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Dirichlet-Multinomial Bayesian Variable Selection

License: GNU General Public License v3.0

Makefile 0.79% C 60.55% R 38.66%

dmbvs's Introduction

dmbvs

Important
This repo is no longer maintained and its contents have been superseded by the library here: https://github.com/mkoslovsky/MicroBVS. Anything you can do with dmbvs can be done better with MicroBVS.

Description

Bayesian variable selection for Dirichlet-Multinomial regression. For $n$ samples, let $Y$ be an $n \times q$ matrix with $q$ taxa. Let $X$ be an $n \times p$ matrix with $p$ covariates. By applying spike-and-slab priors to the Dirichlet-Multinomial regression coefficients, we obtain concise taxa/covariate associations. The methodology is further described in the manuscript:

Wadsworth, W. D., Argiento, R., Guindani, M., Galloway-Pena, J., Samuel, S. A., & Vannucci, M. (2016). An Integrative Bayesian Dirichlet-Multinomial Regression Model for the Analysis of Taxonomic Abundances in Microbiome data.

The code has been updated on 10/02/17 with an option to perform a stochastic search algorithm for Bayesian variable selection instead of the Gibbs sampler. The stochastic search variable selection approach provides gains in computational speed.

The repository contains

C code implementing an MCMC sampler for Dirichlet-Multinomial Bayesian Variable Selection (dmbvs) using spike-and-slab priors,
R code to wrap and run the sampler from within R,
a function for simulating data,
and a "start-to-finish" script (example_analysis_script.R) demonstrating usage of the code. This script gives reasonable default settings for the hyperparameters and MCMC parameters for the example simulated data. Settings may change for other data.

Usage

The R code requires the dirmult and MASS packages. Please ensure those are installed first.
The C code relies on the GNU Scientific Library (GSL). GSL must be installed and modifications may need to be made to the 'library' and 'include' paths in the Makefile.
The main C file (dmbvs.c), as well as the Makefile to be used for compilation of the code, can be found under the directory code/.
On Linux and Mac the C code may be compiled with the Makefile from R using:

# must be in package's root directory
setwd("dmbvs")
system("cd code; make")

If compilation has been successful there will be an executable called dmbvs.x the code/ directory. Data may be simulated and the MCMC code run using:

source(file.path("code", "wrapper.R"))
source(file.path("code", "helper_functions.R"))
simdata = simulate_dirichlet_multinomial_regression(n_obs = 100, n_vars = 50,
                                                    n_taxa = 50, n_relevant_vars = 5,
                                                    n_relevant_taxa = 5)
results = dmbvs(XX = simdata$XX[,-1], YY = simdata$YY, 
                intercept_variance = 10, slab_variance = 10, 
                bb_alpha = 0.02, bb_beta = 1.98, GG = 1100L, thin = 10L, burn = 100L,
                exec = file.path(".", "code", "dmbvs.x"), output_location = ".")

Tested on:
- Mac with R version 3.2.2 and GSL version 2.1 with the Apple LLVM version 7.0.2 compiler
- Red Hat Linux 6.6 with R version 3.1.2 and GSL version 2.1 and gcc version 5.2.0

dmbvs's People

Contributors

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Watchers

Forkers

mguindani yinsenm marinavannucci rimehi andcre87 satopan nuggeus johannesostner

dmbvs's Issues

Using your algorithm

I am trying to find the category slope from your results.

I modified your code to provide a single factor of interest (covariate) simdata$XX[,-1][,1, drop=FALSE]. Am I doing it right

results = dmbvs(XX = simdata$XX[,-1][,1, drop=FALSE], YY = simdata$YY,
                intercept_variance = 10, slab_variance = 10,
                bb_alpha = 0.02, bb_beta = 1.98, GG = 1100L, thin = 10L, burn = 100L,
                exec = file.path(".", "dev/dmbvs-master/dmbvs-master/code", "dmbvs.x"), output_location = "dev/dmbvs-master")

Given this code, I get these results. Which variable represents the coefficients of the slope?

Thanks a lot.

