Last updated: 2019-03-13

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library(susieR)
library(R.utils)

1.

\[ \left(\begin{array} c 2 \\ 2.01 \end{array}\right) \sim N_2(\mathbf{1}\mathbf{1}^{T} \mathbf{0}, \sigma^2 \mathbf{1}\mathbf{1}^{T} + \lambda I) \]

z = c(2, 2.01)
R = matrix(1, 2,2)

Model with var \(\sigma^2(R + \lambda I)\).

sourceDirectory("~/Documents/GitHub/susieR/inst/code/susiez_fix/")
fit_1 = susie_z_general_fix(z, R, lambda = 0.1, restrict = FALSE, estimate_prior_method = 'optim')

The estimated residual variance is

fit_1$sigma2
[1] 0.0005076256

Model with var \(\sigma^2R + \lambda I\).

sourceDirectory("~/Documents/GitHub/susieR/inst/code/susiez_num/")
fit_2 = susie_z_general_num(z, R, lambda = 0.1, restrict = FALSE, estimate_prior_method = 'EM')

The estimated residual variance is

fit_2$sigma2
[1] 3.473333

The model with var \(\sigma^2R + \lambda I\) gives the estimated residual variance close to 4.

We use the model with var \(\sigma^2R + \lambda I\) in the following investigation.

2.

\[ \left(\begin{array} c 1 \\ 1.01 \end{array}\right) \sim N_2(\mathbf{1}\mathbf{1}^{T} \mathbf{0}, \sigma^2 \mathbf{1}\mathbf{1}^{T} + \lambda I) \]

z = c(1, 1.01)
R = matrix(1, 2, 2)

Model with var \(\sigma^2R + \lambda I\). \(\lambda=0.1\)

fit_3 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0.1, restrict = TRUE, estimate_prior_method = 'EM')
[1] "before estimate sigma2 objective:-1.58186763542179"
[1] "after estimate sigma2 objective:-1.570159986685"
[1] "before estimate sigma2 objective:-1.54757446360187"
[1] "after estimate sigma2 objective:-1.53839565170333"
[1] "before estimate sigma2 objective:-1.53839565170333"
[1] "after estimate sigma2 objective:-1.53839565170333"
susie_plot(fit_3, y = 'PIP')

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db8e65c zouyuxin 2019-03-13
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There are no significant signal.

\(\lambda=0\)

fit_4 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0, restrict = TRUE, estimate_prior_method = 'EM')
[1] "before estimate sigma2 objective:-2.72916544264994"
[1] "after estimate sigma2 objective:-2.71998611548902"
[1] "before estimate sigma2 objective:-2.70103469396501"
[1] "after estimate sigma2 objective:-2.68946315685295"
[1] "before estimate sigma2 objective:-2.68946315685295"
[1] "after estimate sigma2 objective:-2.68946315685295"
susie_plot(fit_4, y = 'PIP')

z = c(6, 6.01)
R = matrix(1, 2, 2)

Model with var \(\sigma^2R + \lambda I\). \(\lambda=0.1\)

fit_5 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0.1, restrict = TRUE, estimate_prior_method = 'EM')
[1] "before estimate sigma2 objective:-13.7175796354218"
[1] "after estimate sigma2 objective:-13.7175798672716"
[1] "before estimate sigma2 objective:-7.93041136012025"
[1] "after estimate sigma2 objective:-7.93041137065023"
[1] "before estimate sigma2 objective:-4.34247256666951"
[1] "after estimate sigma2 objective:-4.34247256287466"
[1] "before estimate sigma2 objective:-4.05511126473463"
[1] "after estimate sigma2 objective:-4.05511126490954"
[1] "before estimate sigma2 objective:-3.98220037435143"
[1] "after estimate sigma2 objective:-3.98220037450636"
[1] "before estimate sigma2 objective:-3.89332924059978"
[1] "after estimate sigma2 objective:-3.89332924085191"
[1] "before estimate sigma2 objective:-3.78643889627407"
[1] "after estimate sigma2 objective:-3.78643889667236"
[1] "before estimate sigma2 objective:-3.49517398054299"
[1] "after estimate sigma2 objective:-3.49517398119828"
[1] "before estimate sigma2 objective:-3.33717237322046"
[1] "after estimate sigma2 objective:-3.33717237324268"
[1] "before estimate sigma2 objective:-3.32604327580974"
[1] "after estimate sigma2 objective:-3.32604327580681"
[1] "before estimate sigma2 objective:-3.32600070770375"
[1] "after estimate sigma2 objective:-3.32600070770373"
susie_plot(fit_5, y = 'PIP')

We find the significant signal.

\(\lambda=0\)

fit_6 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0, restrict = TRUE, estimate_prior_method = 'EM')
[1] "before estimate sigma2 objective:-15.3049756278351"
[1] "after estimate sigma2 objective:-15.3049759511923"
[1] "before estimate sigma2 objective:-8.98627879819076"
[1] "after estimate sigma2 objective:-8.98627877687633"
[1] "before estimate sigma2 objective:-5.45914812444076"
[1] "after estimate sigma2 objective:-5.459148128337"
[1] "before estimate sigma2 objective:-5.22028902974184"
[1] "after estimate sigma2 objective:-5.22028902982143"
[1] "before estimate sigma2 objective:-5.14741482535723"
[1] "after estimate sigma2 objective:-5.14741482544165"
[1] "before estimate sigma2 objective:-5.05745094890992"
[1] "after estimate sigma2 objective:-5.05745094904849"
[1] "before estimate sigma2 objective:-4.94886386686558"
[1] "after estimate sigma2 objective:-4.94886386708611"
[1] "before estimate sigma2 objective:-4.65398535880191"
[1] "after estimate sigma2 objective:-4.65398535920978"
[1] "before estimate sigma2 objective:-4.48819479037601"
[1] "after estimate sigma2 objective:-4.48819479032972"
[1] "before estimate sigma2 objective:-4.4770818119199"
[1] "after estimate sigma2 objective:-4.47708181192261"
[1] "before estimate sigma2 objective:-4.47704322901776"
[1] "after estimate sigma2 objective:-4.47704322901777"
susie_plot(fit_6, y = 'PIP')

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.3

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] R.utils_2.7.0     R.oo_1.22.0       R.methodsS3_1.7.1 susieR_0.7.1.0482

loaded via a namespace (and not attached):
 [1] workflowr_1.1.1 Rcpp_1.0.0      lattice_0.20-38 digest_0.6.18  
 [5] rprojroot_1.3-2 grid_3.5.1      backports_1.1.3 git2r_0.24.0   
 [9] magrittr_1.5    evaluate_0.12   stringi_1.2.4   whisker_0.3-2  
[13] Matrix_1.2-15   rmarkdown_1.11  tools_3.5.1     stringr_1.3.1  
[17] yaml_2.2.0      compiler_3.5.1  htmltools_0.3.6 knitr_1.20

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