The goal of fashr is to implement the functional adaptive shrinkage through empirical Bayes.
Note: The code to generate the results for the manuscript is here.
Installation
You can install the development version of fashr from GitHub with:
# install.packages("pak")
pak::pak("stephenslab/fashr")
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#> ✔ Updated metadata database: 7.63 MB in 10 files.
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#> + cli 3.6.5 🔧 ⬇ (1.47 MB)
#> + cowplot 1.2.0 ⬇ (1.38 MB)
#> + farver 2.1.2 🔧 ⬇ (1.97 MB)
#> + fashr 0.1.39 → 0.1.39 👷🏻♂️🔧 ⬇ (GitHub: 3c3390b)
#> + ggplot2 4.0.1 ⬇ (8.47 MB)
#> + glue 1.8.0 🔧 ⬇ (175.14 kB)
#> + gtable 0.3.6 ⬇ (225.12 kB)
#> + irlba 2.3.5.1 🔧 ⬇ (319.80 kB)
#> + isoband 0.2.7 🔧 ⬇ (1.87 MB)
#> + labeling 0.4.3 ⬇ (61.83 kB)
#> + LaplacesDemon 16.1.6
#> + lifecycle 1.0.4 ⬇ (125.64 kB)
#> + magrittr 2.0.4 🔧 ⬇ (231.97 kB)
#> + mixsqp 0.3-54 🔧 ⬇ (994.47 kB)
#> + numDeriv 2016.8-1.1 ⬇ (115.06 kB)
#> + plyr 1.8.9 🔧 ⬇ (984.75 kB)
#> + R6 2.6.1 ⬇ (87.28 kB)
#> + RColorBrewer 1.1-3 ⬇ (51.79 kB)
#> + Rcpp 1.1.0 🔧 ⬇ (3.37 MB)
#> + reshape2 1.4.5 🔧 ⬇ (343.07 kB)
#> + rlang 1.1.6 🔧 ⬇ (1.91 MB)
#> + S7 0.2.1 🔧 ⬇ (343.27 kB)
#> + scales 1.4.0 ⬇ (873.34 kB)
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#> + TMB 1.9.18 🔧 ⬇ (1.47 MB)
#> + vctrs 0.6.5 🔧 ⬇ (1.89 MB)
#> + viridisLite 0.4.2 ⬇ (1.30 MB)
#> + withr 3.0.2 ⬇ (224.91 kB)
#> ℹ Getting 27 pkgs (45.39 MB) and 1 pkg with unknown size, 1 (4.10 MB) cached
#> ✔ Got R6 2.6.1 (aarch64-apple-darwin20) (87.28 kB)
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#> ✔ Got RColorBrewer 1.1-3 (aarch64-apple-darwin20) (51.79 kB)
#> ✔ Got labeling 0.4.3 (aarch64-apple-darwin20) (61.83 kB)
#> ✔ Got gtable 0.3.6 (aarch64-apple-darwin20) (225.12 kB)
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#> ✔ Got magrittr 2.0.4 (aarch64-apple-darwin20) (231.97 kB)
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#> ✔ Got TMB 1.9.18 (aarch64-apple-darwin20) (1.47 MB)
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#> ✔ Got cowplot 1.2.0 (aarch64-apple-darwin20) (1.38 MB)
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#> ✔ Got mixsqp 0.3-54 (aarch64-apple-darwin20) (994.47 kB)
#> ✔ Got reshape2 1.4.5 (aarch64-apple-darwin20) (343.07 kB)
#> ✔ Got rlang 1.1.6 (aarch64-apple-darwin20) (1.91 MB)
#> ✔ Got farver 2.1.2 (aarch64-apple-darwin20) (1.97 MB)
#> ✔ Got scales 1.4.0 (aarch64-apple-darwin20) (873.34 kB)
#> ✔ Got stringi 1.8.7 (aarch64-apple-darwin20) (14.79 MB)
#> ✔ Got fashr 0.1.39 (source) (3.07 MB)
#> ✔ Got ggplot2 4.0.1 (aarch64-apple-darwin20) (8.47 MB)
#> ✔ Installed LaplacesDemon 16.1.6 (143ms)
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#> ✔ Installed RColorBrewer 1.1-3 (149ms)
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#> ✔ Installed Rcpp 1.1.0 (213ms)
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#> ✔ Installed isoband 0.2.7 (42ms)
#> ✔ Installed labeling 0.4.3 (40ms)
#> ✔ Installed lifecycle 1.0.4 (40ms)
#> ✔ Installed magrittr 2.0.4 (41ms)
#> ✔ Installed mixsqp 0.3-54 (44ms)
#> ✔ Installed numDeriv 2016.8-1.1 (67ms)
#> ✔ Installed plyr 1.8.9 (43ms)
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#> ✔ Installed viridisLite 0.4.2 (42ms)
#> ✔ Installed withr 3.0.2 (25ms)
#> ℹ Packaging fashr 0.1.39
#> ✔ Packaged fashr 0.1.39 (714ms)
#> ℹ Building fashr 0.1.39
#> ✔ Built fashr 0.1.39 (1m 37.9s)
#> ✔ Installed fashr 0.1.39 (github::stephenslab/fashr@3c3390b) (80ms)
#> ✔ 1 pkg + 30 deps: kept 1, upd 1, added 28, dld 28 (NA B) [1m 51.7s]Example
This is a basic example, which tries to identify non-linear functions in a set of datasets. We use order = 2 to apply the second order IWP, which has a base model S0 being the space of linear functions.