$alpha
            [,1]      [,2]       [,3]      [,4]         [,5]      [,6]        [,7]      [,8]       [,9]
  [1,] -1.418886 -1.773251 -0.6072518 -1.999764  0.368678200 1.8489090 -0.03596430 1.4113050 -0.2893159
  [2,] -1.314897 -1.871794 -0.6697463 -2.085728  0.371493700 1.7359070 -0.01327474 1.4113050 -0.2234813
  [3,] -1.370964 -1.921591 -0.6133781 -1.814897  0.404262600 1.7359070 -0.23251500 1.2964670 -0.5911376
  [4,] -1.416919 -1.913276 -0.6822267 -1.760696  0.124046800 1.6293680 -0.07024686 1.2964670 -0.3811138
  [5,] -1.364073 -2.088071 -0.6769302 -1.810631  0.087089970 1.4904520 -0.10757790 1.1214230 -0.3186199
  [6,] -1.392633 -1.564183 -0.5366176 -1.977052  0.288110600 1.5218230 -0.09302780 1.0519180 -0.4024529
  [7,] -1.403465 -1.743942 -0.7887165 -1.846594  0.223784400 1.5255170 -0.24464200 1.1501160 -0.4686381
  [8,] -1.470954 -1.638405 -0.7464406 -1.932476  0.170288900 1.3795650 -0.24464200 1.1501160 -0.4404021
  [9,] -1.339014 -1.863100 -0.9364210 -1.843958  0.208295700 1.3693170 -0.24354250 1.1190840 -0.3708937
 [10,] -1.300249 -2.064471 -0.8399152 -1.943197  0.208295700 1.3594750 -0.10324760 1.0728950 -0.5178355
 [11,] -1.378601 -2.019455 -0.8561043 -1.876005  0.204871800 1.4703850 -0.19294230 1.1137910 -0.4038355
 [12,] -1.419485 -1.957874 -0.9701486 -2.065526  0.215455200 1.4703850 -0.17076710 1.0075600 -0.5162941
 [13,] -1.251857 -2.126180 -0.7389570 -1.902823  0.123604000 1.3054010 -0.41276680 1.0075600 -0.4811431
 [14,] -1.586515 -2.081205 -0.9572208 -1.841197  0.214699300 1.3054010 -0.41276680 0.9942930 -0.6373646
 [15,] -1.421381 -2.032756 -0.9572208 -1.841197  0.172743800 1.3856000 -0.41276680 0.9848687 -0.7268597
 [16,] -1.614211 -2.123600 -0.8649054 -1.713356  0.156534300 1.2670890 -0.34953620 0.9848687 -0.5136049
 [17,] -1.535029 -2.180116 -0.8398939 -1.652702  0.063646420 1.2877800 -0.42219630 0.9877969 -0.6322712
 [18,] -1.674418 -2.082477 -1.0742510 -2.162506  0.063646420 1.2877800 -0.50408210 0.9877969 -0.6322712
 [19,] -1.674418 -2.068488 -1.0089590 -2.015105  0.013865430 1.2877800 -0.43227930 0.9512558 -0.6322712
 [20,] -1.524926 -1.978285 -1.0168150 -1.762213  0.011505670 1.2168740 -0.44271860 0.9512558 -0.5633552
              [,10]     [,11]      [,12]      [,13]     [,14]      [,15]     [,16]     [,17]     [,18]    [,19]
  [1,]  0.456333800 -1.544854 -0.5275411 -0.4754097 0.7443196 -0.3788772 -1.492108 -2.229176 -1.808683 1.795332
  [2,]  0.555898200 -1.436137 -0.6487684 -0.2794932 0.6826588 -0.2723497 -1.716684 -2.229176 -1.808683 1.832130
  [3,]  0.541938600 -1.491051 -0.5612087 -0.4381451 0.8189546 -0.2760946 -1.435046 -2.099138 -1.836600 1.666011
  [4,]  0.550287700 -1.854687 -0.5299152 -0.4381451 0.6698549 -0.5990416 -1.327075 -2.134195 -2.009483 1.746040
  [5,]  0.449014400 -1.907405 -0.4804196 -0.4381451 0.6787001 -0.3350436 -1.749586 -2.317274 -2.076423 1.627049
  [6,]  0.376834300 -1.874988 -0.6590886 -0.4480017 0.7390065 -0.3132182 -1.798487 -2.317274 -2.160021 1.627049
