45
  ϵ:         0.013109170393989088
  α:         0.9933155202568289
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 53%  ETA: 0:01:44
  ϵ:         0.013109170393989088
  α:         0.9082470677250689
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 54%  ETA: 0:01:42
  ϵ:         0.013109170393989088
  α:         0.8106847283415165
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 54%  ETA: 0:01:41
  ϵ:         0.013109170393989088
  α:         1.0
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 54%  ETA: 0:01:41
  ϵ:         0.013109170393989088
  α:         0.9734589794803037
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 55%  ETA: 0:01:41
  ϵ:         0.013109170393989088
  α:         0.9293202549111236
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 55%  ETA: 0:01:40
  ϵ:         0.013109170393989088
  α:         0.9468061307971631
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 56%  ETA: 0:01:39
  ϵ:         0.013109170393989088
  α:         0.9984215957795564
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 56%  ETA: 0:01:39
  ϵ:         0.013109170393989088
  α:         0.9835660643994784
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 56%  ETA: 0:01:37
  ϵ:         0.013109170393989088
  α:         0.8845233539409265
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 57%  ETA: 0:01:37
  ϵ:         0.013109170393989088
  α:         0.6206797809048188
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 57%  ETA: 0:01:36
  ϵ:         0.013109170393989088
  α:         0.8254335190404162
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 58%  ETA: 0:01:36
  ϵ:         0.013109170393989088
  α:         0.932208669035429
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 58%  ETA: 0:01:36
  ϵ:         0.013109170393989088
  α:         0.9647060129142845
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 58%  ETA: 0:01:35
  ϵ:         0.013109170393989088
  α:         0.8742164313252938
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 59%  ETA: 0:01:34
  ϵ:         0.013109170393989088
  α:         1.0
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 59%  ETA: 0:01:33
  ϵ:         0.013109170393989088
  α:         0.8584051008323377
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 60%  ETA: 0:01:30
  ϵ:         0.013109170393989088
  α:         0.6772709261039982
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 61%  ETA: 0:01:28
  ϵ:         0.013109170393989088
  α:         0.8983637146409795
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 61%  ETA: 0:01:28
  ϵ:         0.013109170393989088
  α:         0.39019448423443465
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 62%  ETA: 0:01:28
  ϵ:         0.013109170393989088
  α:         0.9891341812654892
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 62%  ETA: 0:01:27
  ϵ:         0.013109170393989088
  α:         0.9720512803349747
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 63%  ETA: 0:01:25
  ϵ:         0.013109170393989088
  α:         0.3813413804788552
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 63%  ETA: 0:01:24
  ϵ:         0.013109170393989088
  α:         0.9312047627168744
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 64%  ETA: 0:01:22
  ϵ:         0.013109170393989088
  α:         0.7422415353174983
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 65%  ETA: 0:01:20
  ϵ:         0.013109170393989088
  α:         0.7869903504720592
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 66%  ETA: 0:01:18
  ϵ:         0.013109170393989088
  α:         0.9505649307490288
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 66%  ETA: 0:01:18
  ϵ:         0.013109170393989088
  α:         0.7979356852575008
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 67%  ETA: 0:01:17
  ϵ:         0.013109170393989088
  α:         0.9905368623409823
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 68%  ETA: 0:01:12
  ϵ:         0.013109170393989088
  α:         0.951665549842708
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 69%  ETA: 0:01:11
  ϵ:         0.013109170393989088
  α:         0.022127310556418162
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 70%  ETA: 0:01:08
  ϵ:         0.013109170393989088
  α:         0.9104921285142276
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 71%  ETA: 0:01:06
  ϵ:         0.013109170393989088
  α:         0.29719887767172304
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 72%  ETA: 0:01:03
  ϵ:         0.013109170393989088
  α:         8.336410328488203e-5
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 72%  ETA: 0:01:01
  ϵ:         0.013109170393989088
  α:         0.0006277866637373233
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 73%  ETA: 0:00:59
  ϵ:         0.013109170393989088
  α:         0.44471857574623347
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 74%  ETA: 0:00:56
  ϵ:         0.013109170393989088
  α:         0.8380728543289289
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 75%  ETA: 0:00:54
  ϵ:         0.013109170393989088
  α:         0.0002628834688017792
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 77%  ETA: 0:00:50
  ϵ:         0.013109170393989088
  α:         0.3896701756259306
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 77%  ETA: 0:00:49
  ϵ:         0.013109170393989088
  α:         0.6356450444122348
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 78%  ETA: 0:00:47
  ϵ:         0.013109170393989088
  α:         0.2328391210737752
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 79%  ETA: 0:00:45
  ϵ:         0.013109170393989088
  α:         0.6283551382163406
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 79%  ETA: 0:00:44
  ϵ:         0.013109170393989088
  α:         0.11196407716772744
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 80%  ETA: 0:00:42
  ϵ:         0.013109170393989088
  α:         0.470555856021405
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 81%  ETA: 0:00:41
  ϵ:         0.013109170393989088
  α:         0.5637925631104987
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 82%  ETA: 0:00:39
  ϵ:         0.013109170393989088
  α:         0.052202591288156776
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 82%  ETA: 0:00:38
  ϵ:         0.013109170393989088
  α:         0.00874300330640224
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 83%  ETA: 0:00:35
  ϵ:         0.013109170393989088
  α:         0.12971398792108216
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 84%  ETA: 0:00:32
  ϵ:         0.013109170393989088
  α:         2.2904692378334666e-27
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 86%  ETA: 0:00:29
  ϵ:         0.013109170393989088
  α:         1.3835388541105442e-6
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 88%  ETA: 0:00:25
  ϵ:         0.013109170393989088
  α:         9.53094295080429e-21
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 89%  ETA: 0:00:22
  ϵ:         0.013109170393989088
  α:         0.13767285927717623
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 91%  ETA: 0:00:19
  ϵ:         0.013109170393989088
  α:         0.20630790916330802
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 93%  ETA: 0:00:13
  ϵ:         0.013109170393989088
  α:         1.0
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 95%  ETA: 0:00:10
  ϵ:         0.013109170393989088
  α:         0.6333069293764164
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 96%  ETA: 0:00:08
  ϵ:         0.013109170393989088
  α:         0.4732912353973532
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 98%  ETA: 0:00:05
  ϵ:         0.013109170393989088
  α:         0.35141304863388073
4m  pre_cond:  [1.0, 1.0, 1.0]


