# This is the user-interface definition of a Shiny web application.
# You can find out more about building applications with Shiny here:
#
# http://shiny.rstudio.com
#
library(shiny)
shinyUI(fluidPage(
# Application title
titlePanel("Bayesian priors: beta and binomial"),
# Sidebar with a slider input for number of bins
fluidRow(
p("In Bayesian Statistics, we use prior information (gathered
from previous research, intuition, or well-informed hypotheses)
as part of our statistical formulation. This document focuses on
working with a prior for the parameter p in a Binomial(n,p) distribution.
The beta distribution is the conjugate prior for the Binomial,
because we start with a beta prior distribution, utilize the likelihood from our experiment,
then end up with a beta posterior distribution that uses both the prior
and the experimental likelihood.")),
fluidRow(
column(4,plotOutput("betapriorPlot")),
column(4,plotOutput("binlikPlot")),
column(4,plotOutput("betapostPlot"))),
fluidRow(
column(4,sliderInput("alpha",
"Alpha Parameter:",
min = 0.1,
max = 5,
value = 1,
step=0.1),
sliderInput("beta",
"Beta Parameter:",
min = 0.1,
max = 5,
value = 1,
step=0.1)),
column(4,sliderInput("n",
"Number of trials for the binomial:",
min = 1,
max = 100,
value = 1,
step=1),
htmlOutput("sUI")),
column(4)
),
fluidRow(
p("As you can see, you can choose a Beta distribution that looks like what you expect
the distribution of p to look like. We start with a default beta of (1,1), which is
equivalent to a Uniform(0,1) prior on p, but you set the prior distribution to whatever you'd like."),
p("Note how the Posterior likelihood follows a Beta (alpha + s,beta + n - s) distribution. "))
)
)
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