  [7,]  0.312498000 -1.993874 -0.6449998 -0.5473154 0.5302061 -0.3132182 -1.608831 -2.390122 -1.966884 1.594449
  [8,]  0.341303500 -1.774634 -0.5584018 -0.5599691 0.5286694 -0.3132182 -1.704802 -2.541592 -1.988154 1.594449
  [9,]  0.291455800 -1.774634 -0.7024024 -0.8799518 0.4968055 -0.4840942 -1.606137 -2.122684 -2.174105 1.455281
 [10,]  0.209449700 -1.790220 -0.7024024 -0.8510632 0.5693789 -0.5832100 -1.702927 -2.338948 -1.810332 1.455281
 [11,]  0.209449700 -1.854762 -0.7296754 -0.5053499 0.5111702 -0.4541627 -1.524236 -2.391694 -1.974409 1.455281
 [12,]  0.209449700 -1.943116 -0.7749396 -0.4722336 0.6015694 -0.6207317 -1.678882 -2.413987 -1.949357 1.485445
 [13,]  0.240833500 -1.664922 -0.6314549 -0.7410894 0.6325014 -0.5691691 -1.507021 -2.456995 -2.489878 1.479519
 [14,]  0.252936600 -1.984975 -0.6518966 -0.5975761 0.5387108 -0.5850941 -1.488017 -2.357476 -2.188097 1.373157
 [15,]  0.346749700 -1.937689 -0.6171337 -0.6008068 0.4230485 -0.8198907 -1.488017 -2.303446 -1.813556 1.393589
 [16,]  0.346749700 -1.885293 -0.6171337 -0.6008068 0.5004741 -0.4420135 -1.713864 -2.387198 -1.846792 1.422857
 [17,]  0.224379400 -1.760764 -0.6712243 -0.5550274 0.4802942 -0.4668331 -1.701444 -2.313126 -1.846792 1.425832
 [18,]  0.118290900 -1.760764 -0.6734823 -0.6445415 0.3922029 -0.4968474 -1.617311 -2.583829 -1.852902 1.411895
 [19,]  0.175121600 -1.871591 -0.6854074 -0.5501105 0.3057655 -0.5379934 -1.730119 -2.583829 -2.198199 1.348453
 [20,]  0.228192500 -1.631836 -0.6854074 -0.7410107 0.3839355 -0.6869462 -1.893069 -2.451747 -1.632314 1.348453
           [,20]     [,21]       [,22]     [,23]     [,24]     [,25]      [,26]     [,27]     [,28]    [,29]
  [1,] 1.2170100 -1.827305 -0.10296620 -1.912746 1.5884860 -1.326364 -0.4549106 -1.111221 -2.630313 1.726517
  [2,] 1.0893160 -2.219460 -0.09817377 -1.918113 1.5884860 -1.326364 -0.5048934 -1.111221 -2.679002 1.714246
  [3,] 1.1737370 -1.965406 -0.31976170 -1.912513 1.4877040 -1.531270 -0.6366157 -1.216495 -2.876764 1.765809
  [4,] 1.1737370 -1.860518 -0.20976330 -1.964482 1.4851920 -1.395709 -0.6957341 -1.292770 -2.601742 1.637422
  [5,] 1.0198420 -2.015633 -0.34626980 -1.820645 1.4851920 -1.449136 -0.6957341 -1.206363 -2.561212 1.616046
  [6,] 1.0198420 -1.882758 -0.35131830 -1.926781 1.4320860 -1.441886 -0.5445308 -1.053147 -2.623242 1.498881
  [7,] 0.9137436 -2.322265 -0.25916850 -2.049717 1.3324550 -1.441886 -0.5208666 -1.386058 -2.720666 1.498881
  [8,] 0.9942941 -2.051128 -0.05186930 -2.060564 1.4089240 -1.571096 -0.7001906 -1.417317 -2.874243 1.498881
  [9,] 0.8396000 -1.993526 -0.33865770 -1.956571 1.3207750 -1.565242 -0.6263891 -1.528692 -2.561822 1.400101
 [10,] 0.8306025 -1.825229 -0.33865770 -1.839220 1.3207750 -1.539036 -0.8724169 -1.528692 -2.561822 1.453102
 [11,] 0.8306025 -2.172716 -0.30104680 -1.681292 1.3207750 -1.539036 -0.5690336 -1.445197 -2.615104 1.409908
 [12,] 0.8306025 -2.163588 -0.33490730 -1.791161 1.2226440 -1.392054 -0.7287441 -1.320078 -2.766916 1.409908
 [13,] 0.7859070 -1.962878 -0.50730740 -1.905183 1.2540760 -1.516840 -0.6804956 -1.320078 -2.708029 1.359005
