Plots and tables summarizing results of Poisson simulations

Last updated: 2018-12-21

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    Modified:   analysis/index.Rmd

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File	Version	Author	Date	Message
Rmd	7db6b71	Peter Carbonetto	2018-12-21	wflow_publish(“poisson.Rmd”)
Rmd	e8bc009	Peter Carbonetto	2018-12-21	wflow_publish(“poisson.Rmd”)
html	5adee34	Peter Carbonetto	2018-12-21	Addd plots and table for Bursts simulations.
Rmd	3776af8	Peter Carbonetto	2018-12-21	wflow_publish(“poisson.Rmd”)
html	c333197	Peter Carbonetto	2018-12-21	A few small revsions to the code at the beginning of poisson.Rmd.
Rmd	b42715c	Peter Carbonetto	2018-12-21	wflow_publish(“poisson.Rmd”)
html	bd84eae	Peter Carbonetto	2018-12-20	Build site.
Rmd	51620b3	Peter Carbonetto	2018-12-20	wflow_publish(“poisson.Rmd”)
html	bda4fbc	Peter Carbonetto	2018-12-20	Wrote function create.violin.plots in poisson.Rmd.
html	ed961b1	Peter Carbonetto	2018-12-20	Added violin plots for the Spikes and Angles Poisson simulation results.
Rmd	68ce493	Peter Carbonetto	2018-12-20	wflow_publish(“poisson.Rmd”)
html	2acee22	Peter Carbonetto	2018-12-20	Added plots for all test functions.
Rmd	987a861	Peter Carbonetto	2018-12-20	wflow_publish(“poisson.Rmd”)
Rmd	b3f5b57	Peter Carbonetto	2018-12-20	wflow_publish(“poisson.Rmd”)
Rmd	d36bfca	Peter Carbonetto	2018-12-20	Misc. revisions to READMEs and documentation.
Rmd	7aa0b11	Peter Carbonetto	2018-12-20	Working on poisson analysis.
Rmd	3c562ea	Peter Carbonetto	2018-12-19	Moved poisson_tables.Rmd to poisson.Rmd.
Rmd	25ff9c3	Peter Carbonetto	2018-12-19	Re-organized some of the files used in the Poisson numerical comparisons.

Here we create plots and tables to compare various methods, including SMASH, for reconstructing a spatially structured signal from Poisson-distributed data. Similar to the Gaussian simulations, we generated data sets using a variety of test functions and intensity ranges. Specifically, we considered 6 test functions, rescaling the test function so that the smallest intensity was x and the largest intensity was y, with (x,y) set to either (1/100, 3), (1/8, 8) or (1/128, 128). For each combination of test function and intensity range, we simulated 100 data sets. In the plots and tables below, we summarize the error (MISE) in the estimates computed in the 100 data sets from each simulation setting.

The plots for the “Bursts” simulations were included in the manuscript.

Analysis settings

We will extract the results from these methods:

methods <- c("ash","BMSM","haarfisz_R")

These variables specify the row and column names for the tables:

table.row.names <- c("SMASH","BMSM","Haar-Fisz")
table.col.names <- c("(1/100,3)","(1/8,8)","(1/128,128)")

These are settings used in plotting the test functions:

n <- 1024
t <- 1:n/n

Set up environment

Load the ggplot2 cowplot and xtable packages.

library(ggplot2)
library(cowplot)
library(xtable)

Some of the test functions are defined in signals.R, so we load them here:

source("../code/signals.R")

Load results

Load the results of the simulation experiments.

load("../output/pois.RData")

Spikes data

This is the function used to simulate the “Spikes” data sets at different ranges of intensities:

mu.s <- spike.f(t)
plot(t,mu.s,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-spikes-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Spikes simulations:

mise.s.table <- cbind(mise.s.1[methods],
                      mise.s.8[methods],
                      mise.s.128[methods])
rownames(mise.s.table) <- table.row.names
colnames(mise.s.table) <- table.col.names
print(xtable(mise.s.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	690.01	329.26	48.87
BMSM	1007.34	397.79	41.88
Haar-Fisz	722.19	287.44	18.06

Each column shows the results at a different range of intensities. The individual table entries give the average error (MISE) in the estimates, in which the average is taken over the 100 data sets simulated at the given range of intensities.

