Last updated: 2018-05-21

workflowr checks: (Click a bullet for more information)

  • ✔ R Markdown file: up-to-date

    Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

  • ✔ Environment: empty

    Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

  • ✔ Seed: set.seed(20180501)

    The command set.seed(20180501) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

  • ✔ Session information: recorded

    Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

  • ✔ Repository version: 341aecb

    Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.

    Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: 
    
Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    log/

Untracked files:
    Untracked:  analysis/binom.Rmd
    Untracked:  analysis/overdis.Rmd
    Untracked:  analysis/smashtutorial.Rmd
    Untracked:  analysis/test.Rmd
    Untracked:  data/treas_bill.csv
    Untracked:  docs/figure/smashtutorial.Rmd/
    Untracked:  docs/figure/test.Rmd/

Unstaged changes:
    Modified:   analysis/ashpmean.Rmd
    Modified:   analysis/nugget.Rmd
    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.
Expand here to see past versions:
    File Version Author Date Message
    Rmd 341aecb Dongyue 2018-05-21 poi unknown version revise
    Rmd ca1e50a Dongyue 2018-05-21 edit
    Rmd f7be0e4 Dongyue 2018-05-21 edit
    html 594edf1 Dongyue 2018-05-17 edit
    Rmd f7f7273 Dongyue 2018-05-16 edit
    Rmd fc2c755 Dongyue 2018-05-16 edit
    Rmd 996d337 Dongyue 2018-05-14 poisson data unkown variance

Simulations of Poisson nugget effect(unkown).

Previously, we have studies the methods to estimate unknown \(\sigma\) in the model \(Y_t=\mu_t+N(0,\sigma^2)+N(0,s_t^2)\). Here, we apply mle and smashu methods and compare them with smash as well as smashgen with known \(sigma\). The measure of accuracy is mean square error. Plots are also given as visual aid.

library(smashrgen)
library(ggplot2)
#' Simulation study comparing smash and smashgen

simu_study=function(m,sigma,nsimu=100,seed=12345,
                    niter=1,family='DaubExPhase',ashp=TRUE,verbose=FALSE,robust=FALSE,
                    tol=1e-2,return.x=F,filter.number=1){
  set.seed(seed)
  smash.err=c()
  smashgen.err=c()
  smashgen.smashu.err=c()
  smashgen.mle.err=c()
  x.data=c()
  smashgen.smashu.out=c()
  for(k in 1:nsimu){
    lamda=exp(m+rnorm(length(m),0,sigma))
    x=rpois(length(m),lamda)
    x.data=rbind(x.data,x)
    #fit data
    smash.out=smash.poiss(x)
    smashgen.out=smash_gen(x,dist_family = 'poisson',sigma = sigma,ashp=ashp,robust=robust,niter=niter,verbose = verbose,wave_family = family,filter.number = filter.number)
    smashu.out=smash_gen(x,dist_family = 'poisson',y_var_est = 'smashu',ashp=ashp,robust=robust,niter=niter,verbose = verbose,wave_family = family,filter.number = filter.number)
    smashgen.smashu.out=rbind(smashgen.smashu.out,smashu.out)
    mle.out=smash_gen(x,dist_family = 'poisson',y_var_est = 'mle',
                      ashp=ashp,robust=robust,niter=niter,verbose = verbose,wave_family = family,filter.number = filter.number)
    smash.err[k]=mse(exp(m),smash.out)
    smashgen.err[k]=mse(exp(m),smashgen.out)
    smashgen.smashu.err[k]=mse(exp(m),smashu.out)
    smashgen.mle.err[k]=mse(exp(m),mle.out)
  }
  if(return.x){
    return(list(est=list(smash.out=smash.out,smashgen.out=smashgen.out,smashu.out=smashu.out,mle.out=mle.out,x=x.data,smashgen.smashu.out=smashgen.smashu.out),err=data.frame(smash=smash.err,smashgen=smashgen.err,
              smashgen.smashu=smashgen.smashu.err,smashgen.mle=smashgen.mle.err)))
  }else{
    return(list(est=list(smash.out=smash.out,smashgen.out=smashgen.out,smashu.out=smashu.out,mle.out=mle.out,x=x),err=data.frame(smash=smash.err,smashgen=smashgen.err,
              smashgen.smashu=smashgen.smashu.err,smashgen.mle=smashgen.mle.err)))
  }
  
}

Simulation 1: Constant trend Poisson nugget

\(\sigma=0.1\)

m=rep(1,128)
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-3-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
         0.0318          0.0299          0.0313          0.0299 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Expand here to see past versions of unnamed-chunk-3-2.png:
Version Author Date
594edf1 Dongyue 2018-05-17

\(\sigma=1\)

m=rep(1,128)
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-4-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
        29.7351          0.2339          0.2236          0.2884 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

\(\sigma=2\)

m=rep(1,128)
result=simu_study(m,2)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-5-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
      8372.2699          0.4992          0.5851          0.5626 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Simulation 2: Step trend

\(\sigma=0.1\)

m=c(rep(3,128), rep(5, 128), rep(6, 128), rep(3, 128))
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-6-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
       368.4722         29.2009         31.9006         36.4252 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

\(\sigma=1\)

m=c(rep(3,128), rep(5, 128), rep(6, 128), rep(3, 128))
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-7-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
     223491.625        1658.668        1650.308        1660.029 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Simulation 3: Bumps

\(\sigma=0.1\)

m=seq(0,1,length.out = 256)
h = c(4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2)
w = c(0.005, 0.005, 0.006, 0.01, 0.01, 0.03, 0.01, 0.01, 0.005,0.008,0.005)
t=c(.1,.13,.15,.23,.25,.4,.44,.65,.76,.78,.81)
f = c()
for(i in 1:length(m)){
  f[i]=sum(h*(1+((m[i]-t)/w)^4)^(-1))
}
m=f
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-8-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
        23.2597         35.1707        276.9639         36.6836 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