 [14,] 0.7859070 -2.014358 -0.11491410 -1.853725 1.3172830 -1.783103 -0.9269942 -1.208502 -2.657404 1.257277
 [15,] 0.8266847 -1.976393 -0.19392020 -1.872357 1.1280630 -1.595184 -0.9957866 -1.550208 -2.646206 1.219284
 [16,] 0.8266847 -2.097659 -0.45724810 -1.918346 1.1280630 -1.595184 -0.8328793 -1.550208 -2.729720 1.428809
 [17,] 0.8630974 -1.848362 -0.42014820 -1.666628 1.1952350 -1.851976 -0.8062419 -1.374907 -3.071743 1.288396
 [18,] 0.8896960 -1.955736 -0.46743130 -1.852852 1.1738480 -1.572063 -0.8062419 -1.467980 -3.115873 1.261024
 [19,] 0.7281018 -2.214997 -0.43154030 -1.957945 1.2026870 -1.474509 -0.7940811 -1.267781 -3.126305 1.261024
 [20,] 0.6438107 -1.941339 -0.28493290 -1.726966 1.1057230 -1.413931 -0.7097141 -1.498613 -2.896851 1.299437
           [,30]     [,31]       [,32]      [,33]      [,34]      [,35]     [,36]     [,37]      [,38]
  [1,] 1.4703970 -1.599531  0.59428430 -1.0006360 -0.9349933 -0.6094856 -1.891044 1.2031750 -0.3674350
  [2,] 1.3453730 -1.500930  0.59428430 -1.1044940 -1.2568930 -0.5489470 -1.868935 1.3703610 -0.6285417
  [3,] 1.4141660 -1.526182  0.57074930 -0.5932873 -0.8792015 -0.5720609 -1.950552 1.2544370 -0.4974890
  [4,] 1.2927190 -1.656929  0.52181250 -0.8261369 -0.8672254 -0.6706910 -1.956362 1.1888070 -0.5427185
  [5,] 1.2213090 -1.494219  0.40111990 -0.9637734 -1.0375920 -0.6610143 -2.112314 1.1888070 -0.4873734
  [6,] 1.2585270 -1.615151  0.36816800 -0.9199978 -1.1935080 -0.7205450 -2.250223 1.0766420 -0.5194802
  [7,] 1.1610170 -1.487729  0.32607720 -0.9270646 -0.9445677 -0.7406812 -2.523023 1.1513640 -0.5166327
  [8,] 1.1167970 -1.536307  0.27303960 -0.9270646 -1.0712600 -0.8048086 -2.657673 1.0951650 -0.5107454
  [9,] 1.1518530 -1.557524  0.28743010 -1.0117420 -1.1267520 -0.7775622 -2.563289 0.9616072 -0.5107454
 [10,] 1.1518530 -1.486922  0.19023130 -1.0517290 -1.2363460 -0.6760320 -2.376480 1.1460940 -0.7848961
 [11,] 1.0792550 -1.486922  0.29939160 -1.0416210 -1.0552840 -1.0472730 -2.566561 0.9632942 -0.7586191
 [12,] 1.0088650 -1.636570  0.26238590 -1.1508530 -1.1267360 -0.6808852 -2.601545 0.9632942 -0.5936181
 [13,] 1.0678950 -1.693990  0.21393680 -1.1249280 -1.0842760 -0.8137157 -2.197405 0.9632942 -0.5284036
 [14,] 1.0678950 -1.686367  0.27836240 -1.1249280 -1.0842760 -0.8633933 -1.996407 1.0133810 -0.4659891
 [15,] 1.0589380 -1.686367  0.29051400 -1.1249280 -0.9604404 -0.7426738 -2.320115 0.8948683 -0.6177153
 [16,] 0.9536984 -1.747901  0.26642530 -1.2055640 -0.9039858 -0.9782398 -2.215664 1.0357380 -0.6298480
 [17,] 0.9361924 -1.600381  0.09382066 -1.0334390 -1.0116370 -0.6259247 -1.949520 0.9669471 -0.7946234
 [18,] 1.0613580 -1.628890  0.32013570 -1.0857450 -1.1633470 -0.8062320 -1.944724 0.9669471 -0.6295109
 [19,] 1.0408520 -1.834916  0.42266570 -1.0381210 -1.3012910 -0.7483777 -2.001453 0.8119757 -0.7648215
 [20,] 1.0408520 -1.533823  0.20656350 -1.1767680 -1.0594860 -1.0057820 -1.945807 0.8949320 -0.7028089
              [,39]        [,40]     [,41]       [,42]      [,43]     [,44]      [,45]        [,46]     [,47]
