Baes’ Theorem is a statistical theory which enables the calculation of posterior probability from prior knowledge. It was named after the English mathematician Thomas Bayes, who developed the theorem in 1763. The theorem has been used in various fields, such as machine learning, natural language processing, and medical diagnosis. This article will discuss the basics of Bayes’ Theorem and its application in various fields.
Bayes’ Theorem is a way of calculating the probability of an event based on prior knowledge of conditions that might be related to the event. It is expressed as:
P(A|B) = P(B|A)P(A) / P(B)
Where P(A|B) is the posterior probability; P(B|A) is the likelihood of B given A; P(A) is the prior probability; and P(B) is the marginal probability.
In machine learning, Bayes’ Theorem is used to calculate the probability of a certain hypothesis given the evidence. For example, if a machine learning algorithm is trained to recognize cats, it can use Bayes’ Theorem to calculate the probability of a certain image containing a cat, given the evidence of the image.
In natural language processing, Bayes’ Theorem is used to calculate the probability of a certain sentence given the evidence of the words in the sentence. For example, if a natural language processing algorithm is trained to recognize sentences with a positive sentiment, it can use Bayes’ Theorem to calculate the probability of a certain sentence having a positive sentiment, given the evidence of the words in the sentence.
In medical diagnosis, Bayes’ Theorem is used to calculate the probability of a certain disease, given the evidence of the patient’s symptoms. For example, if a patient presents with a fever, a doctor can use Bayes’ Theorem to calculate the probability of the patient having a certain disease, given the evidence of the fever.
In conclusion, Bayes’ Theorem is a useful statistical theory which enables the calculation of posterior probability from prior knowledge. It has been used in various fields, such as machine learning, natural language processing, and medical diagnosis.
References
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Boca Raton: Chapman & Hall/CRC.
McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and Stan (2nd ed.). CRC Press.
Peters, J. (2017). Bayesian methods for hackers: Probabilistic programming and Bayesian inference. Addison-Wesley Professional.