using StatisticalRethinking
using Turing

Turing.setadbackend(:reverse_diff)

d = CSV.read(joinpath(dirname(Base.pathof(StatisticalRethinking)), "..", "data",
    "reedfrogs.csv"), delim=';')
size(d) # Should be 48x5

(48, 5)

Set number of tanks

d[:tank] = 1:size(d,1)

@model m12_1(density, tank, surv) = begin

Number of unique tanks in the data set

    N_tank = length(tank)

Set an TArray for the priors/param

    a_tank = Vector{Real}(undef, N_tank)

For each tank [1,..,48] set prior N(0,5)

    a_tank ~ [Normal(0,5)]

    logitp = [a_tank[tank[i]] for i = 1:N_tank]
    surv ~ VecBinomialLogit(density, logitp)
end

posterior = sample(m12_1(Vector{Int64}(d[:density]), Vector{Int64}(d[:tank]),
    Vector{Int64}(d[:surv])), Turing.NUTS(4000, 1000, 0.8))
describe(posterior)

            Mean           SD         Naive SE       MCSE         ESS

atank[33] 3.7925121923 1.069473492 0.01690986065 0.0181583984 3468.84559 atank[2] 5.6619233751 2.661975386 0.04208952648 0.0984382340 731.27452 atank[44] -0.4076755205 0.349650208 0.00552845521 0.0051973560 4000.00000 atank[40] 2.4882548674 0.642093720 0.01015239313 0.0087774011 4000.00000 atank[41] -2.1368737936 0.588205639 0.00930034776 0.0091150511 4000.00000 atank[42] -0.6773019465 0.370413780 0.00585675610 0.0052435688 4000.00000 atank[11] 0.9259845291 0.729448255 0.01153358961 0.0077243130 4000.00000 atank[16] 2.5669573506 1.256913239 0.01987354329 0.0240073491 2741.08301 atank[46] -0.6654705830 0.370650246 0.00586049496 0.0058669658 3991.18148 atank[8] 2.5385573941 1.151976429 0.01821434663 0.0232427286 2456.47849 atank[14] 0.0006786356 0.680697609 0.01076277421 0.0069893413 4000.00000 atank[47] 2.1388988496 0.532096615 0.00841318620 0.0078518462 4000.00000 atank[43] -0.5364419223 0.354074917 0.00559841600 0.0058512095 3661.83713 atank[24] 1.7486397297 0.597014797 0.00943963278 0.0071524317 4000.00000 atank[34] 2.9828401383 0.793129631 0.01254048056 0.0113862941 4000.00000 atank[9] -0.4362986938 0.655848632 0.01036987739 0.0065852640 4000.00000 atank[28] -0.5903300678 0.430889431 0.00681296010 0.0061191595 4000.00000 atank[31] -0.7790724381 0.438852449 0.00693886648 0.0062867441 4000.00000 atank[29] 0.0892476063 0.403319027 0.00637703374 0.0065342700 3809.80961 atank[18] 2.5984354254 0.789739347 0.01248687547 0.0116099713 4000.00000 atank[1] 2.5169564861 1.202252233 0.01900927690 0.0261521039 2113.38159 atank[38] 6.5730591701 2.577397287 0.04075222931 0.0960321899 720.32596 atank[37] 2.1321270081 0.542445637 0.00857681860 0.0067553411 4000.00000 atank[30] 1.4436385748 0.510944886 0.00807874799 0.0061875938 4000.00000 atank[35] 2.9837870684 0.798955606 0.01263259732 0.0111689405 4000.00000 atank[20] 6.4209696786 2.614898794 0.04134518019 0.0934495614 782.98823 atank[15] 2.4852422308 1.182168671 0.01869172789 0.0235303705 2524.06980 atank[45] 0.5431043960 0.369638488 0.00584449767 0.0046883639 4000.00000 atank[26] 0.0840349555 0.395331366 0.00625073774 0.0067906853 3389.18550 atank[21] 2.6516314895 0.851902518 0.01346976151 0.0118211120 4000.00000 atank[48] -0.0571820248 0.337815684 0.00534133495 0.0051459323 4000.00000 atank[10] 2.5310386381 1.157968533 0.01830909012 0.0251590089 2118.39263 atank[3] 0.9295620334 0.735176403 0.01162415958 0.0127307257 3334.85377 atank[7] 5.7185532309 2.796270760 0.04421292278 0.1047192286 713.02634 atank[6] 2.5050631208 1.183397045 0.01871115019 0.0243016893 2371.30836 atank[25] -1.2007745016 0.470201538 0.00743453910 0.0071826339 4000.00000 atank[32] -0.4234910116 0.414945560 0.00656086537 0.0060452516 4000.00000 atank[5] 2.5286171889 1.207469316 0.01909176622 0.0250131147 2330.32587 atank[13] 0.9170279823 0.723356937 0.01143727741 0.0091140235 4000.00000 atank[19] 2.1126922998 0.642028977 0.01015136946 0.0086040212 4000.00000 atank[12] 0.4476884510 0.682975434 0.01079878979 0.0070550762 4000.00000 atank[4] 5.5617118510 2.607791677 0.04123280681 0.1041546582 626.88574 atank[17] 3.4763818329 1.091795631 0.01726280467 0.0199830235 2985.10977 atank[27] -1.7411510659 0.578372766 0.00914487638 0.0085613085 4000.00000 atank[22] 2.6038964868 0.779764455 0.01232915859 0.0107305461 4000.00000 atank[23] 2.6217848846 0.808680221 0.01278635699 0.0105079615 4000.00000 atank[36] 2.1205525264 0.557014163 0.00880716721 0.0077309477 4000.00000 atank[39] 2.9653158635 0.795061058 0.01257101910 0.0110571371 4000.00000

