Last updated: 2019-12-18

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File Version Author Date Message
Rmd c76fbf7 Peter Carbonetto 2019-12-18 wflow_publish(“motorcycle.Rmd”)
Rmd 35a397a Peter Carbonetto 2019-11-12 Simplifying some of the code in poisson.Rmd.
Rmd 500381a Zhengrong Xing 2019-10-28 move gausdemo; add HF for chipseq
html 500381a Zhengrong Xing 2019-10-28 move gausdemo; add HF for chipseq
html f0221c5 Zhengrong Xing 2019-10-28 address some reviewer comments
html 99d1f34 Peter Carbonetto 2018-12-07 Re-built all the outdated workflowr webpages.
Rmd a09d13e Peter Carbonetto 2018-11-09 Adjusted setup steps in a few of the R Markdown files.
Rmd f9f193c Peter Carbonetto 2018-11-07 Revised setup instructions for a couple .Rmd files.
html 85368eb Peter Carbonetto 2018-11-06 A few final adjustments to the motorcycle example.
Rmd 3b7071b Peter Carbonetto 2018-11-06 wflow_publish(“motorcycle.Rmd”)
html 3ce045f Peter Carbonetto 2018-11-06 Added explanatory text to motorcycle example.
Rmd 4a73ed9 Peter Carbonetto 2018-11-06 wflow_publish(“motorcycle.Rmd”)
html d51e8f8 Peter Carbonetto 2018-11-06 Adjusted the plots in the motorcycle example.
Rmd fd51be8 Peter Carbonetto 2018-11-06 wflow_publish(“motorcycle.Rmd”)
html fdc9c33 Peter Carbonetto 2018-11-06 Build site.
Rmd 1ab1447 Peter Carbonetto 2018-11-06 wflow_publish(“motorcycle.Rmd”)
html 7d7ce92 Peter Carbonetto 2018-11-06 Added setup instructions to motorcycle example.
Rmd f0059b3 Peter Carbonetto 2018-11-06 wflow_publish(“motorcycle.Rmd”)
Rmd 507a261 Peter Carbonetto 2018-11-06 Having trouble re-building spikesdemo.html.
html f6a9477 Peter Carbonetto 2018-10-10 Completed revisions of motorcycle example.
Rmd 7f2ef79 Peter Carbonetto 2018-10-10 wflow_publish(“motorcycle.Rmd”)
Rmd 3b3d373 Peter Carbonetto 2018-10-09 Some more improvements to the motorcycle example.
Rmd 757462c Peter Carbonetto 2018-10-09 Working on motorcycle .Rmd example.

This is an illustration of “smoothing via adaptive shrinkage” (SMASH) applied to the Motorcycle Accident data. This implements the “illustrative application” presented in Sec. 5.1 of the manuscript.

Initial setup instructions

To run this example on your own computer, please follow these setup instructions. These instructions assume you already have R and/or RStudio installed on your computer.

Download or clone the git repository on your computer.

Launch R, and change the working directory to be the “analysis” folder inside your local copy of the git repository.

Install the devtools, wavethresh and EbayesThresh packages used here and in the code below:

install.packages(c("devtools","wavethresh","EbayesThresh"))

Finally, install the smashr package from GitHub:

devtools::install_github("stephenslab/smashr")

See the “Session Info” at the bottom for the versions of the software and R packages that were used to generate the results shown below.

Set up R environment

Load the MASS, lattice wavethresh, EbayesThresh and smashr packages. The MASS package is loaded only for the Motorcycle Accident data. Some additional functions are defined in file motorcycle.functions.R.

library(MASS)
library(lattice)
library(smashr)
library(wavethresh)
library(EbayesThresh)
source("../code/motorcycle.functions.R")

Note that the MASS and lattice packages are included in most standard R installations, so you probably don’t need to install these packages separately.

Prepare data for SMASH

Load the motorcycle data from the MASS package, and order the data points by time.

data(mcycle)
x.ini.mc <- sort(mcycle$times)
y.ini.mc <- mcycle$accel[order(mcycle$times)]

Run SMASH

Apply SMASH to the Motorcycle Accident data set.

res.mc <- smash.wrapper(x.ini.mc,y.ini.mc)

Summarize results of SMASH analysis

Create a plot showing the Motorcycle Accident data and the smash estimates (with the dashed red lines showing the confidence intervals).

plot(res.mc$x,res.mc$mu.est,type = "l",
     ylim = c(min(res.mc$y - 2 * sqrt(res.mc$var.est)),
              max(res.mc$y + 2 * sqrt(res.mc$var.est))),
     xlab = "time (ms)", ylab = "acceleration (g)",lwd = 2,
     col = "darkorange",xlim = c(0,60),xaxp = c(0,60,6))
lines(res.mc$x, res.mc$mu.est + 2*sqrt(res.mc$var.est),lty = 5,
     lwd = 2,col = "dodgerblue")
lines(res.mc$x,res.mc$mu.est - 2*sqrt(res.mc$var.est),
      lty = 5,lwd = 2,col = "dodgerblue")
points(res.mc$x,res.mc$y,pch = 1,cex = 1,col = "black")

