Last updated: 2018-05-24

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```
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    Modified:   analysis/ashpmean.Rmd
    Modified:   analysis/nugget.Rmd
```
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File	Version	Author	Date	Message
Rmd	1abd9ff	Dongyue	2018-05-24	increase n

simu_study_basis=function(mu,nsimu=100,seed=1234,niter=1,robust=F){
  n=length(mu)
  set.seed(seed)
  smash.err=c()
  gen.haar.err=c()
  gen.sym.err=c()
  for(iter in 1:nsimu){
    y=rpois(n,mu)
    smash.out=smash.poiss(y)
    gen.haar.out=smash_gen(y,niter = niter,robust=robust)
    gen.sym.out=smash_gen(y,wave_family = 'DaubLeAsymm',filter.number = 8,niter=niter,robust=robust)
    smash.err[iter]=mse(smash.out,mu)
    gen.haar.err[iter]=mse(gen.haar.out,mu)
    gen.sym.err[iter]=mse(gen.sym.out,mu)
  }
  return(list(est=data.frame(smash=smash.out,smashgen.haar=gen.haar.out,smashgen.sym=gen.sym.out,y=y),err=data.frame(smash=smash.err,smashgen.haar=gen.haar.err,smashgen.sym=gen.sym.err)))
}

HeaviSine

library(smashrgen)
library(ggplot2)
mu=DJ.EX(256,signal = 7)$heavi
mu=(mu-min(mu)+5)*10
range(mu)

[1]  50.0000 285.1265

result=simu_study_basis(mu)
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Doppler

mu=DJ.EX(256,signal = 7)$doppler
mu=(mu-min(mu)+5)*10
range(mu)

[1]  50.0000 292.5644

#plot(mu,type='l')
result=simu_study_basis(mu)
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Parabola

r=function(x,c){return((x-c)^2*(x>c)*(x<=1))}
f=function(x){return(0.8 − 30*r(x,0.1) + 60*r(x, 0.2) − 30*r(x, 0.3) +
500*r(x, 0.35) − 1000*r(x, 0.37) + 1000*r(x, 0.41) − 500*r(x, 0.43) +
7.5*r(x, 0.5) − 15*r(x, 0.7) + 7.5*r(x, 0.9))}
mu=f(1:256/256)
mu=mu*250
range(mu)

[1]  50 200

result=simu_study_basis(mu)
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Step

range of \(\mu\) roughly \((1,6)\).

mu=c(rep(50,64), rep(80, 64), rep(160, 64), rep(50, 64))
result=simu_study_basis(mu)
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Wave

f=function(x){return(0.5 + 0.2*cos(4*pi*x) + 0.1*cos(24*pi*x))}
mu=f(1:256/256)
mu=mu*250
range(mu)

[1]  56.3843 200.0000

result=simu_study_basis(mu)

ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Time shifted sine

g=function(x){return((1 − cos(pi*x))/2)}
f=function(x){return(0.3*sin(3*pi*(g(g(g(g(x)))) + x) + 0.5))}
mu=f(1:256/256)
mu=mu*250+159
range(mu)

[1]  84.00303 233.99963

result=simu_study_basis(mu)

ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

par(mfrow=c(2,2))
plot(result$est$y,col='gray80',main='smash')
lines(result$est$smash,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Haar')
lines(result$est$smashgen.haar,col=4)
lines(mu)

plot(result$est$y,col='gray80',main='smashgen-Symm8')
lines(result$est$smashgen.sym,col=4)
lines(mu)

Session information

sessionInfo()

R version 3.4.0 (2017-04-21)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 16299)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_2.2.1    smashrgen_0.1.0  wavethresh_4.6.8 MASS_7.3-47     
[5] caTools_1.17.1   ashr_2.2-7       smashr_1.1-5    

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16        plyr_1.8.4          compiler_3.4.0     
 [4] git2r_0.21.0        workflowr_1.0.1     R.methodsS3_1.7.1  
 [7] R.utils_2.6.0       bitops_1.0-6        iterators_1.0.8    
[10] tools_3.4.0         digest_0.6.13       tibble_1.3.3       
[13] evaluate_0.10       gtable_0.2.0        lattice_0.20-35    
[16] rlang_0.1.2         Matrix_1.2-9        foreach_1.4.3      
[19] yaml_2.1.19         parallel_3.4.0      stringr_1.3.0      
[22] knitr_1.20          REBayes_1.3         rprojroot_1.3-2    
[25] grid_3.4.0          data.table_1.10.4-3 rmarkdown_1.8      
[28] magrittr_1.5        whisker_0.3-2       backports_1.0.5    
[31] scales_0.4.1        codetools_0.2-15    htmltools_0.3.5    
[34] assertthat_0.2.0    colorspace_1.3-2    labeling_0.3       
[37] stringi_1.1.6       Rmosek_8.0.69       lazyeval_0.2.1     
[40] munsell_0.4.3       doParallel_1.0.11   pscl_1.4.9         
[43] truncnorm_1.0-7     SQUAREM_2017.10-1   R.oo_1.21.0

This reproducible R Markdown analysis was created with workflowr 1.0.1

Poisson seq and wave basis

Dongyue Xie

May 24, 2018