Bayesian and Naive Bayesian

British mathematician. 1702 was born in London. Bayes mainly studied probability theory in mathematics and made contributions to statistical decision function, statistical inference and statistical estimation. His statistical probability theory is called Bayesian Thomas Bayes. Before Bayes wrote this article, people could already calculate the "positive probability", for example, "Suppose there are n white balls and m black balls in the bag, if you reach in and touch them, the probability of finding the black ball is M/(M+N)". A natural question is the other way around: "If we don't know the proportion of black and white balls in the bag in advance, but touch out one (or several) balls with our eyes closed and observe the colors of these balls, then we can make some guesses about the proportion of black and white balls in the bag." This problem is called the inverse probability problem. Bayesian is born to solve this inverse probability.

P(An|B) = p(An) p(B|An)/p(B)

Formula application:

It is known that * * * has 100 emails, including 70 normal emails and 30 spam emails. The word' part-time job' appears 10 times in ordinary mail and 20 times in spam.

Need to be solved: What is the probability that an email containing the word' part-time job' is spam?

P (garbage | part-time job) =p (garbage) p (part-time job | garbage) /p (part-time job)

P (spam) = 30/(70+30)=0.3

P (part-time job) = (10+20)/ 100=0.3

P (part-time | spam) = 20/30

P (garbage | part-time job) =0.3*0.67/0.3=0.67

Naive Bayes is a simple but extremely powerful prediction modeling algorithm, so it is called Naive Bayes because every feature he assumes is independent.

For example:

Simplified to: