Motorcycle Acceleration example

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 ashr and smashr packages from GitHub:

library(devtools)
install_github("stephens999/ashr",upgrade_dependencies = FALSE)
install_github("stephenslab/smashr",upgrade_dependencies = FALSE)

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 functions.motorcycle.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")

Apply SMASH again, this time assuming equal variances

Apply SMASH (assuming equal variances) to the Motorcycle Accident data set.

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

Apply TI thresholding to the Motorcycle Accident data

Apply TI thresholding to the Motorcycle Accident data set.

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 by SMASH.

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

Compare results from all methods

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")

And in this next plot, we compare the SMASH estimates (the orange line) against the the mean estimates obtained by TI thresholding (dark 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.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")

The TI thresholding estimate and the SMASH estimate with homoskedastic variances both show notable artifacts. When the TI thresholding method is provided with the SMASH variance estimate, the mean signal is substantially smoother.

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 10.13.6
# 
# 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_1.4-12 wavethresh_4.6.8    smashr_1.2-0       
# [4] lattice_0.20-35     MASS_7.3-48        
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_0.12.19      knitr_1.20        whisker_0.3-2    
#  [4] magrittr_1.5      workflowr_1.1.1   REBayes_1.3      
#  [7] pscl_1.5.2        doParallel_1.0.11 SQUAREM_2017.10-1
# [10] foreach_1.4.4     ashr_2.2-23       stringr_1.3.1    
# [13] caTools_1.17.1    tools_3.4.3       parallel_3.4.3   
# [16] grid_3.4.3        data.table_1.11.4 R.oo_1.21.0      
# [19] git2r_0.23.0      iterators_1.0.9   htmltools_0.3.6  
# [22] assertthat_0.2.0  yaml_2.2.0        rprojroot_1.3-2  
# [25] digest_0.6.17     Matrix_1.2-12     bitops_1.0-6     
# [28] codetools_0.2-15  R.utils_2.6.0     evaluate_0.11    
# [31] rmarkdown_1.10    stringi_1.2.4     compiler_3.4.3   
# [34] Rmosek_8.0.69     backports_1.1.2   R.methodsS3_1.7.1
# [37] truncnorm_1.0-8