  [1,]  0.384317000  0.007963392 -1.734677 -0.05189428 -0.6663659 -1.782053 -0.3640737  0.447628500 1.6562350
  [2,]  0.573446000 -0.188695700 -1.560938 -0.23060750 -0.4034068 -1.796230 -0.3186509  0.436945100 1.5962810
  [3,]  0.444107600  0.076939200 -1.636813 -0.11820420 -0.6753803 -2.402139 -0.5781131  0.400756100 1.5601830
  [4,]  0.363022400 -0.260919800 -1.900464 -0.12043800 -0.6837200 -2.285158 -0.5055840  0.295678100 1.4219620
  [5,]  0.363022400 -0.182438500 -1.612266 -0.11774240 -0.6132213 -2.415184 -0.5038202  0.330291500 1.4219620
  [6,]  0.206622300  0.048323030 -1.638584 -0.20254600 -0.6106830 -2.557931 -0.5641900  0.378596900 1.3678900
  [7,]  0.213995500 -0.165511600 -1.814017 -0.13770650 -0.6364151 -2.282553 -0.5986615  0.318305300 1.3678900
  [8,]  0.231340800 -0.068794150 -2.067627 -0.12001820 -0.5837232 -2.306302 -0.6869133  0.112180600 1.3136330
  [9,]  0.177515400 -0.180718000 -1.763305 -0.33562350 -0.7314133 -2.638164 -0.6409333  0.089030710 1.3231490
 [10,]  0.177515400 -0.161179700 -1.586537 -0.26005150 -0.7491947 -2.580414 -0.6564046  0.069682940 1.3231490
 [11,] -0.004650063 -0.137525400 -1.713459 -0.23105330 -0.7409744 -2.688724 -0.6564046 -0.074417950 1.3231490
 [12,]  0.029917380 -0.231979700 -1.811302 -0.23105330 -0.7944916 -2.535066 -0.5992294  0.180521700 1.1468480
 [13,]  0.172611700 -0.173306900 -1.677719 -0.27026880 -0.7177729 -2.602495 -0.4317266  0.160669700 1.2265690
 [14,]  0.131604900 -0.242258000 -1.976754 -0.19875840 -0.9356538 -2.544541 -0.8248848  0.260270900 1.2067420
 [15,]  0.043171470 -0.201555700 -1.956390 -0.49319880 -0.5936061 -2.454039 -0.8808056  0.193407600 1.2638640
 [16,]  0.178172800 -0.201555700 -1.806070 -0.30665240 -0.8898050 -2.574118 -0.8695682  0.193407600 1.2833330
 [17,]  0.050888310 -0.197644000 -2.037469 -0.44642050 -0.9347796 -2.389860 -0.6839889  0.116680200 1.2833330
 [18,]  0.113492300 -0.166430900 -1.786558 -0.44642050 -0.7313230 -2.596947 -0.6528923  0.187336500 1.2318330
 [19,]  0.113492300 -0.225357900 -1.942425 -0.37268980 -0.6563107 -2.383797 -0.9576082  0.076817380 1.2411270
 [20,]  0.112608900 -0.230070600 -1.684929 -0.21799440 -0.6806913 -2.214749 -0.8788627  0.106103600 1.1702730
           [,48]     [,49]    [,50]
  [1,] -3.388326 1.0260770 1.915078
  [2,] -3.180799 0.9589677 1.779945
  [3,] -3.180799 0.9346070 1.779945
  [4,] -3.195031 0.7713324 1.788631
  [5,] -2.811244 0.8127999 1.750932
  [6,] -2.494217 0.8620186 1.641431
  [7,] -2.528345 0.8027208 1.586068
  [8,] -2.598460 0.7454984 1.586068
  [9,] -2.897914 0.7454984 1.586068
 [10,] -2.826271 0.8983194 1.605036
 [11,] -2.849651 0.7697966 1.548475
 [12,] -2.797681 0.7310058 1.498044
 [13,] -2.634745 0.7310058 1.498044
 [14,] -2.663821 0.7225162 1.382487
 [15,] -3.182244 0.7983458 1.381473
 [16,] -3.182244 0.6097289 1.476652
 [17,] -3.293649 0.6097289 1.476652
 [18,] -3.125621 0.6696709 1.421561
 [19,] -2.636697 0.6570127 1.421561
 [20,] -2.954512 0.5480306 1.321848
 [ reached getOption("max.print") -- omitted 80 rows ]

