NaiveBayes

# Install and load the required package
#install.packages("e1071")
library(e1071)

# Create the dataset
data <- data.frame(
  Charges_Filed = c('y', 'n', 'n', 'n', 'n', 'n', 'y', 'y', 'n', 'y'),
  Company_Size = c('small', 'small', 'large', 'large', 'small', 'small', 'small', 'large', 'large', 'large'),
  Status = c('truthful', 'truthful', 'truthful', 'truthful', 'truthful', 'truthful', 'fraudulent', 'fraudulent', 'fraudulent', 'fraudulent')
)

# Fit the naive Bayes model without Laplace smoothing
model <- naiveBayes(Status ~ ., data = data)

model

## 
## Naive Bayes Classifier for Discrete Predictors
## 
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
## 
## A-priori probabilities:
## Y
## fraudulent   truthful 
##        0.4        0.6 
## 
## Conditional probabilities:
##             Charges_Filed
## Y                    n         y
##   fraudulent 0.2500000 0.7500000
##   truthful   0.8333333 0.1666667
## 
##             Company_Size
## Y                large     small
##   fraudulent 0.7500000 0.2500000
##   truthful   0.3333333 0.6666667

# Fit the naive Bayes model with Laplace smoothing
model2 <- naiveBayes(Status ~ ., data = data,laplace =1)

model2

## 
## Naive Bayes Classifier for Discrete Predictors
## 
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
## 
## A-priori probabilities:
## Y
## fraudulent   truthful 
##        0.4        0.6 
## 
## Conditional probabilities:
##             Charges_Filed
## Y                    n         y
##   fraudulent 0.5000000 1.0000000
##   truthful   1.0000000 0.3333333
## 
##             Company_Size
## Y                large     small
##   fraudulent 1.0000000 0.5000000
##   truthful   0.5000000 0.8333333

# Predict the probabilities for the dataset
predictions <- predict(model, data, type = "raw")
predictions2 <- predict(model2, data, type = "raw")

# Print the predictions
print(predictions) # Without Laplace

##       fraudulent  truthful
##  [1,] 0.52941176 0.4705882
##  [2,] 0.06976744 0.9302326
##  [3,] 0.31034483 0.6896552
##  [4,] 0.31034483 0.6896552
##  [5,] 0.06976744 0.9302326
##  [6,] 0.06976744 0.9302326
##  [7,] 0.52941176 0.4705882
##  [8,] 0.87096774 0.1290323
##  [9,] 0.31034483 0.6896552
## [10,] 0.87096774 0.1290323

print(predictions2) # With Laplace

##       fraudulent  truthful
##  [1,]  0.5454545 0.4545455
##  [2,]  0.1666667 0.8333333
##  [3,]  0.4000000 0.6000000
##  [4,]  0.4000000 0.6000000
##  [5,]  0.1666667 0.8333333
##  [6,]  0.1666667 0.8333333
##  [7,]  0.5454545 0.4545455
##  [8,]  0.8000000 0.2000000
##  [9,]  0.4000000 0.6000000
## [10,]  0.8000000 0.2000000