# Bayes Theorem

## In order to determine where a student would go in Simscript, we needed to assign it attributes. These attributes would determine its mental health needs and determine whether or not the student would go to Let’s Talk.

We decided to use the naive Bayes probability model. The principle of Bayes theorem states that prior probabilities of items can be used to assign a classification to that item. The prior probabilities should be for characteristics that have high independence, hence the name “naive”. It is used in a number of situations to determine classifications of objects in different categories. The reason that we decided to use naïve Bayes because of the nature of mental health and the way that Simscript works. Since we assign attributes such as gender, year, and school to a student, those attributes can be considered the prior probabilities and that the classification we are determining is whether a student attends Let’s Talk. In this way, we use the following equation and defined C to be either a crisis state or A3N and x to be defined as the characteristics of gender, year, and school:

Naive Bayes equation with multiple variables.

After we determined this equation, we realized we needed to define p(characteristic | crisis) or p(characteristic | A3N). Because of that, we used the following Bayes equation:

In this case, C is defined as the characteristic (either gender, year, or school) and x is defined as crisis or A3N. From our data, we had the information that defined p(crisis | characteristic) which represents the quantity p(x | C). This information can be shown in the table below.

 Characteristic Did you suffer from a crisis, and seek help from campus resources? Score at or above a 3.5 but do not identify as having mental health problems? Yes Yes Year Freshmen 7.22% 4.12% Sophomore 9.09% 5% Junior 6.25% 1.04% Senior 5.83% 0.83% School Art/Architecture 3.70% 0% ArtSci 8.25% 2.97% Engineering 5.56% 3.70% Olin 0% 0% Gender Male 3.81% 2.86% Female 7.79% 2.56% Other 20% 0%