\(\sigma=1\)

result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-9-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
      6462.4945        480.1025        471.4280        856.6609 
#ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Simulation 4: Doppler

\(\sigma=0.1\)

Small range of \(\mu\)

\(\mu\) in around \((0.1,3.6)\).

m=DJ.EX(256,signal = 1)$doppler
m=log(m-min(m)+0.1)
range(exp(m))
[1] 0.100000 3.565205
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-10-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
         0.2596          0.3996          0.3716          0.4022 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Large range of \(\mu\)

\(\mu\) in around \((0.1,70)\).

m=DJ.EX(256,signal = 20)$doppler
m=log(m-min(m)+0.1)
range(exp(m))
[1]  0.10000 69.40411
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

Expand here to see past versions of unnamed-chunk-11-1.png:
Version Author Date
594edf1 Dongyue 2018-05-17 

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
        26.4471         19.4918         30.7811         20.0644 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

\(\sigma=1\)

Small range of \(\mu\)

\(\mu\) in around \((0.1,3.6)\).

m=DJ.EX(256,signal = 1)$doppler
m=log(m-min(m)+0.1)
range(exp(m))
[1] 0.100000 3.565205
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
   2.053750e+01    2.449446e+06    4.712080e+05    1.169379e+07 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Large range of \(\mu\)

\(\mu\) in around \((0.1,70)\).

m=DJ.EX(256,signal = 20)$doppler
m=log(m-min(m)+0.1)
range(exp(m))
[1]  0.10000 69.40411
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
      9545.5716        131.5410        138.5879        132.0084 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Simulation 5: Spike mean

\(\sigma=0.1\)

Small range of \(\mu\)

\(\mu\) in around \((0.1,6)\).

spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
n = 256
t = 1:n/n
m = spike.f(t)

m=m*2+0.1
m=log(m)
range(exp(m))
[1] 0.100000 6.025467
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
          0.173    28345959.626      426017.822    28731128.430 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Large range of \(\mu\)

\(\mu\) in around \((0.1,60)\).

spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
n = 256
t = 1:n/n
m = spike.f(t)

m=m*20+0.1
m=log(m)
range(exp(m))
[1]  0.10000 59.35467
result=simu_study(m,0.1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
         3.3231         22.6070          7.3361         26.9417 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

\(\sigma=1\)

Small range of \(\mu\)

\(\mu\) in around \((0.1,6)\).

spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
n = 256
t = 1:n/n
m = spike.f(t)

m=m*2+0.1
m=log(m)
range(exp(m))
[1] 0.100000 6.025467
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
   4.853800e+00    1.250056e+31    4.210894e+29    1.563109e+31 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

Large range of \(\mu\)

\(\mu\) in around \((0.1,60)\).

spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
n = 256
t = 1:n/n
m = spike.f(t)

m=m*20+0.1
m=log(m)
range(exp(m))
[1]  0.10000 59.35467
result=simu_study(m,1)
par(mfrow=c(2,2))
plot(result$est$x,col='gray80',ylab='',main='smash')
lines(exp(m),col=1)
lines(result$est$smash.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: known sigma')
lines(exp(m),col=1)
lines(result$est$smashgen.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: (sigma^2+s_t^2) from smash')
lines(exp(m),col=1)
lines(result$est$smashu.out,col=4)
plot(result$est$x,col='gray80',ylab='',main='smashgen: sigma from mle')
lines(exp(m),col=1)
lines(result$est$mle.out,col=4)

round(apply(result$err,2,mean),4)
          smash        smashgen smashgen.smashu    smashgen.mle 
       704.7864         32.2910         48.5103       1280.0942 
ggplot(df2gg(result$err),aes(x=method,y=MSE))+geom_boxplot(aes(fill=method))+labs(x='')

The performance of smashgen is worse than smash.pois for spike mean, especialy when the range of \(\mu\) is small. Smashgen cannot capture the spikes properly which results in huge squared errors. The smash.pois could capture the spikes and it gives noisy fit for the low mean area so it’s MSE is much smaller. Let’s figure out the reason.

One possible reason that causes the issue is that smashgen gives very large fit to the spikes.

Plots of smashgen smoothed wavelets. Blue curves are from smashgen and the black ones are truth.

spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
n = 256
t = 1:n/n
m = spike.f(t)

m=m*2+0.1
m=log(m)

result=simu_study(m,1,nsimu = 6,return.x = T)
par(mfrow=c(3,2))
plot(result$est$x[1,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[1,],col=4)

plot(result$est$x[2,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[2,],col=4)

plot(result$est$x[3,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[3,],col=4)

plot(result$est$x[4,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[4,],col=4)

plot(result$est$x[5,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[5,],col=4)

plot(result$est$x[6,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[6,],col=4)

Larger range of \(\mu\).

m = spike.f(t)

m=m*20+0.1
m=log(m)

result=simu_study(m,1,nsimu = 6,return.x = T)
par(mfrow=c(3,2))
plot(result$est$x[1,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[1,],col=4)

plot(result$est$x[2,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[2,],col=4)

plot(result$est$x[3,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[3,],col=4)

plot(result$est$x[4,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[4,],col=4)

plot(result$est$x[5,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[5,],col=4)

plot(result$est$x[6,],col='gray80')
lines(exp(m),col='gray30')
lines(result$est$smashgen.smashu.out[6,],col=4)

See here for a saperate analysis on this issue.

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