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<h1 class="title toc-ignore">Motorcycle Acceleration example</h1>
<h4 class="author"><em>Zhengrong Xing, Peter Carbonetto and Matthew Stephens</em></h4>
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<p><strong>Last updated:</strong> 2018-10-10</p>
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<pre><code>
Ignored files:
Ignored: dsc/code/Wavelab850/MEXSource/CPAnalysis.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/DownDyadHi.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/DownDyadLo.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FAIPT.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FCPSynthesis.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FMIPT.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FWPSynthesis.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FWT2_PO.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FWT_PBS.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FWT_PO.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/FWT_TI.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IAIPT.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IMIPT.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IWT2_PO.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IWT_PBS.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IWT_PO.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/IWT_TI.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/LMIRefineSeq.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/MedRefineSeq.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/UpDyadHi.mexmac
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Ignored: dsc/code/Wavelab850/MEXSource/WPAnalysis.mexmac
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Ignored: dsc/code/Wavelab850/MEXSource/dst_ii.mexmac
Ignored: dsc/code/Wavelab850/MEXSource/dst_iii.mexmac
</code></pre>
Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes. </details>
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Rmd
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<a href="https://github.com/stephenslab/smash-paper/blob/7f2ef79eee1a716d35dab617abe74a0ae83d9e2e/analysis/motorcycle.Rmd" target="_blank">7f2ef79</a>
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Peter Carbonetto
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2018-10-10
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wflow_publish(“motorcycle.Rmd”)
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Rmd
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<a href="https://github.com/stephenslab/smash-paper/blob/3b3d3738cde2fbcb3a271a51afc80a3e34fda0a7/analysis/motorcycle.Rmd" target="_blank">3b3d373</a>
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<td style="text-align:left;">
Peter Carbonetto
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<td style="text-align:left;">
2018-10-09
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<td style="text-align:left;">
Some more improvements to the motorcycle example.
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Rmd
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<a href="https://github.com/stephenslab/smash-paper/blob/757462cb31ff4d9419459f78d6abbee39d65ab6f/analysis/motorcycle.Rmd" target="_blank">757462c</a>
</td>
<td style="text-align:left;">
Peter Carbonetto
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2018-10-09
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Working on motorcycle .Rmd example.
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<p></details></p>
<hr />
<p>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.</p>
<div id="set-up-environment" class="section level2">
<h2>Set up environment</h2>
<p>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 <code>functions.motorcycle.R</code>.</p>
<pre class="r"><code>library(MASS)
library(lattice)
library(smashr)
library(scales)
library(wavethresh)
library(EbayesThresh)
source("../code/motorcycle.functions.R")</code></pre>
</div>
<div id="prepare-data-for-smash" class="section level2">
<h2>Prepare data for SMASH</h2>
<p>Load the motorcycle data from the MASS package, and order the data points by time.</p>
<pre class="r"><code>data(mcycle)
x.ini.mc <- sort(mcycle$times)
y.ini.mc <- mcycle$accel[order(mcycle$times)]</code></pre>
</div>
<div id="run-smash" class="section level2">
<h2>Run SMASH</h2>
<p>Apply SMASH to the Motorcycle Accident data set.</p>
<pre class="r"><code>res.mc <- smash.wrapper(x.ini.mc,y.ini.mc)</code></pre>
</div>
<div id="summarize-results-of-smash-analysis" class="section level2">
<h2>Summarize results of SMASH analysis</h2>
<p>Create a plot showing the Motorcycle Accident data and the smash estimates (with the dashed red lines showing the confidence intervals).</p>
<pre class="r"><code>plot(res.mc$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$y,pch = 1,cex = 1,col = "black")</code></pre>
<p><img src="figure/motorcycle.Rmd/plot-smash-estimates-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="apply-smash-again-this-time-assuming-equal-variances" class="section level2">
<h2>Apply SMASH again, this time assuming equal variances</h2>
<p>Apply SMASH (assuming with equal variances) to the Motorcycle Accident data set.</p>
<pre class="r"><code>res.cons.mc <- smash.cons.wrapper(x.ini.mc,y.ini.mc)</code></pre>
</div>
<div id="apply-ti-thresholding-to-the-motorcycle-accident-data" class="section level2">
<h2>Apply TI thresholding to the Motorcycle Accident data</h2>
<p>Apply TI thresholding to the Motorcycle Accident data set.</p>
<pre class="r"><code>res.ti.cons.mc <- tithresh.cons.wrapper(x.ini.mc,y.ini.mc)</code></pre>
<p>Apply TI thresholding to the Motorcycle Accident data, this time using the variances estimated by SMASH.</p>
<pre class="r"><code>res.ti.mc <- tithresh.wrapper(x.ini.mc,y.ini.mc)</code></pre>
</div>
<div id="compare-results-from-all-methods" class="section level2">
<h2>Compare results from all methods</h2>
<p>In this second plot, we compare the mean estimate provided by SMASH (with heteroskedastic variances; orange line) against homoskedastic SMASH (dotted magenta line), TI thresholding (dark blue line), and TI thresholding when the variances have been estimated by SMASH (dotted green line).</p>
<pre class="r"><code>plot(res.mc$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")</code></pre>
<p><img src="figure/motorcycle.Rmd/plot-all-estimates-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>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</code></pre>
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