Last updated: 2019-03-12

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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)
fit_1$sigma2
[1] 0.0005078433

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)
fit_2$sigma2
[1] 3.7

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 \(\sigma^2R + \lambda I\).

fit_3 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0.1)
[1] "before estimate sigma2 objective:-1.58186763542179"
[1] "after estimate sigma2 objective:-1.57020328695054"
[1] "before estimate sigma2 objective:-1.54628099838458"
[1] "after estimate sigma2 objective:-1.5387674779913"
[1] "before estimate sigma2 objective:-1.5387674779913"
[1] "after estimate sigma2 objective:-1.5387674779913"
susie_plot(fit_3, y = 'PIP')

There are no significant signal.

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

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

fit_4 = susie_z_general_num(z, R, verbose=TRUE, lambda = 0.1)
[1] "before estimate sigma2 objective:-13.7175796354218"
[1] "after estimate sigma2 objective:-13.7175796354218"
[1] "before estimate sigma2 objective:-7.93041128986574"
[1] "after estimate sigma2 objective:-7.93041128986574"
[1] "before estimate sigma2 objective:-4.34247256678977"
[1] "after estimate sigma2 objective:-4.34247256678977"
[1] "before estimate sigma2 objective:-4.05511125597767"
[1] "after estimate sigma2 objective:-4.05511125597767"
[1] "before estimate sigma2 objective:-3.98220036510767"
[1] "after estimate sigma2 objective:-3.98220036510767"
[1] "before estimate sigma2 objective:-3.89332923147985"
[1] "after estimate sigma2 objective:-3.89332923147985"
[1] "before estimate sigma2 objective:-3.78643888763794"
[1] "after estimate sigma2 objective:-3.78643888763794"
[1] "before estimate sigma2 objective:-3.49517397351547"
[1] "after estimate sigma2 objective:-3.49517397351547"
[1] "before estimate sigma2 objective:-3.33717237303734"
[1] "after estimate sigma2 objective:-3.33717237303734"
[1] "before estimate sigma2 objective:-3.32604327581057"
[1] "after estimate sigma2 objective:-3.32604327581057"
[1] "before estimate sigma2 objective:-3.32600070770394"
[1] "after estimate sigma2 objective:-3.32600070770394"
susie_plot(fit_4, y = 'PIP')

We find the significant signal.

The model doesn’t work with lambda = 0.

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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