The combined violin-boxplots provide a visualization of the same results:

m                  <- length(mise.ash.s.1)
method.labels      <- c("Haar-Fisz","BMSM","SMASH")
mise.hf.ti.r.s.1   <- colMeans(rbind(mise.hf.ti.r.4.s.1,
                                     mise.hf.ti.r.5.s.1,
                                     mise.hf.ti.r.6.s.1,
                                     mise.hf.ti.r.7.s.1))
mise.hf.ti.r.s.8   <- colMeans(rbind(mise.hf.ti.r.4.s.8,
                                     mise.hf.ti.r.5.s.8,
                                     mise.hf.ti.r.6.s.8,
                                     mise.hf.ti.r.7.s.8))
mise.hf.ti.r.s.128 <- colMeans(rbind(mise.hf.ti.r.4.s.128,
                                     mise.hf.ti.r.5.s.128,
                                     mise.hf.ti.r.6.s.128,
                                     mise.hf.ti.r.7.s.128))
pdat1 <- data.frame(method = factor(rep(method.labels,each = m),method.labels),
                    mise   = c(mise.hf.ti.r.s.1,mise.BMSM.s.1,mise.ash.s.1))
pdat8 <- data.frame(method = factor(rep(method.labels,each = m),method.labels),
                    mise   = c(mise.hf.ti.r.s.8,mise.BMSM.s.8,mise.ash.s.8))
pdat128 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.s.128,mise.BMSM.s.128,mise.ash.s.128))
create.violin.plots <- function (pdat1, pdat8, pdat128) {
  p1 <- ggplot(pdat1,aes(x = method,y = mise)) +
        geom_violin(fill = "skyblue",color = "skyblue") +
        geom_boxplot(width = 0.15,outlier.shape = NA) +
        coord_flip() +
        labs(x = "",y = "MISE",title = "intensities (1/100,3)") +
        theme(axis.line = element_blank())
  p8 <- ggplot(pdat8,aes(x = method,y = mise)) +
        geom_violin(fill = "skyblue",color = "skyblue") +
        geom_boxplot(width = 0.15,outlier.shape = NA) +
        scale_x_discrete(breaks = NULL) +
        coord_flip() +
        labs(x = "",y = "MISE",title = "intensities (1/8,8)") +
        theme(axis.line = element_blank())
  p128 <- ggplot(pdat128,aes(x = method,y = mise)) +
        geom_violin(fill = "skyblue",color = "skyblue") +
        geom_boxplot(width = 0.15,outlier.shape = NA) +
        scale_x_discrete(breaks = NULL) +
        coord_flip() +
        labs(x = "",y = "MISE",title = "intensities (1/128,128)") +
        theme(axis.line = element_blank())
  return(plot_grid(p1,p8,p128,nrow = 1,ncol = 3))
}
create.violin.plots(pdat1,pdat8,pdat128)

Expand here to see past versions of spikes-violin-plots-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20

Angles data

This is the function used to simulate the “Angles” data sets at different ranges of intensities:

mu.ang <- dop.f(t)
sig <- ((2 * t + 0.5) * (t <= 0.15)) +
  ((-12 * (t - 0.15) + 0.8) * (t > 0.15 & t <= 0.2)) +
  0.2 * (t > 0.2 & t <= 0.5) + 
  ((6 * (t - 0.5) + 0.2) * (t > 0.5 & t <= 0.6)) +
  ((-10 * (t - 0.6) + 0.8) * (t > 0.6 & t <= 0.65)) +
  ((-0.5 * (t - 0.65) + 0.3) * (t > 0.65 & t <= 0.85)) +
  ((2 * (t - 0.85) + 0.2) * (t > 0.85))
mu.ang <- 3/5 * ((5/(max(sig) - min(sig))) * sig - 1.6) - 0.0419569
plot(t,mu.ang,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-angles-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Angles simulations:

mise.ang.table <- cbind(mise.ang.1[methods],
                        mise.ang.8[methods],
                        mise.ang.128[methods])
rownames(mise.ang.table) <- table.row.names
colnames(mise.ang.table) <- table.col.names
print(xtable(mise.ang.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	145.26	68.47	10.25
BMSM	147.40	73.87	10.49
Haar-Fisz	314.41	122.79	9.08

