Motorcycle Acceleration example

Set up environment

Load the MASS, scales, 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(scales)
library(wavethresh)
library(EbayesThresh)
source("../code/motorcycle.functions.R")

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 with 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 magenta line), 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.cons.mc$x,res.cons.mc$mu.est,lwd = 2,lty = "dotted",col = "magenta")
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")

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_1.3.2 wavethresh_4.6.8   scales_0.5.0      
# [4] smashr_1.2-0       lattice_0.20-35    MASS_7.3-48       
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_0.12.19      compiler_3.4.3    git2r_0.23.0     
#  [4] plyr_1.8.4        workflowr_1.1.1   R.methodsS3_1.7.1
#  [7] R.utils_2.6.0     bitops_1.0-6      iterators_1.0.9  
# [10] tools_3.4.3       digest_0.6.17     evaluate_0.11    
# [13] Matrix_1.2-12     foreach_1.4.4     yaml_2.2.0       
# [16] parallel_3.4.3    stringr_1.3.1     knitr_1.20       
# [19] REBayes_1.3       caTools_1.17.1    rprojroot_1.3-2  
# [22] grid_3.4.3        data.table_1.11.4 rmarkdown_1.10   
# [25] ashr_2.2-15       magrittr_1.5      whisker_0.3-2    
# [28] backports_1.1.2   codetools_0.2-15  htmltools_0.3.6  
# [31] assertthat_0.2.0  colorspace_1.4-0  stringi_1.2.4    
# [34] Rmosek_8.0.69     doParallel_1.0.11 pscl_1.5.2       
# [37] munsell_0.4.3     truncnorm_1.0-8   SQUAREM_2017.10-1
# [40] R.oo_1.21.0