Bayesian inferenceExample E of section 3.5 of Rice 3rd edition, page 94-95 beta prior, likelihood is binomial, posterior is beta See Figure 3.16 for results from a beta(1, 1) prior and 13 successes out of 20 attempts |
shinyServer(function(input, output) {
output$distPrior <- renderPlot({
require(mosaic)
trellis.par.set(theme=theme.mosaic())
print(plotDist('beta', params=list(input$alpha, input$beta),
main="Prior distribution", xlim=c(0, 1), lwd=2))
})
output$distPost <- renderPlot({
require(mosaic)
trellis.par.set(theme=theme.mosaic())
print(plotDist('beta',
params=list((input$alpha + input$y), (input$beta + input$n - input$y)),
main="Posterior distribution", xlim=c(0, 1), lwd=2))
})
}
)
library(shiny)
shinyUI(fluidPage(
# Application title
titlePanel("Bayesian inference"),
p("Example E of section 3.5 of Rice 3rd edition, page 94-95"),
p("beta prior, likelihood is binomial, posterior is beta"),
p("See Figure 3.16 for results from a beta(1, 1) prior and 13 successes out of 20 attempts"),
sidebarLayout(
sidebarPanel(
numericInput("alpha", "alpha parameter for Beta prior:", 1,
min = 1, max = 100),
numericInput("beta", "beta parameter for Beta prior:", 1,
min = 1, max = 100),
numericInput("y", "number of successes observed:", 13,
min = 1, max = 100),
numericInput("n", "out of this many trials (must be larger than # successes):", 20,
min = 1, max = 100)),
# Show a plot of the generated distribution
mainPanel(plotOutput("distPrior"),
plotOutput("distPost"))
)
))