The combined violin-boxplots provide a visualization of the same results:

mise.hf.ti.r.ang.1   <- colMeans(rbind(mise.hf.ti.r.4.ang.1,
                                       mise.hf.ti.r.5.ang.1,
                                       mise.hf.ti.r.6.ang.1,
                                       mise.hf.ti.r.7.ang.1))
mise.hf.ti.r.ang.8   <- colMeans(rbind(mise.hf.ti.r.4.ang.8,
                                       mise.hf.ti.r.5.ang.8,
                                       mise.hf.ti.r.6.ang.8,
                                       mise.hf.ti.r.7.ang.8))
mise.hf.ti.r.ang.128 <- colMeans(rbind(mise.hf.ti.r.4.ang.128,
                                       mise.hf.ti.r.5.ang.128,
                                       mise.hf.ti.r.6.ang.128,
                                       mise.hf.ti.r.7.ang.128))
pdat1 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.ang.1,mise.BMSM.ang.1,mise.ash.ang.1))
pdat8 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.ang.8,mise.BMSM.ang.8,mise.ash.ang.8))
pdat128 <-
  data.frame(method=factor(rep(method.labels,each = m),method.labels),
             mise  =c(mise.hf.ti.r.ang.128,mise.BMSM.ang.128,mise.ash.ang.128))
create.violin.plots(pdat1,pdat8,pdat128)

Expand here to see past versions of angles-violin-plots-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20

Heavisine data

This is the function used to simulate the “Heavisine” data sets at different ranges of intensities:

heavi <- 4 * sin(4 * pi * t) - sign(t - 0.3) - sign(0.72 - t)
mu.hs <- heavi/sqrt(var(heavi)) * 1 * 2.99/3.366185
mu.hs <- mu.hs - min(mu.hs)
plot(t,mu.hs,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-heavisine-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Heavisine simulations:

mise.hs.table <- cbind(mise.hs.1[methods],
                       mise.hs.8[methods],
                       mise.hs.128[methods])
rownames(mise.hs.table) <- table.row.names
colnames(mise.hs.table) <- table.col.names
print(xtable(mise.hs.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	81.41	43.21	7.21
BMSM	85.29	44.22	7.35
Haar-Fisz	274.26	105.47	9.23

Each column shows results at a different range of intensities. The individual table entries give the average error (MISE) in the estimates, in which the average is taken over the 100 data sets simulated at the given range of intensities.

The combined violin-boxplots provide a visualization of the same results:

mise.hf.ti.r.hs.1   <- colMeans(rbind(mise.hf.ti.r.4.hs.1,
                                      mise.hf.ti.r.5.hs.1,
                                      mise.hf.ti.r.6.hs.1,
                                      mise.hf.ti.r.7.hs.1))
mise.hf.ti.r.hs.8   <- colMeans(rbind(mise.hf.ti.r.4.hs.8,
                                      mise.hf.ti.r.5.hs.8,
                                      mise.hf.ti.r.6.hs.8,
                                      mise.hf.ti.r.7.hs.8))
mise.hf.ti.r.hs.128 <- colMeans(rbind(mise.hf.ti.r.4.hs.128,
                                      mise.hf.ti.r.5.hs.128,
                                      mise.hf.ti.r.6.hs.128,
                                      mise.hf.ti.r.7.hs.128))
pdat1 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.hs.1,mise.BMSM.hs.1,mise.ash.hs.1))
pdat8 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.hs.8,mise.BMSM.hs.8,mise.ash.hs.8))
pdat128 <-
  data.frame(method=factor(rep(method.labels,each = m),method.labels),
             mise  =c(mise.hf.ti.r.hs.128,mise.BMSM.hs.128,mise.ash.hs.128))
create.violin.plots(pdat1,pdat8,pdat128)

Expand here to see past versions of heavisine-violin-plots-1.png:

Version	Author	Date
bd84eae	Peter Carbonetto	2018-12-20

Bursts data

This is the function used to simulate the “Bursts” data sets at different ranges of intensities:

I_1 <- exp(-(abs(t - 0.2)/0.01)^1.2) * (t <= 0.2) +
       exp(-(abs(t - 0.2)/0.03)^1.2) * (t > 0.2)
I_2 <- exp(-(abs(t - 0.3)/0.01)^1.2) * (t <= 0.3) +
       exp(-(abs(t - 0.3)/0.03)^1.2) * (t > 0.3)
I_3 <- exp(-(abs(t - 0.4)/0.01)^1.2) * (t <= 0.4) +
       exp(-(abs(t - 0.4)/0.03)^1.2) * (t > 0.4)
mu.bur <- 2.99/4.51804 * (4 * I_1 + 3 * I_2 + 4.5 * I_3)
plot(t,mu.bur,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-bursts-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Bursts simulations:

mise.bur.table <- cbind(mise.bur.1[methods],
                        mise.bur.8[methods],
                        mise.bur.128[methods])
rownames(mise.bur.table) <- table.row.names
colnames(mise.bur.table) <- table.col.names
print(xtable(mise.bur.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	487.34	234.35	33.11
BMSM	706.04	301.86	34.42
Haar-Fisz	618.39	299.39	25.20