$alpha_accept
 [1] 0.94 0.95 0.91 0.91 0.93 0.77 0.86 0.81 0.94 0.87 0.94 0.89 0.88 0.93 0.86 0.92 0.92 0.91 0.80 0.82 0.94
[22] 0.93 0.98 0.76 0.91 0.91 0.92 0.93 0.80 0.74 0.90 0.89 0.91 0.91 0.95 0.94 0.76 0.85 0.87 0.90 0.92 0.91
[43] 0.90 0.96 0.97 0.91 0.80 0.95 0.82 0.67

$beta
            [,1]      [,2]       [,3]       [,4]      [,5] [,6] [,7] [,8] [,9] [,10]       [,11] [,12]
  [1,] 0.8499575 0.6695774 -0.7909273 -0.7683737 0.8032444    0    0    0    0     0  0.00000000     0
  [2,] 0.8403646 0.6392943 -0.5703427 -0.9196081 0.8358736    0    0    0    0     0  0.00000000     0
  [3,] 0.6686810 0.5608166 -0.5963623 -0.9665158 0.8054401    0    0    0    0     0  0.00000000     0
  [4,] 0.4858712 0.5374670 -0.6240182 -0.7124432 0.7918975    0    0    0    0     0  0.00000000     0
  [5,] 0.6210771 0.5545324 -0.7018994 -0.8268143 0.7729989    0    0    0    0     0  0.00000000     0
  [6,] 0.5549224 0.5433842 -0.5542063 -0.8169709 0.8150294    0    0    0    0     0  0.00000000     0
  [7,] 0.8203472 0.4320159 -0.6326700 -0.8001188 0.7507514    0    0    0    0     0  0.00000000     0
  [8,] 0.6330988 0.7048131 -0.6916614 -0.7897143 0.7627062    0    0    0    0     0  0.00000000     0
  [9,] 0.5651009 0.4924043 -0.6860272 -0.8537561 0.7257137    0    0    0    0     0  0.00000000     0
 [10,] 0.4612200 0.8017508 -0.6540078 -1.0305690 0.6273339    0    0    0    0     0  0.00000000     0
 [11,] 0.6324391 0.5415515 -0.6513756 -0.9832755 0.6204670    0    0    0    0     0  0.00000000     0
 [12,] 0.5839064 0.5415515 -0.6214456 -0.7131989 0.5478639    0    0    0    0     0  0.00000000     0
 [13,] 0.5440329 0.7004292 -0.6537521 -0.6915001 0.5032996    0    0    0    0     0  0.00000000     0
 [14,] 0.6915420 0.7014379 -0.6640724 -0.5162670 0.5079815    0    0    0    0     0  0.00000000     0
 [15,] 0.8401475 0.4662788 -0.6640724 -0.5224059 0.5079815    0    0    0    0     0  0.00000000     0
 [16,] 0.7498082 0.8029066 -0.6799667 -0.6250936 0.4403896    0    0    0    0     0  0.00000000     0
 [17,] 0.9197503 0.5758149 -0.5924062 -0.8336596 0.5023529    0    0    0    0     0  0.00000000     0
 [18,] 0.8169270 0.3699032 -0.4247393 -0.7689715 0.7248978    0    0    0    0     0  0.00000000     0
 [19,] 0.6938103 0.4245262 -0.6947541 -0.5442819 0.7155102    0    0    0    0     0  0.00000000     0
 [20,] 0.4131674 0.5087606 -0.5721966 -0.6493814 0.5361747    0    0    0    0     0  0.00000000     0
              [,13] [,14] [,15] [,16]      [,17]      [,18] [,19] [,20]      [,21] [,22]     [,23] [,24]
  [1,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [2,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [3,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [4,]  0.000000000     0     0     0  0.0828812  0.0000000     0     0 0.00000000     0 0.0000000     0
  [5,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [6,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [7,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [8,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
  [9,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [10,]  0.000000000     0     0     0 -0.2637127  0.0000000     0     0 0.00000000     0 0.0000000     0
 [11,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [12,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [13,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [14,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [15,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [16,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [17,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [18,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [19,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
 [20,]  0.000000000     0     0     0  0.0000000  0.0000000     0     0 0.00000000     0 0.0000000     0
             [,25] [,26]       [,27]      [,28] [,29] [,30]       [,31]      [,32] [,33]       [,34] [,35]
  [1,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [2,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [3,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [4,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [5,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [6,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [7,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [8,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
  [9,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [10,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [11,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [12,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [13,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [14,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [15,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [16,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [17,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [18,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [19,]  0.00000000     0  0.00000000  0.0000000     0     0  0.00000000 0.00000000     0  0.00000000     0
 [20,]  0.00000000     0  0.00000000  0.0000000     0     0 -0.07510908 0.00000000     0  0.00000000     0
       [,36] [,37]       [,38]      [,39]       [,40] [,41] [,42]      [,43]      [,44] [,45]      [,46] [,47]
  [1,]     0     0  0.00000000  0.0000000  0.00000000     0     0 -0.0440988  0.0000000     0 0.00000000     0
  [2,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [3,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [4,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [5,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [6,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [7,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [8,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
  [9,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [10,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [11,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [12,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [13,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [14,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [15,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [16,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [17,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [18,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
 [19,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000 -0.1100676     0 0.00000000     0
 [20,]     0     0  0.00000000  0.0000000  0.00000000     0     0  0.0000000  0.0000000     0 0.00000000     0
       [,48] [,49] [,50]
  [1,]     0     0     0
  [2,]     0     0     0
  [3,]     0     0     0
  [4,]     0     0     0
  [5,]     0     0     0
  [6,]     0     0     0
  [7,]     0     0     0
  [8,]     0     0     0
  [9,]     0     0     0
 [10,]     0     0     0
 [11,]     0     0     0
 [12,]     0     0     0
 [13,]     0     0     0
 [14,]     0     0     0
 [15,]     0     0     0
 [16,]     0     0     0
 [17,]     0     0     0
 [18,]     0     0     0
 [19,]     0     0     0
 [20,]     0     0     0
 [ reached getOption("max.print") -- omitted 80 rows ]

