Estimating the speed of light using normal model BDA3 p. 66
ggplot2, and gridExtra are used for plotting, tidyr for manipulating data frames
library(ggplot2)
theme_set(theme_minimal())
library(gridExtra)
library(tidyr)
library(rprojroot)
root<-has_file(".BDA_R_demos_root")$make_fix_file()
Data
y <- read.table(root("demos_ch3","light.txt"))$V1
Sufficient statistics
n <- length(y)
s2 <- var(y)
my <- mean(y)
Positive values only
y_pos <- y[y > 0]
Sufficient statistics
n_pos <- length(y_pos)
s2_pos <- var(y_pos)
my_pos <- mean(y_pos)
Compute the density of mu in these points
tl1 <- c(18, 34)
df1 <- data.frame(t1 = seq(tl1[1], tl1[2], length.out = 1000))
Compute the exact marginal density for mu
# multiplication by 1./sqrt(s2/n) is due to the transformation of variable
# z=(x-mean(y))/sqrt(s2/n), see BDA3 p. 21
df1$pm_mu <- dt((df1$t1 - my) / sqrt(s2/n), n-1) / sqrt(s2/n)
Compute the exact marginal density for mu for the positive data
df1$pm_mu_pos = dt((df1$t1 - my_pos) / sqrt(s2_pos/n_pos), n_pos-1) / sqrt(s2_pos/n_pos)
Create a histogram of the measurements
p1 <- ggplot() +
geom_histogram(aes(y), binwidth = 2, fill = 'steelblue', color = 'black') +
coord_cartesian(xlim = c(-42, 42)) +
scale_y_continuous(breaks = NULL) +
labs(title = 'Newcomb\'s measurements', x = 'y')
Create a plot of the normal model
# pivot the data points into key-value pairs
df2 <- df1 %>% pivot_longer(cols = !t1, names_to="grp", values_to="p")
# legend labels
labs2 <- c('Posterior of mu', 'Posterior of mu given y > 0', 'Modern estimate')
p2 <- ggplot(data = df2) +
geom_line(aes(t1, p, color = grp)) +
geom_vline(aes(xintercept = 33, color = 'q'),
linetype = 'dashed', show.legend = F) +
coord_cartesian(xlim = c(-42, 42)) +
scale_y_continuous(breaks = NULL) +
labs(title = 'Normal model', x = 'mu', y = '') +
scale_color_manual(values = c('blue', 'darkgreen', 'black')) +
guides(color="none") +
annotate("text", x=24, y=0.26, label=labs2[1], hjust="right", size=5) +
annotate("text", x=26, y=0.58, label=labs2[2], hjust="right", size=5) +
annotate("text", x=32, y=0.7, label=labs2[3], hjust="right", size=5)
Combine the plots
grid.arrange(p1, p2)
![](data:image/png;base64,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)
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