The combined violin-boxplots provide a visualization of the same results:

mise.hf.ti.r.bur.1   <- colMeans(rbind(mise.hf.ti.r.4.bur.1,
                                       mise.hf.ti.r.5.bur.1,
                                       mise.hf.ti.r.6.bur.1,
                                       mise.hf.ti.r.7.bur.1))
mise.hf.ti.r.bur.8   <- colMeans(rbind(mise.hf.ti.r.4.bur.8,
                                       mise.hf.ti.r.5.bur.8,
                                       mise.hf.ti.r.6.bur.8,
                                       mise.hf.ti.r.7.bur.8))
mise.hf.ti.r.bur.128 <- colMeans(rbind(mise.hf.ti.r.4.bur.128,
                                       mise.hf.ti.r.5.bur.128,
                                       mise.hf.ti.r.6.bur.128,
                                       mise.hf.ti.r.7.bur.128))
pdat1 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.bur.1,mise.BMSM.bur.1,mise.ash.bur.1))
pdat8 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.bur.8,mise.BMSM.bur.8,mise.ash.bur.8))
pdat128 <-
  data.frame(method=factor(rep(method.labels,each = m),method.labels),
             mise  =c(mise.hf.ti.r.bur.128,mise.BMSM.bur.128,mise.ash.bur.128))
create.violin.plots(pdat1,pdat8,pdat128)

Expand here to see past versions of bursts-violin-plots-1.png:

Version	Author	Date
5adee34	Peter Carbonetto	2018-12-21

Clipped Blocks data

This is the function used to simulate the “Clipped Blocks” data sets at different ranges of intensities:

pos   <- c(0.1,0.13,0.15,0.23,0.25,0.4,0.44,0.65,0.76,0.78,0.81)
hgt   <- 2.88/5 * c(4,-5,3,-4,5,-4.2,2.1,4.3,-3.1,2.1,-4.2)
mu.cb <- rep(0,n)
for (j in 1:length(pos))
  mu.cb <- mu.cb + (1 + sign(t - pos[j])) * (hgt[j]/2)
mu.cb[mu.cb < 0] <- 0
plot(t,mu.cb,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-cb-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Clipped Blocks simulations:

mise.cb.table <- cbind(mise.cb.1[methods],
                       mise.cb.8[methods],
                       mise.cb.128[methods])
rownames(mise.cb.table) <- table.row.names
colnames(mise.cb.table) <- table.col.names
print(xtable(mise.cb.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	307.80	137.28	6.82
BMSM	355.15	143.09	6.91
Haar-Fisz	632.21	338.55	29.72

The combined violin-boxplots provide a visualization of the same results:

mise.hf.ti.r.cb.1   <- colMeans(rbind(mise.hf.ti.r.4.cb.1,
                                      mise.hf.ti.r.5.cb.1,
                                      mise.hf.ti.r.6.cb.1,
                                      mise.hf.ti.r.7.cb.1))
mise.hf.ti.r.cb.8   <- colMeans(rbind(mise.hf.ti.r.4.cb.8,
                                      mise.hf.ti.r.5.cb.8,
                                      mise.hf.ti.r.6.cb.8,
                                      mise.hf.ti.r.7.cb.8))
mise.hf.ti.r.cb.128 <- colMeans(rbind(mise.hf.ti.r.4.cb.128,
                                      mise.hf.ti.r.5.cb.128,
                                      mise.hf.ti.r.6.cb.128,
                                      mise.hf.ti.r.7.cb.128))
pdat1 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.cb.1,mise.BMSM.cb.1,mise.ash.cb.1))
pdat8 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.cb.8,mise.BMSM.cb.8,mise.ash.cb.8))
pdat128 <-
  data.frame(method=factor(rep(method.labels,each = m),method.labels),
             mise  =c(mise.hf.ti.r.cb.128,mise.BMSM.cb.128,mise.ash.cb.128))
create.violin.plots(pdat1,pdat8,pdat128)