Version Author Date
f0221c5 Zhengrong Xing 2019-10-28
f6a9477 Peter Carbonetto 2018-10-10

SMASH, homoskedastic vs. heteroskedastic

Apply SMASH, this time assuming equal variances, to the Motorcycle Accident data set:

res.cons.mc <- smash.cons.wrapper(x.ini.mc,y.ini.mc)

In this second plot, we compare the mean estimate provided by SMASH (with heteroskedastic variances; orange line) against homoskedastic SMASH (dotted, light blue line).

plot(res.mc$x,res.mc$mu.est,type = "l",
     ylim = c(min(res.mc$y - 2 * sqrt(res.mc$var.est)),
              max(res.mc$y + 2 * sqrt(res.mc$var.est))),
     xlab = "time (ms)",ylab = "acceleration (g)",lwd = 2,
     col = "darkorange",xlim = c(0,60),xaxp = c(0,60,6))
lines(res.cons.mc$x,res.cons.mc$mu.est,lwd = 2,lty = "dotted",
      col = "dodgerblue")
points(res.mc$x,res.mc$y,pch = 1,cex = 0.8,col = "black")

Version Author Date
f0221c5 Zhengrong Xing 2019-10-28
3ce045f Peter Carbonetto 2018-11-06
d51e8f8 Peter Carbonetto 2018-11-06

While the estimates are similar, heteroskedastic SMASH yields a noticeably smoother curve.

Apply TI thresholding to the Motorcycle Accident data

Apply TI thresholding to the Motorcycle Accident data set. In this first run, the variance is assumed to be constant.

res.ti.cons.mc <- tithresh.cons.wrapper(x.ini.mc,y.ini.mc)

Apply TI thresholding to the Motorcycle Accident data, this time using the variances estimated using the “median absolute deviation”, or RMAD, method.

res.ti.rmad.mc <- tithresh.rmad.wrapper(x.ini.mc,y.ini.mc)

Apply TI thresholding to the Motorcycle Accident data, this time using the variances estimated by SMASH.

res.ti.mc <- tithresh.wrapper(x.ini.mc,y.ini.mc)

Compare SMASH vs. TI thresholding

In this next plot, we compare the SMASH estimates with heteroskedastic variances (the same orange line as above) against the the mean estimates obtained by TI thresholding with constant variance (solid dark blue line), TI thresholding with RMAD variance estimates (solid light blue line), and TI thresholding when the variances have been estimated by SMASH (dotted green line).

plot(res.mc$x,res.mc$mu.est,type = "l",
     ylim = c(min(res.mc$y - 2 * sqrt(res.mc$var.est)),
              max(res.mc$y + 2 * sqrt(res.mc$var.est))),
     xlab = "time (ms)",ylab = "acceleration (g)",lwd = 2,
     col = "darkorange",xlim = c(0,60),xaxp = c(0,60,6))
lines(res.ti.cons.mc$x,res.ti.cons.mc$mu.est,lwd = 2,lty = "solid",
     col = "darkblue")
lines(res.ti.rmad.mc$x,res.ti.rmad.mc$mu.est,lwd = 2,lty = "solid",
      col = "dodgerblue")
lines(res.ti.mc$x,res.ti.mc$mu.est,lwd = 2,col = "limegreen",lty = "dotted")
points(res.mc$x,res.mc$y,pch = 1,cex = 0.8,col = "black")

Version Author Date
f0221c5 Zhengrong Xing 2019-10-28
d51e8f8 Peter Carbonetto 2018-11-06

The TI thresholding estimate, like the SMASH estimate with homoskedastic variances, shows notable artifacts. When TI thresholding estimates the variance using RMAD, or when it is provided with the SMASH variance estimate, the mean signal is substantially smoother.


sessionInfo()
# R version 3.4.3 (2017-11-30)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS High Sierra 10.13.6
# 
# 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] EbayesThresh_1.4-13 wavethresh_4.6.8    smashr_1.2-5       
# [4] lattice_0.20-35     MASS_7.3-48        
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.1           compiler_3.4.3       later_0.8.0         
#  [4] git2r_0.26.1         workflowr_1.5.0.9000 bitops_1.0-6        
#  [7] iterators_1.0.10     tools_3.4.3          digest_0.6.18       
# [10] evaluate_0.13        Matrix_1.2-12        foreach_1.4.4       
# [13] yaml_2.2.0           parallel_3.4.3       xfun_0.7            
# [16] stringr_1.4.0        knitr_1.23           fs_1.2.7            
# [19] caTools_1.17.1.2     rprojroot_1.3-2      grid_3.4.3          
# [22] glue_1.3.1           data.table_1.12.0    R6_2.4.0            
# [25] rmarkdown_1.17       mixsqp_0.3-6         ashr_2.2-39         
# [28] magrittr_1.5         whisker_0.3-2        backports_1.1.2     
# [31] promises_1.0.1       codetools_0.2-15     htmltools_0.3.6     
# [34] httpuv_1.5.0         stringi_1.4.3        doParallel_1.0.14   
# [37] pscl_1.5.2           truncnorm_1.0-8      SQUAREM_2017.10-1