Homework_4_AH_EP.Rmd

---
title: "Homework_4"
author: "Andrea Hemmelmann - Eric Parra"
date: "2 de diciembre de 2018"
output: html_document
runtime: shiny
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Homework Nº4 - Bayes' Rule / Shiny app

## Task

Design and upload a Shiny App with R Markdown explaining Bayes’ Rule with an 
example from the field of natural hazards and disasters. Use the interactive
functions to allow different input values. Explain the example in your
own words.

### Example from the field of natural hazards and disaster

Magician Michelle says that she can predict large megathrust earthquakes… well, 
at least 95% of the time. Assume that these earthquakes occur with a probability 
of 10−5. How likely will Michelle cause a false alarm with her next prediction?

As in the last homework (Homework Nº3), this problem can be solve by using the 
Bayes' Rule:

Bayes' rule = p(H|D) = (p(D|H)) p(H)) / p(D)

Where p(D)= (p(D|H)) p(H)) + (p(D|H_f)) p(H_o))

E= A large megathrust earthquake occur
p(E)= 0.00001
NE=  A large megathrust earthquake does not occur
p(NE)=0.99999
M= Magician Michelle is right
p(M)= 0.95
NM= Michelle is wrong
p(NM)= 0.05

p(M|E)= (p(M)*p(E)) / p(M)*p(E)+ p(NM)*p(NE)

As a result we obtained a probability (that Michelle is right) of 0.00019. This 
result is very low because, although Michelle's percentage of success is 
high, the probability of occurrence of a large megathrust earthquake is very low
(0.0001)

Therefore, the probability of Michelle is wrong (and then she cause a false 
alarm) is 1 - 0.0019= 0.099981. 

Now, we make a Shiny app in which it is possible to change the values of both
the probability of occurrence of a large megathrust eartquake and/or the 
reliability values in the Michelle's prediction.

```{r}

library(shiny)

# First we lay out the user interface with an UI object (controls the layout and
#appearence of app)

ui <- fluidPage(
  
     # Application title
   titlePanel("Probability of a large megathrust earthquake's false alarm based
on the prediction of a magician"), 
  
# Sidebar
   sidebarLayout(
     sidebarPanel(
       numericInput("E",
                "Probability that a large megathrust earthquake occur",
                min = 0,
                max = 1,
                value = 0.00001, #default value
                step = 0.00001), #Interval to use when stepping between min 
    #and max
       
       numericInput("M",
                "Reliability of Michelle's prediction ",
                     min = 0,
                     max = 1,
                     value = 0.95, #default value
                     step = 0.05) #Interval to use when stepping between min 
    #and max

     ),
   
# Show the result in the main panel (right side of layout)
      mainPanel(
        textOutput(outputId = "NM") # output variable to read the value from
      )
   )
)

# Then, we defined the server function that contains instructions needed to 
#build the app (it defines the relationship between inputs and outputs)

server <- function(input, output){
  
  output$NM <- renderText({
     NM <-(1-((input$M*input$E) / ((input$M*input$E)+(1-input$M*1-input$E))))
   })
}
  
#Finally, we called to the shiny app function

shinyApp(ui = ui, server = server)
  
```