Last updated: 2018-05-12

workflowr checks: (Click a bullet for more information)

  • ✔ R Markdown file: up-to-date

    Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

  • ✔ Environment: empty

    Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

  • ✔ Seed: set.seed(12345)

    The command set.seed(12345) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

  • ✔ Session information: recorded

    Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

  • ✔ Repository version: ddf9062

    Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.

    Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: 
    
Ignored files:
    Ignored:    .DS_Store
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    analysis/.DS_Store
    Ignored:    analysis/BH_robustness_cache/
    Ignored:    analysis/FDR_Null_cache/
    Ignored:    analysis/FDR_null_betahat_cache/
    Ignored:    analysis/Rmosek_cache/
    Ignored:    analysis/StepDown_cache/
    Ignored:    analysis/alternative2_cache/
    Ignored:    analysis/alternative_cache/
    Ignored:    analysis/ash_gd_cache/
    Ignored:    analysis/average_cor_gtex_2_cache/
    Ignored:    analysis/average_cor_gtex_cache/
    Ignored:    analysis/brca_cache/
    Ignored:    analysis/cash_deconv_cache/
    Ignored:    analysis/cash_fdr_1_cache/
    Ignored:    analysis/cash_fdr_2_cache/
    Ignored:    analysis/cash_fdr_3_cache/
    Ignored:    analysis/cash_fdr_4_cache/
    Ignored:    analysis/cash_fdr_5_cache/
    Ignored:    analysis/cash_fdr_6_cache/
    Ignored:    analysis/cash_plots_cache/
    Ignored:    analysis/cash_sim_1_cache/
    Ignored:    analysis/cash_sim_2_cache/
    Ignored:    analysis/cash_sim_3_cache/
    Ignored:    analysis/cash_sim_4_cache/
    Ignored:    analysis/cash_sim_5_cache/
    Ignored:    analysis/cash_sim_6_cache/
    Ignored:    analysis/cash_sim_7_cache/
    Ignored:    analysis/correlated_z_2_cache/
    Ignored:    analysis/correlated_z_3_cache/
    Ignored:    analysis/correlated_z_cache/
    Ignored:    analysis/create_null_cache/
    Ignored:    analysis/cutoff_null_cache/
    Ignored:    analysis/design_matrix_2_cache/
    Ignored:    analysis/design_matrix_cache/
    Ignored:    analysis/diagnostic_ash_cache/
    Ignored:    analysis/diagnostic_correlated_z_2_cache/
    Ignored:    analysis/diagnostic_correlated_z_3_cache/
    Ignored:    analysis/diagnostic_correlated_z_cache/
    Ignored:    analysis/diagnostic_plot_2_cache/
    Ignored:    analysis/diagnostic_plot_cache/
    Ignored:    analysis/efron_leukemia_cache/
    Ignored:    analysis/fitting_normal_cache/
    Ignored:    analysis/gaussian_derivatives_2_cache/
    Ignored:    analysis/gaussian_derivatives_3_cache/
    Ignored:    analysis/gaussian_derivatives_4_cache/
    Ignored:    analysis/gaussian_derivatives_5_cache/
    Ignored:    analysis/gaussian_derivatives_cache/
    Ignored:    analysis/gd-ash_cache/
    Ignored:    analysis/gd_delta_cache/
    Ignored:    analysis/gd_lik_2_cache/
    Ignored:    analysis/gd_lik_cache/
    Ignored:    analysis/gd_w_cache/
    Ignored:    analysis/knockoff_10_cache/
    Ignored:    analysis/knockoff_2_cache/
    Ignored:    analysis/knockoff_3_cache/
    Ignored:    analysis/knockoff_4_cache/
    Ignored:    analysis/knockoff_5_cache/
    Ignored:    analysis/knockoff_6_cache/
    Ignored:    analysis/knockoff_7_cache/
    Ignored:    analysis/knockoff_8_cache/
    Ignored:    analysis/knockoff_9_cache/
    Ignored:    analysis/knockoff_cache/
    Ignored:    analysis/knockoff_var_cache/
    Ignored:    analysis/marginal_z_alternative_cache/
    Ignored:    analysis/marginal_z_cache/
    Ignored:    analysis/mosek_reg_2_cache/
    Ignored:    analysis/mosek_reg_4_cache/
    Ignored:    analysis/mosek_reg_5_cache/
    Ignored:    analysis/mosek_reg_6_cache/
    Ignored:    analysis/mosek_reg_cache/
    Ignored:    analysis/pihat0_null_cache/
    Ignored:    analysis/plot_diagnostic_cache/
    Ignored:    analysis/poster_obayes17_cache/
    Ignored:    analysis/real_data_simulation_2_cache/
    Ignored:    analysis/real_data_simulation_3_cache/
    Ignored:    analysis/real_data_simulation_4_cache/
    Ignored:    analysis/real_data_simulation_5_cache/
    Ignored:    analysis/real_data_simulation_cache/
    Ignored:    analysis/rmosek_primal_dual_2_cache/
    Ignored:    analysis/rmosek_primal_dual_cache/
    Ignored:    analysis/seqgendiff_cache/
    Ignored:    analysis/simulated_correlated_null_2_cache/
    Ignored:    analysis/simulated_correlated_null_3_cache/
    Ignored:    analysis/simulated_correlated_null_cache/
    Ignored:    analysis/simulation_real_se_2_cache/
    Ignored:    analysis/simulation_real_se_cache/
    Ignored:    analysis/smemo_2_cache/
    Ignored:    data/LSI/
    Ignored:    docs/.DS_Store
    Ignored:    docs/figure/.DS_Store
    Ignored:    output/fig/