Rethinking mean sd 5.5% 94.5% neff Rhat atank[1] 2.49 1.16 0.85 4.53 1079 1 atank[2] 5.69 2.75 2.22 10.89 1055 1 atank[3] 0.89 0.75 -0.23 2.16 1891 1 atank[4] 5.71 2.70 2.21 10.85 684 1 atank[5] 2.52 1.14 0.92 4.42 1640 1 atank[6] 2.49 1.13 0.94 4.52 1164 1 atank[7] 5.74 2.71 2.25 10.86 777 1 atank[8] 2.52 1.19 0.95 4.42 1000 1 atank[9] -0.46 0.69 -1.62 0.55 2673 1 atank[10] 2.53 1.19 0.93 4.59 1430 1 atank[11] 0.93 0.72 -0.17 2.11 1387 1 atank[12] 0.47 0.74 -0.63 1.70 1346 1 atank[13] 0.91 0.76 -0.25 2.30 1559 1 atank[14] 0.00 0.66 -1.04 1.06 2085 1 atank[15] 2.50 1.19 0.95 4.40 1317 1 atank[16] 2.50 1.14 0.98 4.31 1412 1 atank[17] 3.49 1.12 1.94 5.49 945 1 atank[18] 2.59 0.75 1.50 3.81 1561 1 atank[19] 2.11 0.64 1.15 3.15 1712 1 atank[20] 6.40 2.57 3.11 11.04 996 1 atank[21] 2.59 0.74 1.54 3.93 1233 1 atank[22] 2.63 0.79 1.49 4.01 1184 1 atank[23] 2.64 0.83 1.45 4.13 1379 1 atank[24] 1.74 0.59 0.85 2.72 1736 1 atank[25] -1.19 0.45 -1.90 -0.50 2145 1 atank[26] 0.09 0.41 -0.53 0.78 2167 1 atank[27] -1.75 0.56 -2.65 -0.88 1666 1 atank[28] -0.58 0.43 -1.25 0.08 1567 1 atank[29] 0.08 0.39 -0.54 0.71 3053 1 atank[30] 1.43 0.49 0.66 2.24 2754 1 atank[31] -0.79 0.44 -1.50 -0.12 1299 1 atank[32] -0.42 0.41 -1.12 0.23 1661 1 atank[33] 3.84 1.08 2.31 5.70 808 1 atank[34] 3.00 0.85 1.83 4.36 1038 1 atank[35] 2.96 0.82 1.82 4.25 1578 1 atank[36] 2.14 0.55 1.31 3.08 1734 1 atank[37] 2.12 0.56 1.31 3.04 1131 1 atank[38] 6.72 2.62 3.45 11.44 706 1 atank[39] 2.95 0.73 1.85 4.08 1509 1 atank[40] 2.48 0.65 1.53 3.61 1731 1 atank[41] -2.15 0.57 -3.11 -1.29 1231 1 atank[42] -0.67 0.35 -1.22 -0.14 1444 1 atank[43] -0.54 0.35 -1.12 0.03 1776 1 atank[44] -0.43 0.34 -1.00 0.10 1735 1 atank[45] 0.54 0.36 -0.04 1.14 1376 1 atank[46] -0.67 0.34 -1.25 -0.15 1619 1 atank[47] 2.14 0.55 1.31 3.04 1916 1 a_tank[48] -0.06 0.35 -0.61 0.50 1932 1

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