$beta_accept
 [1] 0.01 0.20 0.01 0.01 0.01 0.06 0.08 0.04 0.05 0.06 0.11 0.03 0.07 0.06 0.06 0.09 0.15 0.09 0.11 0.03 0.06
[22] 0.10 0.08 0.06 0.13 0.05 0.08 0.11 0.03 0.01 0.09 0.07 0.08 0.12 0.01 0.07 0.10 0.07 0.06 0.12 0.08 0.02
[43] 0.06 0.08 0.08 0.12 0.02 0.04 0.05 0.02

$hyperparameters
$hyperparameters$mcmc
    GG thin burn proposal_alpha proposal_beta random_seed
1 1100   10  100            0.5           0.5      376075

$hyperparameters$priors
  intercept_variance slab_variance bb_alpha bb_beta
1                 10            10     0.02    1.98

$hyperparameters$inputdata
$hyperparameters$inputdata$XX
              [,1]
  [1,] -1.46344784
  [2,]  2.03257164
  [3,] -0.46247065
  [4,]  0.06962129
  [5,] -0.79851765
  [6,] -0.44228723
  [7,]  0.71703403
  [8,]  0.15782627
  [9,]  0.27826931
 [10,] -0.38876926
 [11,] -0.33361527
 [12,]  0.25123585
 [13,]  0.35292801
 [14,]  0.72774682
 [15,]  0.14401536
 [16,] -2.06109494
 [17,]  1.35127907
 [18,] -0.80326106
 [19,]  0.10591133
 [20,]  0.91485694
 [21,]  0.88760647
 [22,]  0.11213618
 [23,] -1.17797179
 [24,]  1.36586436
 [25,] -1.40274128
 [26,] -0.61223723
 [27,] -1.58730602
 [28,]  0.75084769
 [29,] -1.35951690
 [30,]  0.33845651
 [31,] -1.08893521
 [32,]  1.06313237
 [33,] -1.06802604
 [34,]  0.58367201
 [35,]  1.63762827
 [36,]  0.81502031
 [37,] -0.69906415
 [38,]  0.19682389
 [39,]  1.01010761
 [40,]  0.19028162
 [41,] -1.75030390
 [42,]  0.04610347
 [43,] -0.15328986
 [44,]  1.31750081
 [45,]  0.41809822
 [46,]  0.88489075
 [47,]  0.07938542
 [48,] -0.34494626
 [49,]  1.11186857
 [50,]  0.14508321
 [51,]  0.06015045
 [52,]  0.56669084
 [53,]  1.34212806
 [54,] -0.78611323
 [55,] -1.86788687
 [56,]  0.20424367
 [57,]  0.55158248
 [58,] -0.20439619
 [59,] -0.99362501
 [60,] -2.49266940
 [61,] -0.30464771
 [62,] -0.18860355
 [63,]  1.45515011
 [64,] -0.33871514
 [65,] -1.91463847
 [66,]  0.29729905
 [67,]  2.81636815
 [68,] -1.12316099
 [69,]  0.65395172
 [70,]  0.54665374
 [71,] -0.35695360
 [72,] -0.65888840
 [73,]  1.30811388
 [74,] -0.09659515
 [75,] -0.40531238
 [76,]  1.84362623
 [77,] -1.54946817
 [78,] -1.70540583
 [79,]  0.62267720
 [80,] -0.14844914
 [81,]  0.49106127
 [82,]  1.12270356
 [83,] -0.95652961
 [84,] -0.72398345
 [85,] -0.91493719
 [86,] -1.82977684
 [87,]  1.30341373
 [88,]  0.36664428
 [89,] -0.81743143
 [90,] -0.39123003
 [91,]  0.02762621
 [92,]  0.46126920
 [93,]  1.58513324
 [94,] -0.10081579
 [95,]  0.46717749
 [96,]  0.52632634
 [97,]  0.47827309
 [98,]  0.10312598
 [99,] -0.64668147
[100,]  0.25552395