Unstaged changes:
    Deleted:    analysis/cash_plots_fdp.Rmd
    Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.
Expand here to see past versions:
    File Version Author Date Message
    rmd cc0ab83 Lei Sun 2018-05-11 update
    html 0f36d99 LSun 2017-12-21 Build site.
    html 853a484 LSun 2017-11-07 Build site.
    html 4f032ad LSun 2017-11-05 transfer
    html 27bcaf9 LSun 2017-05-08 writeups
    rmd 6bac69e LSun 2017-05-08 writeups
    html e368074 LSun 2017-05-06 Rmosek
    rmd 06eff07 LSun 2017-05-06 Rmosek
    rmd a58d5c1 LSun 2017-05-06 Rmosek

Introduction

Being in the development stage, cvxr is not very efficient at the convex optimization in fitting Gaussian derivatives. We are moving to Rmosek.

source("../code/gdash.R")
z.mat = read.table("../output/z_null_liver_777.txt")
fd.bh = scan("../output/fd.bh.0.05_null_liver_777.txt")
pihat0 = scan("../output/pihat0_z_null_liver_777.txt")

Bad

These data sets are unfriendly for both BH and ASH.

Data Set  355 :
 Number of BH false discoveries:  639 ;
 ASH's pihat0 =  0.04750946 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0225585778660563 ; 2 : 1.30307541409737 ; 3 : 0.0529119988564207 ; 4 : 0.86434625413445 ; 5 : 0 ; 6 : 0.115991285668782 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0.012768069558034 ;

Data Set  23 :
 Number of BH false discoveries:  408 ;
 ASH's pihat0 =  0.03139009 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.016039132567407 ; 2 : 1.34993003351774 ; 3 : 0.081263929095916 ; 4 : 0.714486051374311 ; 5 : 0.139320458700019 ; 6 : 0 ; 7 : 0.100823265137825 ; 8 : 0 ; 9 : 0.0608462191710317 ; 10 : 0.000964802431909129 ;

Data Set  122 :
 Number of BH false discoveries:  331 ;
 ASH's pihat0 =  0.04301549 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.00711459304239053 ; 2 : 1.1037821799492 ; 3 : 0 ; 4 : 0.528402132228434 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0.000977244957534518 ; 10 : 0 ;

Data Set  749 :
 Number of BH false discoveries:  114 ;
 ASH's pihat0 =  0.02583276 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0458626422285871 ; 2 : 1.0692347200711 ; 3 : 0.00127673630293041 ; 4 : 0.437875595583542 ; 5 : 0 ; 6 : 0 ; 7 : 0.110561067339144 ; 8 : 0 ; 9 : 0.104817311821469 ; 10 : 0 ;

Data Set  724 :
 Number of BH false discoveries:  79 ;
 ASH's pihat0 =  0.01606004 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0352454327180146 ; 2 : 1.085621208483 ; 3 : 0.072031313135509 ; 4 : 0.313477034131008 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;

Data Set  56 :
 Number of BH false discoveries:  35 ;
 ASH's pihat0 =  0.04829662 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.015603437988185 ; 2 : 0.863695602978145 ; 3 : 0.135238823162622 ; 4 : 0.336622180491709 ; 5 : 0.18630322261983 ; 6 : 0.00268136598387189 ; 7 : 0.0339747362866559 ; 8 : 0.0181307043838827 ; 9 : 0 ; 10 : 0.0344310653486728 ;

