bayes theorem Algorithm
Bayes' Theorem, named after Reverend Thomas Bayes, is a fundamental concept in probability theory and statistics that describes the relationship between conditional probabilities. It provides a way to update prior beliefs or probabilities based on new evidence, allowing for more accurate and informed decision-making. The theorem is expressed mathematically as P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) represents the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In practical applications, Bayes' Theorem is commonly used in machine learning, data science, and artificial intelligence for tasks like classification, prediction, and diagnostics. The algorithm based on this theorem, known as the Bayesian Classifier or Naive Bayes Classifier, is a simple yet powerful technique that assumes independence between features to predict the class of an input data point. It has been widely used in various fields, including natural language processing, spam filtering, medical diagnosis, and recommender systems, providing a solid foundation for more advanced probabilistic models and techniques.
#include <iostream>
// bayes' theorem > https://en.wikipedia.org/wiki/Bayes%27_theorem
// bayes' theorem allows one to find P(A|B) given P(B|A)
// or P(B|A) given P(A|B) and P(A) and P(B)
// note P(A|B) is read 'The probability of A given that the event B has occured'
// returns P(A|B)
double bayes_AgivenB(double BgivenA, double A, double B) {
return (BgivenA * A) / B;
}
// returns P(B|A)
double bayes_BgivenA(double AgivenB, double A, double B) {
return (AgivenB * B) / A;
}
int main() {
double A = 0.01;
double B = 0.1;
double BgivenA = 0.9;
double AgivenB = bayes_AgivenB(BgivenA, A, B);
std::cout << "A given B = " << AgivenB << std::endl;
std::cout << "B given A = " << bayes_BgivenA(AgivenB, A, B) << std::endl;
return 0;
}