$hyperparameters$inputdata$YY
       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19]
  [1,]    0    0   28  120    0   53    0   60    2    79     1     0     2    50    14     3     1     1    96
  [2,]   40   12    0    0   88    8  141  106   32    26     0     3     1    33     1     2     0     2    82
  [3,]    0    0    0    0  170   51  112  239    3    78     0     5     0    38    31     0     0     1    73
  [4,]    0    0    0    0  131  143   41  119    6    16     0    13     1    23     4     0     0     1   141
  [5,]    8    0    0    0  268    7    0   14    0    43     0    12     6    41     3     0     0     0   116
  [6,]   20    0    4    8   63  142    2   65    2    33    11     3     9    40     3     4     0     1   130
  [7,]   24    6    2    0   96  191    0   49   30   102     1    16     5    20     3     6     0     0   131
  [8,]    0    0    4    1  101   95    4   12    7    19     0     6     7    31    11    10     0     3   127
  [9,]    0    0    7    0    0   79   58  258   68     5     6     4     0    16    14     0     7     1    80
 [10,]    3    7    0    0   93   58   15   32    3    63     1     4     8    33     2     6     3     0   153
 [11,]    1    0   29    6    3  240    8   51    2    20     1     2    10     6    13     0     9     0   149
 [12,]   12    0    0    0  154  173    6   10    0    30     2    15     8    69    14     0     0     0   178
 [13,]    1    0    1    0   29   10   76   99    6    42     0     0    13    78    23     0     0     0   175
 [14,]    2    0    0    0  113  154   23   64    2    52     0     2    28    51    12     1     0     0    94
 [15,]    0   17   76    0    0  126   67  139    5   108     0     9    13    15     4     1     0     1   113
 [16,]    0    0  141    3    0  165    0   33    5    16     0     6     2    41    11     0     0     1    94
 [17,]    2   15   10    0   38  175    9   55    1    12     3     4    17    42     7     0     5     0    52
 [18,]    0    0    3    0    9  397   17  149    3    33     4     6     3    15     5     0     0     0    23
 [19,]    1    0    2   19   76    5    0    9    3    25     2    17     0    43    14    14     0     0    73
 [20,]    5    3    0    0  124   11    7   40   18    20     0    14     1   121    11     0     0     0   158
       [,20] [,21] [,22] [,23] [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36]
  [1,]    26     0    11     1   142    11     2     3     3   112    99     0    12     1     5     7     2
  [2,]    60     1     2    10   123     0     0     0     0    64    39     0    17    27     0    20     3
  [3,]    44    18    10     1   239     5     8     5     0   119    50     2    50     6     0    27     1
  [4,]   101     0    60     0    81     0     7     9     1   118   115     0    21    25     4     0     0
  [5,]    59     0     4     0    77     0    13     0     0    56   128     0    11     1     3     3    13
  [6,]    63     0    33     0   137     0     8     0    13   197    88     0    93     0    16     2    15
  [7,]    65     0    19    17    98     0     3     1     0   166   150     2    16     1     0    40     1
  [8,]    59     1     5     5    41     0    14     6     0    73   128     1     7     1    36     4     1
  [9,]    57     3    10     4    38     4    11     2     0    29    34     0    32    13     1     5     0
 [10,]    29     0    20     1    45     0     9     0     0    51    56     0    25     3     5     1     0
 [11,]    15     0    50     0    79     1     0    10     0   111    76     2     9     4     0     4     1
 [12,]    48     0    13     4    80     0     6    16     0    87    91     0    35    71     2    11     1
 [13,]    53     9    16     0   123     3     1     0     0    59   121     0    49     1     0     0     0
 [14,]    63     0     3     0   110     1     2     0     0    21    42     0    35     1     2     2     0
 [15,]    14     3    44     1    35     0     6     4     0   125    72     3    15     9     0     0     0
 [16,]    54     1    17     9    81     1     0     0     0   150    19     0    14     0     6     9     0
 [17,]    38     0     7     0    58     2    17     2     0    41    48     2    20     0     4    28     0
 [18,]    38     0     5     0    19     4     2     0     0    53    31     0    27     0     2    41     0
 [19,]    27     2    46     0    71     0     5     5     0   105    59     3    55     4     5    18     0
 [20,]    66     0     1     0    83     0     8     8     0    54    93     2    86    26     1     8     0
       [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
  [1,]   156     0    41    21     0    35    26    40    15     9    88     0    87   158
  [2,]    74    18     1    10     0     2     4     0     6    15    54     0    25    89
  [3,]    50    56   105     5     3    12     1     0     4    40   107     0   100    60
  [4,]    30     4    60     5     2    10    25     0     8    35   104     0    24    81
  [5,]    67     0    34    47     0    13     4     0    24     7    85     0    18   108
  [6,]    50    39     8     5     8     6     2     2     5    58    69     0    86   215
  [7,]    29    29    12    20     0    32     1     1     6     6    61     0    94   221
  [8,]    40     1    17    11     1    18    17     4     7     7    40     0    33    51
  [9,]    35     7    32    17     0     8     6     0     0    22    72     0    44    54
 [10,]    67    61    70    12     3    12     5     0    26    15    65     0    28    60
 [11,]    45     4    28    13     6     2     0     0     9    20   159     0    25   238
 [12,]    68    20    33    22     0     2     8    15     2    29    99     0    67   123
 [13,]   102    16    30     5     0    28    13     0     8    25    91     1    52   147
 [14,]    46     0    27    16     0    14    28     0    13    33    47     0    36    58
 [15,]   116     0    48    15     0     3     1     0     4    18   129     0    24   149
 [16,]    25    29    10     7     0    15     2     0     5     5    66     0    46   145
 [17,]    23    15     5    19    12    41     0     0     8    27    88     0    31    43
 [18,]    16    17    22    25     0     7     7     0    10    42    23     0    18    60
 [19,]    47     6     2     6    11    42    19     0     0    63   131     0    11   102
 [20,]    93     8    10    31    17     6    18     0    31    64   152     0    17   110
 [ reached getOption("max.print") -- omitted 80 rows ]

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