Data Set  840 :
 Number of BH false discoveries:  28 ;
 ASH's pihat0 =  0.02316832 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 1.03471486197017 ; 3 : 0 ; 4 : 0.329235042804543 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0.00321461375022215 ; 10 : 0.0593306511691146 ;

Data Set  858 :
 Number of BH false discoveries:  16 ;
 ASH's pihat0 =  0.05110069 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 1.00711281742885 ; 3 : 0 ; 4 : 0.390477482047559 ; 5 : 0 ; 6 : 0 ; 7 : 0.0551377637495718 ; 8 : 0 ; 9 : 0.0479292544081263 ; 10 : 0.0837572023674743 ;

Data Set  771 :
 Number of BH false discoveries:  12 ;
 ASH's pihat0 =  0.04316169 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0.73920141158121 ; 3 : 0.077182005444609 ; 4 : 0.167446690539398 ; 5 : 0.114289140310117 ; 6 : 0 ; 7 : 0.00550636320542386 ; 8 : 0.0464055959765927 ; 9 : 0 ; 10 : 0.0398398101639301 ;

Data Set  389 :
 Number of BH false discoveries:  11 ;
 ASH's pihat0 =  0.03156173 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0104278129211743 ; 2 : 0.81975416226431 ; 3 : 0.175093847880514 ; 4 : 0.237691296370699 ; 5 : 0.0928656721296627 ; 6 : 0 ; 7 : 0 ; 8 : 0.0957748191090392 ; 9 : 0 ; 10 : 0.14869448917214 ;

Data Set  485 :
 Number of BH false discoveries:  9 ;
 ASH's pihat0 =  0.04794909 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0.688297974677999 ; 3 : 0.102717821163846 ; 4 : 0.1348683673964 ; 5 : 0.0774735270815003 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;

Data Set  77 :
 Number of BH false discoveries:  7 ;
 ASH's pihat0 =  0.05151585 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0316698203536559 ; 2 : 0.900083565443527 ; 3 : 0.369105500650609 ; 4 : 0.348606888712178 ; 5 : 0.225564147471124 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;

Data Set  984 :
 Number of BH false discoveries:  7 ;
 ASH's pihat0 =  0.04567195 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0.699043214591173 ; 3 : 0.100302581737407 ; 4 : 0.145190970625763 ; 5 : 0.0474679405200551 ; 6 : 0 ; 7 : 0 ; 8 : 0.134635889035747 ; 9 : 0 ; 10 : 0.110318005619196 ;

Data Set  360 :
 Number of BH false discoveries:  6 ;
 ASH's pihat0 =  0.0308234 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0370729985554797 ; 2 : 0.965843584122268 ; 3 : 0.113777617637278 ; 4 : 0.182892304104783 ; 5 : 0.0985758556513691 ; 6 : 0 ; 7 : 0 ; 8 : 0.175602983077514 ; 9 : 0 ; 10 : 0.128160801611689 ;

Data Set  522 :
 Number of BH false discoveries:  4 ;
 ASH's pihat0 =  0.02083846 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0.836683104968565 ; 3 : 0 ; 4 : 0.0380324164945556 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0.299307885307397 ; 9 : 0 ; 10 : 0.0990067134691387 ;

Data Set  22 :
 Number of BH false discoveries:  1 ;
 ASH's pihat0 =  0.03271534 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.011182140702874 ; 2 : 0.637669154664922 ; 3 : 0.0954740117610049 ; 4 : 0.0145362179577236 ; 5 : 0.0384875211132818 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0.0366040528004269 ;

Data Set  269 :
 Number of BH false discoveries:  1 ;
 ASH's pihat0 =  0.02787007 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0350127752264117 ; 2 : 0.665763246213506 ; 3 : 0 ; 4 : 0 ; 5 : 0.360745065018111 ; 6 : 0 ; 7 : 0.660778015759139 ; 8 : 0 ; 9 : 0.341451404165077 ; 10 : 0 ;

Data Set  403 :
 Number of BH false discoveries:  1 ;
 ASH's pihat0 =  0.0531628 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.00287620650301181 ; 2 : 0.547191548824974 ; 3 : 0 ; 4 : 0 ; 5 : 0.0381682188675178 ; 6 : 0.000237362926646135 ; 7 : 0.0760788952836512 ; 8 : 0.155507732499129 ; 9 : 0.0557968950438762 ; 10 : 0.00176813778552284 ;

Data Set  923 :
 Number of BH false discoveries:  1 ;
 ASH's pihat0 =  0.03239883 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0237509340668928 ; 2 : 0.920816163763449 ; 3 : 0.126877447333694 ; 4 : 0.158793996465808 ; 5 : 0.0298935777348498 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;

Data Set  3 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  0.0465218 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0232314826078553 ; 2 : 0.491281828479503 ; 3 : 0.165633823951823 ; 4 : 0 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;

Good

These data sets are friendly for both BH and ASH.

