diff --git a/demos_ch2/demo2_4.html b/demos_ch2/demo2_4.html index 6deb7ec..0ad844e 100644 --- a/demos_ch2/demo2_4.html +++ b/demos_ch2/demo2_4.html @@ -11,10 +11,23 @@ - + Bayesian data analysis demo 2.4 + @@ -241,7 +254,7 @@ $(this).detach().appendTo(div); // add a show code button right above - var showCodeText = $('' + (showThis ? 'Hide' : 'Code') + ''); + var showCodeText = $('' + (showThis ? 'Hide' : 'Show') + ''); var showCodeButton = $(''); showCodeButton.append(showCodeText); showCodeButton @@ -267,7 +280,7 @@ // * Change text // * add a class for intermediate states styling div.on('hide.bs.collapse', function () { - showCodeText.text('Code'); + showCodeText.text('Show'); showCodeButton.addClass('btn-collapsing'); }); div.on('hidden.bs.collapse', function () { @@ -394,8 +407,8 @@ border-radius: 4px; } -.tabset-dropdown > .nav-tabs > li.active:before { - content: ""; +.tabset-dropdown > .nav-tabs > li.active:before, .tabset-dropdown > .nav-tabs.nav-tabs-open:before { + content: "\e259"; font-family: 'Glyphicons Halflings'; display: inline-block; padding: 10px; @@ -403,16 +416,9 @@ } .tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before { - content: ""; - border: none; -} - -.tabset-dropdown > .nav-tabs.nav-tabs-open:before { - content: ""; + content: "\e258"; font-family: 'Glyphicons Halflings'; - display: inline-block; - padding: 10px; - border-right: 1px solid #ddd; + border: none; } .tabset-dropdown > .nav-tabs > li.active { @@ -469,14 +475,14 @@

Bayesian data analysis demo 2.4

Aki Vehtari, Markus Paasiniemi

-

2022-08-29

+

2023-11-07

Probability of a girl birth given placenta previa (BDA3 p. 37).

-

Calculate the posterior distribution on a discrete grid of points by multiplying the likelihood and a non-conjugate prior at each point, and normalizing over the points. Simulate samples from the resulting non-standard posterior distribution using inverse cdf using the discrete grid.

+

Calculate the posterior distribution on a discrete grid of points by multiplying the likelihood and a non-conjugate prior at each point, and normalizing over the points. Simulate draws from the resulting non-standard posterior distribution using inverse cdf using the discrete grid.

ggplot2 and gridExtra are used for plotting, tidyr for manipulating data frames

library(ggplot2)
 theme_set(theme_minimal())
@@ -490,7 +496,7 @@ 

Evaluating posterior with non-conjugate prior in grid

b <- 543

Evaluate densities at evenly spaced points between 0.1 and 1

df1 <- data.frame(theta = seq(0.1, 1, 0.001))
-df1$con <- dbeta(df1$theta, a, b)
+df1$con <- dbeta(df1$theta, a+1, b+1)

Compute the density of non-conjugate prior in discrete points, i.e. in a grid this non-conjugate prior is the same as in figure 2.4 in the book

pp <- rep(1, nrow(df1))
 pi <- sapply(c(0.388, 0.488, 0.588), function(pi) which(df1$theta == pi))
@@ -500,7 +506,7 @@ 

Evaluating posterior with non-conjugate prior in grid

normalize the prior

df1$nc_p <- pp / sum(pp)

compute the un-normalized non-conjugate posterior in a grid

-
po <- dbeta(df1$theta, a, b) * pp
+
po <- dbinom(a, a+b, df1$theta) * pp

normalize the posterior

df1$nc_po <- po / sum(po)

Plot posterior with uniform prior, non-conjugate prior and the corresponding non-conjugate posterior

@@ -518,7 +524,7 @@

Evaluating posterior with non-conjugate prior in grid

coord_cartesian(xlim = c(0.35,0.6)) + scale_y_continuous(breaks=NULL) + labs(x = '', y = '')
-

+

Inverse cdf sampling

@@ -536,7 +542,7 @@

Inverse cdf sampling

# sapply function for each sample r. The returned values s are now # random draws from the distribution. s <- sapply(r, invcdf, df1) -

Create three plots: p1 is the posterior, p2 is the cdf of the posterior and p3 is the histogram of posterior samples (drawn using inv-cdf)

+

Create three plots: p1 is the posterior, p2 is the cdf of the posterior and p3 is the histogram of posterior draws (drawn using inv-cdf)

p1 <- ggplot(data = df1) +
   geom_line(aes(theta, nc_po)) +
   coord_cartesian(xlim = c(0.35, 0.6)) +
@@ -550,15 +556,15 @@ 

Inverse cdf sampling

p3 <- ggplot() + geom_histogram(aes(s), binwidth = 0.003) + coord_cartesian(xlim = c(0.35, 0.6)) + - labs(title = 'Histogram of posterior samples', x = '', y = '') + + labs(title = 'Histogram of posterior draws', x = '', y = '') + scale_y_continuous(breaks = NULL) # combine the plots grid.arrange(p1, p2, p3)
-

+

-
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+
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PSAnSGlzdG9ncmFtIG9mIHBvc3RlcmlvciBkcmF3cycsIHggPSAnJywgeSA9ICcnKSArCiAgc2NhbGVfeV9jb250aW51b3VzKGJyZWFrcyA9IE5VTEwpCiMgY29tYmluZSB0aGUgcGxvdHMKZ3JpZC5hcnJhbmdlKHAxLCBwMiwgcDMpCmBgYAoK