Bumps data

This is the function used to simulate the “Bumps” data sets at different ranges of intensities:

pos  <- c(0.1,0.13,0.15,0.23,0.25,0.4,0.44,0.65,0.76,0.78,0.81)
hgt  <- 2.97/5 * c(4,5,3,4,5,4.2,2.1,4.3,3.1,5.1,4.2)
wth  <- c(0.005,0.005,0.006,0.01,0.01,0.03,0.01,0.01,0.005,0.008,0.005)
mu.b <- rep(0, n)
for (j in 1:length(pos))
  mu.b <- mu.b + hgt[j]/((1 + (abs(t - pos[j])/wth[j]))^4)
plot(t,mu.b,xlab = "",ylab = "",type = "l")

Expand here to see past versions of plot-bumps-function-1.png:

Version	Author	Date
ed961b1	Peter Carbonetto	2018-12-20
2acee22	Peter Carbonetto	2018-12-20

This table summarizes the results from the Bumps simulations:

mise.b.table <- cbind(mise.b.1[methods],
                      mise.b.8[methods],
                      mise.b.128[methods])
rownames(mise.b.table) <- table.row.names
colnames(mise.b.table) <- table.col.names
print(xtable(mise.b.table,caption = " "),type = "html",
      html.table.attributes = "border=0")


	(1/100,3)	(1/8,8)	(1/128,128)
SMASH	2597.46	1194.62	141.21
BMSM	4036.77	1889.94	171.07
Haar-Fisz	3113.37	1658.74	184.66

The combined violin-boxplots provide a visualization of the same results:

mise.hf.ti.r.b.1   <- colMeans(rbind(mise.hf.ti.r.4.b.1,
                                     mise.hf.ti.r.5.b.1,
                                     mise.hf.ti.r.6.b.1,
                                     mise.hf.ti.r.7.b.1))
mise.hf.ti.r.b.8   <- colMeans(rbind(mise.hf.ti.r.4.b.8,
                                     mise.hf.ti.r.5.b.8,
                                     mise.hf.ti.r.6.b.8,
                                     mise.hf.ti.r.7.b.8))
mise.hf.ti.r.b.128 <- colMeans(rbind(mise.hf.ti.r.4.b.128,
                                     mise.hf.ti.r.5.b.128,
                                     mise.hf.ti.r.6.b.128,
                                     mise.hf.ti.r.7.b.128))
pdat1 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.cb.1,mise.BMSM.cb.1,mise.ash.cb.1))
pdat8 <-
  data.frame(method = factor(rep(method.labels,each = m),method.labels),
             mise   = c(mise.hf.ti.r.cb.8,mise.BMSM.cb.8,mise.ash.cb.8))
pdat128 <-
  data.frame(method=factor(rep(method.labels,each = m),method.labels),
             mise  =c(mise.hf.ti.r.cb.128,mise.BMSM.cb.128,mise.ash.cb.128))
create.violin.plots(pdat1,pdat8,pdat128)

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] xtable_1.8-2  cowplot_0.9.3 ggplot2_3.1.0
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.0        compiler_3.4.3    pillar_1.2.1     
#  [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
#  [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.6.0    
# [10] tools_3.4.3       digest_0.6.17     evaluate_0.11    
# [13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.2  
# [16] rlang_0.2.2       yaml_2.2.0        bindrcpp_0.2.2   
# [19] withr_2.1.2       stringr_1.3.1     dplyr_0.7.6      
# [22] knitr_1.20        rprojroot_1.3-2   grid_3.4.3       
# [25] tidyselect_0.2.4  glue_1.3.0        R6_2.2.2         
# [28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
# [31] whisker_0.3-2     backports_1.1.2   scales_0.5.0     
# [34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.4-0 
# [37] labeling_0.3      stringi_1.2.4     lazyeval_0.2.1   
# [40] munsell_0.4.3     R.oo_1.21.0

This reproducible R Markdown analysis was created with workflowr 1.1.1

Plots and tables summarizing results of Poisson simulations

Zhengrong Xing, Peter Carbonetto and Matthew Stephens

Analysis settings

Set up environment

Load results

Spikes data

Angles data

Heavisine data

Bursts data

Clipped Blocks data

Bumps data

Session information