# Application of Bayes Theorem in R

Application of Bayes Theorem, Bayes’ theorem describes the likelihood of an event occurring in relation to any condition. It is also considered in the case of conditional probability.

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The Bayes theorem is sometimes known as the “causes probability formula.”

The Bayes’ Theorem is one of the most important principles in statistics, and it’s a must-know for data scientists.

Learn about Bayes’ Theorem, how it works, and the many and varied uses it has.

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Bayes Theorem defined as,

`P(A|B) = P(A)*P(B|A) / P(B)`

where:

P(A|B): Given event B, the probability of event A has occurred.

P(B|A): Given that event A has occurred, the probability of occurrence B.

P(A): The probability of event A.

P(B): The probability of event B.

## Application of Bayes Theorem

The Bayes’ Theorem has a wide range of applications in the real world. To begin, simply understanding how it works is sufficient.

Bayesian Decision Theory is a statistical approach to the problem of pattern classification. In this theory, the underlying probability distribution for the categories is assumed to be known.

As a result, we now have an ideal Bayes Classifier against which all other classifiers are judged.

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The following are the three most common applications of the Bayes theorem

1) Bayes’ Naive Classifiers

2) Decision Surfaces and Discriminant Functions

3) Estimation of Bayesian Parameters

We will not go into the intricacies of the above applications; instead, we will show you how to use the Bayes theorem in R.

Assume that there is a 20% chance of cloudy weather. Assume that the probability of a sunny day is 65 percent and that the probability of clouds on a sunny day is 30 percent.

What are the chances that it will be sunny on a given day if it is 20% cloudy outside?

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### Approach 1:- Based on Manual Calculation

p(cloudy) = 0.20

p(sunny) = 0.65

p(cloudy | sunny) = 0.30

Now we can calculate following conditions.

p(sunny | cloudy) = P(sunny) * P(cloudy | sunny) / P(cloudy)

p(sunny | cloudy) = (0.65 * 0.30) / 0.20

p(sunny | cloudy) = 0.975

Based on given conditions, there’s a 97.5 percent chance it’ll sunny that day.

To implement Bayes’ Theorem in R, we can write the following simple function:

```bayesTheorem <- function(pA, pB, pBA) {
pAB <- pA * pBA / pB
return(pAB)
}```

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### Approach 2: Bayes’ Theorem in R

Assume we have knowledge of the following probabilities:

p(sunny) = 0.65

p(cloudy) = 0.20

p(cloudy | sunny) = 0.30

We may use the following syntax to calculate p(sunny | cloudy):

```psunny <- 0.65
pcloudy <- 0.20
pcloudysunny <- 0.30```

Let’s make use of the function to calculate the conditional probability

`bayesTheorem(psunny, pcloudy, pcloudysunny)`
`0.975`

Based on certain conditions, the probability of it sunny day is 0.9The probability of a sunny day is 0.975 based on certain conditions.

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