In hcrews47/Bayes: Basic functions involving Bayes Theorem

knitr::opts_chunk$set(echo = TRUE)
library(ggplot2)
library(Bayes)

Overview

The Bayes package allows the user to implement lightweight and easy to use functions that calculate and chart conditional probabilities using Bayes Theorem.

Here is Bayes Theorem: $$ P(X \mid Y) = \frac{P(Y \mid X) \, P(X)}{P(Y)} $$

Installation

# The package is currently only available on gitHub

# First install the "devtools" package from CRAN if you have not already done so and then load this 
# package. From the "devtools" package, use the "install_github" function to install the Bayes package

install.packages("devtools")
library(devtools)
install_github("hcrews47/Bayes")

Usage

There are three functions in this Bayes Package: bayes_theor, bayes_theor_extended, and bayes_theor_pie. Each function is tailored to a specific aspect of the utilization of Bayes Theorem.

bayes_theor()

bayes_theor(x, y, cond_xy) is the most basic function within the package. bayes_theor() calculates the conditional probability of y given x. This function requires 2 parameters and has an optional third parameter that is only necessary if a conditional probability for x given y is already given. Otherwise, bayes_theor() assumes that the probabilities for x and y are independent of one another and calculates y givenx with this assumption.

# In this example the probability of x is .1, the probability of y is .05

# default third parameter:
bayes_theor(.1, .05)

# third parameter changed with the probability of x given y as .07:
bayes_theor(.1, .05, .07)

bayes_theor_extended()

bayes_theor_extended(x, y) is a more general application of Bayes Theorem; it takes a vector x that is a partition of probabilities and a probability y as input and returns a vector of conditional probabilities of each value x given y. bayes_theor_extended(x, y) always assumes that the partition y and the probability x are independent of one another.

This form of Bayes Theorem is shown here:

$$P(A_{i}\mid B)={\frac {P(B\mid A_{i})\,P(A_{i})}{\sum \limits {j}P(B\mid A{j})\,P(A_{j})}}\cdot$$

# In this example the probabilities of the partition x are given as a vector c(.2, .4, .4) and the 
# probability of y is .3

bayes_theor_extended(c(.2, .4, .4), .3)

bayes_theor_pie()

The final function in this Bayes Package, bayes_theor_pie(), fundamentally calculates the conditional probability in the same way as the bayes_theor() function, but instead of just returning the probability of the conditional requrested, bayes_theor_pie() draws a pie chart visualization of the probability of the conditional, a portion of which is the likelihood of the conditional and a portion is the unlikelihood of the conditional. bayes_theor_pie() depends on the "ggplot2" package to draw the pie chart.

# This example uses the same probabilities as the example for bayes_theor()

# default third parameter:
bayes_theor_pie(.1, .05)

# third parameter changed with the probability of x given y as .07:
bayes_theor_pie(.1, .05, .57)