library(fashr)
# Simulate five datasets
set.seed(123)
datasets <- list()
for (i in 1:20) {
n <- 50
t <- seq(0, 5, length.out = n)
sd <- sample(c(2, 1), size = n, replace = TRUE)
u <- runif(1); if (u < 0.5) {f <- function(t) 3*cos(t)} else {f <- function(t) (t)}
y <- f(t) + rnorm(n, sd = 0.5)
datasets[[i]] <- data.frame(t = t, y = y, sd = sd)
}
# Fit the model
fash_fit <- fash(Y = "y", smooth_var = "t", S = "sd", data = datasets,
order = 2, likelihood = "gaussian", verbose = TRUE)
fash_fit
#> Fitted fash Object
#> -------------------
#> Number of datasets: 20
#> Likelihood: gaussian
#> Number of PSD grid values: 25 (initial), 2 (non-trivial)
#> Order of Integrated Wiener Process (IWP): 2Take a look at the structure plot ordered by local false discovery rate:
plot(fash_fit, ordering = "lfdr")
Obtain the posterior summary of the function for the first dataset:
fitted <- predict(fash_fit, index = 1)
str(fitted)
#> 'data.frame': 50 obs. of 5 variables:
#> $ x : num 0 0.102 0.204 0.306 0.408 ...
#> $ mean : num 3.43 3.2 2.98 2.75 2.52 ...
#> $ median: num 3.43 3.2 2.98 2.75 2.53 ...
#> $ lower : num 1.96 1.94 1.89 1.8 1.67 ...
#> $ upper : num 4.88 4.44 4.04 3.68 3.36 ...Obtain the posterior samples of the function:
fitted_samps <- predict(fash_fit, index = 1, only.samples = TRUE, M = 30)
str(fitted_samps)
#> num [1:50, 1:30] 3.36 3.13 2.96 2.78 2.57 ...Visualize the predictions for the first dataset together with the data:
plot(datasets[[1]]$t, datasets[[1]]$y, type = "p", col = "black", ylab = "y", xlab = "t")
lines(fitted$x, fitted$mean, col = "red")
polygon(c(fitted$x, rev(fitted$x)), c(fitted$lower, rev(fitted$upper)), col = rgb(1, 0, 0, 0.2), border = NA)
matlines(fitted$x, fitted_samps[, 1:5], col = "blue", lty = 2, lwd = 0.5)
Compute the FDR, and highlight the datasets with FDR < 0.1:
fdr_result <- fdr_control(fash_fit, alpha = 0.1, plot = TRUE)
#> 5 datasets are significant at alpha level 0.10. Total datasets tested: 20.
fdr_result
#> $fdr_results
#> rank index lfdr FDR
#> Dataset_1 5 1 1.981230e-08 3.988248e-09
#> Dataset_2 18 2 9.794739e-01 7.023167e-01
#> Dataset_3 8 3 9.683893e-01 3.609240e-01
#> Dataset_4 1 4 3.492031e-16 3.492031e-16
#> Dataset_5 11 5 9.719933e-01 5.275334e-01
#> Dataset_6 15 6 9.778700e-01 6.470013e-01
#> Dataset_7 19 7 9.803864e-01 7.169520e-01
#> Dataset_8 17 8 9.788706e-01 6.860134e-01
#> Dataset_9 7 9 9.673522e-01 2.741432e-01
#> Dataset_10 14 10 9.752621e-01 6.233678e-01
#> Dataset_11 13 11 9.748583e-01 5.962990e-01
#> Dataset_12 4 12 1.071022e-10 3.223569e-11
#> Dataset_13 2 13 5.073616e-16 4.282824e-16
#> Dataset_14 10 14 9.719419e-01 4.830874e-01
#> Dataset_15 6 15 9.516504e-01 1.586084e-01
#> Dataset_16 20 16 9.834545e-01 7.302771e-01
#> Dataset_17 3 17 2.183972e-11 7.280192e-12
#> Dataset_18 16 18 9.783377e-01 6.677098e-01
#> Dataset_19 12 19 9.741608e-01 5.647524e-01
#> Dataset_20 9 20 9.715404e-01 4.287703e-01
#>
#> $message
#> [1] "5 datasets are significant at alpha level 0.10. Total datasets tested: 20."
#>
#> $significant_units
#> [1] "Dataset_4" "Dataset_13" "Dataset_17" "Dataset_12" "Dataset_1"