[NUTS] Sampling... 99%  ETA: 0:00:02
  ϵ:         0.013109170393989088
  α:         0.0015076497721120024
4m  pre_cond:  [1.0, 1.0, 1.0]




[NUTS] Finished with
  Running time        = 185.92909549900017;
  #lf / sample        = 0.003;
  #evals / sample     = 41.753;
  pre-cond. metric    = [1.0, 1.0, 1.0].


[NUTS] Sampling...100% Time: 0:03:06

Describe the chain result

println() # src
describe(chn)
println() # src
Iterations = 1:1000
Thinning interval = 1
Chains = 1
Samples per chain = 1000

Empirical Posterior Estimates:
               Mean           SD         Naive SE       MCSE         ESS    
   alpha    60.409980530  33.97261591 1.07430844345 11.259303401    9.104056
    beta     2.068656449   0.73733869 0.02331669656  0.244276471    9.111099
  lf_num     0.003000000   0.09486833 0.00300000000  0.003000000 1000.000000
       s     9.862403542   5.09915312 0.16124937984  1.492241116   11.676646
 elapsed     0.185929095   0.31505705 0.00996297883  0.022829833  190.446487
 epsilon     0.020607726   0.02509401 0.00079354225  0.003087969   66.038052
      lp -1279.530195631 147.20004659 4.65487418920 48.438728977    9.234862
eval_num    41.753000000  51.86665732 1.64016771738  4.503435244  132.644325
  lf_eps     0.020607726   0.02509401 0.00079354225  0.003087969   66.038052

Quantiles:
               2.5%           25.0%           50.0%           75.0%          97.5%     
   alpha     2.179426379    29.969842513    63.669474110    96.00394084    97.762960108
    beta     1.250627139     1.296154284     1.991453093     2.73946472     3.331785333
  lf_num     0.000000000     0.000000000     0.000000000     0.00000000     0.000000000
       s     5.196843840     5.785744140     8.576647750    13.51223427    17.315852848
 elapsed     0.010573971     0.036188186     0.083558916     0.21068199     0.805442231
 epsilon     0.006842698     0.013109170     0.013109170     0.02130787     0.061662663
      lp -1502.572570399 -1413.891700644 -1276.055902488 -1122.36881489 -1115.535976220
eval_num     4.000000000    10.000000000    22.000000000    46.00000000   190.000000000
  lf_eps     0.006842698     0.013109170     0.013109170     0.02130787     0.061662663

Plot the regerssion line and observations

xi = 30.0:0.1:70.0
yi = mean(chn[:alpha]) .+ mean(chn[:beta])*xi

scatter(x, y, lab="Observations")
plot!(xi, yi, lab="Regression line")

##-

svg

This notebook was generated using Literate.jl.