Data Set  4 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0220506376197135 ; 4 : 0 ;

Data Set  5 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.00299571447314808 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;

Data Set  7 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0154789111560678 ;

Data Set  8 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0448250444179864 ; 2 : 0 ; 3 : 0 ; 4 : 0.143559202208159 ;

Data Set  9 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0.00733790864173648 ; 3 : 0.0163403533804334 ; 4 : 0 ;

Data Set  12 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0221346391841642 ;

Data Set  13 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;

Data Set  14 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0319220622489123 ; 4 : 0.0192425975845108 ;

Data Set  16 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0132467627058809 ; 2 : 0 ; 3 : 0.0050633052630629 ; 4 : 0.0460280223671055 ;

Data Set  17 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.019759781277875 ; 2 : 0 ; 3 : 0 ; 4 : 0.0663856267063882 ;

Data Set  18 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0334151016576349 ; 4 : 0.00459370714209619 ;

Data Set  25 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0110557207434819 ; 4 : 0.165219572806289 ;

Data Set  28 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0200505087249252 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;

Data Set  30 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0118483507943389 ; 4 : 0 ;

Data Set  34 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.101371139384381 ; 4 : 0 ;

Data Set  35 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0165529780499778 ; 2 : 0 ; 3 : 0 ; 4 : 0.102360725261069 ;

Data Set  36 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.00780175544762885 ; 2 : 0 ; 3 : 0 ; 4 : 0.0653975820808355 ;

Data Set  38 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0643337534695275 ;

Data Set  42 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0117929353952078 ; 4 : 0.14259210767113 ;

Data Set  43 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0266591670097924 ; 4 : 0.119934975949713 ;

Data Set  45 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0197168202529947 ; 2 : 0 ; 3 : 0.00535774384797348 ; 4 : 0.0981326520063197 ;

Data Set  46 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0142593356797949 ; 4 : 0 ;

Data Set  47 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0553713103730739 ; 2 : 0 ; 3 : 0 ; 4 : 0.0424140129177028 ;

Data Set  49 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0399557075219927 ; 4 : 0.0203389185614439 ;

Data Set  52 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0717118497321021 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;

Data Set  53 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0 ; 2 : 0 ; 3 : 0.0203994359033729 ; 4 : 0 ;

Data Set  54 :
 Number of BH false discoveries:  0 ;
 ASH's pihat0 =  1 ;
Normalized coefficients of Gaussian derivatives:
 1 : 0.0226491329325567 ; 2 : 0 ; 3 : 0 ; 4 : 0.0369913458520336 ;

Remarks

The implementation by Rmosek is more convenient, cleaner, yet more complicated. Need to understand different issues such as initialization, optimal orders, controlling parameters, dual construction, etc.

Session information

sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.4

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] Rmosek_8.0.69     PolynomF_1.0-1    CVXR_0.95         REBayes_1.2      
[5] Matrix_1.2-12     SQUAREM_2017.10-1 EQL_1.0-0         ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16      knitr_1.20        whisker_0.3-2    
 [4] magrittr_1.5      workflowr_1.0.1   bit_1.1-12       
 [7] lattice_0.20-35   R6_2.2.2          stringr_1.3.0    
[10] tools_3.4.3       grid_3.4.3        R.oo_1.21.0      
[13] git2r_0.21.0      scs_1.1-1         htmltools_0.3.6  
[16] bit64_0.9-7       yaml_2.1.18       rprojroot_1.3-2  
[19] digest_0.6.15     gmp_0.5-13.1      ECOSolveR_0.4    
[22] R.utils_2.6.0     evaluate_0.10.1   rmarkdown_1.9    
[25] stringi_1.1.6     Rmpfr_0.6-1       compiler_3.4.3   
[28] backports_1.1.2   R.methodsS3_1.7.1

This reproducible R Markdown analysis was created with workflowr 1.0.1