Bayes theorem formula necessarily introduces a structural format for calculating conditional probability. This formula is basically a gradual calculation in a principled way that helps various machine learning ambits. The formula for Conditional probability is the key to reaching at the conclusion and helps in the basic calculation. Bayes theorem is one of the most powerful yet handy tools for conditional probability. It can also be seen usually in calculating the Naïve Bayes formula, Posterior probability and Bayesian classifiers. 

In this article, we are going to understand that what exactly the Bayes theorem in machine learning is, the formula for conditional probability, Bayes theorem formula, Bayes theorem probability, Bayes theorem examples, Bayesian rule, Conditional probability example, Posterior probability, Bayesian classifiers, Naïve Bayes theorem.

  1. Bayes Theorem of Conditional Probability
  2. Naming the terms in the theorem
  3. Worked Example for Calculating Bayes Theorem In Machine Learning
  4. Bayes Theorem for modelling Hypotheses
  5. Bayes Theorem for Classification
  6. More uses of Bayes Theorem in Machine Learning

1. Bayes Theorem of Conditional Probability

P(A/B) = P(B/A) P(A)/ P(B)

Bayes theorem is standing on the 3 probabilities i.e.  

  • Marginal Probabilities: Probabilities based on a particular event and not on random variables. It uses the sum rule for finding the probability by adding the two variables to get the outcome. P(A) is an example of marginal Probabilities.
  • Joint Probabilities: Probabilities of the happening of two events on the same event of time. P (A, B) is the set example.

P (A, B) = P(A/B) * P(B)

This shows that the joint probability is symmetrical in nature.

P (A, B) = P (B, A)

  • Conditional Probabilities: Probabilities that gives the occurrence of another event simultaneously are conditional probabilities. P (A/B) is an example. It can be calculated using the formula of joint probability, as mentioned below.

P (A/B) = P (A, B) / P(B) 

It is not symmetrical in nature.

P(A/B)! = P (B/A)

These probabilities will help in understanding the base of the above-mentioned theorem.

(do refer to the above-mentioned formula for understanding the examples)

2. Naming the terms in the theorem

Bayes theorem in machine learning has given multiple names according to their place of uses in the various equations. This type of categorization is helpful to get more command over understanding the formula more bitterly with more perfection.

Some of the names as categorized are P (A/B), which is related to the posterior probability, and P (A) is referred to as the prior probability. 

P(B|A) is marked as ‘likelihood’, and P(B) is mentioned as the ‘evidence’.

Hence, the new formula formed looks like: – Posterior = Likelihood * Prior / Evidence

3. Worked Example for Calculating Bayes Theorem In Machine Learning

Bayes theorem formula can be better understood with some live working examples having real numbers to represent the calculations. For this, we will take the help of Diagnostic Test Scenario, Python-related code calculation, Binary Classifier Terminology and Manual Calculation. 

4. Bayes Theorem for modelling Hypotheses

Bayes theorem is used as a handy tool which is used in the field of machine learning and python coding. A machine learning algorithm is, however, a more formatting way of structuring the relationship of data by keeping hypothetical data relationships. For example, input X and output Y in the above said formula. 

However, the Bayes theorem is quite harsh on the hypothetical field on the given dataset. For instance, P(h/D) = P(D/h) * P(h)/ P(D)

Here, in the above-mentioned structure, data (D) remains constant because of its use in every assessment of each hypothesis. To remove the basic unstructured estimated solution, D is left constant. This is the ultimate aim of the Bayes theorem formula to identify and use a hypothesis that gives a better explanation to the identifies data.

5. Bayes Theorem for Classification

Bayes theorem classification is an assumption-based modelling problem that includes allotting a label to a given output & input data sample.

The above statement can be better understood by the following Bayesian theorem example: –

P (class| data) = (P (data |class) * P(class)) / P(data)

Here, P (class| data) = class probability in the given data.

For every class, this formula will be used and came into the light to find the largest assigned probability, which can be selected and allotted for the data input.

The term (P (data |class) in the above structure is based on conditional probability observations. It can only be used when the numbers are in big amount or counting. For smaller terms and numbers, the assigned probability is used, and for counting bigger outputs, conditional probability is used. But always having a bigger digit is merely a chance and hardly come to the practical life. Hence, in some dimensions and phases, the Bayes theorem formula is insufficient for the coverage.

Although, with the emergence of time, there is the solution for this conditional probability has been already prepared. Some of them are Naïve bayes formula, Naïve bayes theorem, Bayesian classifiers.

6. More uses of Bayes Theorem in Machine Learning

Bayesian Classifiers are one of the key feature dimensions where the Bayes theorem formula ambit fit perfectly in machine learning. Talking about in brief and understanding the uses more precisely, these models are divided into two grounds.

1. Bayesian Optimization

It gives a more structured technique-based concept having its root related to the Bayes theorem in machine learning, providing a global view that is relatively more efficient and effective. It is used in some other fields, including hyperparameters pf some pre-defined models. 

2. Bayesian Causal Models 

This is a system of calculating probabilities by defining the relationship between one or more variable terms. It is a corrective remedy for the conditional models, which requires a large piece of data and big chunks of digits and numerical terminology. It simply simplifies the variables by breaking them down into smaller quantities.


In this article, the writer has tried to throw light on each and every dimension related to the Application of Bayes theorem, Bayes theorem probability, Bayes theorem examples and Bayesian rule.

Also, the readers, after reading the article, can easily able to answer the following topics and terms related to the 

  • Bayes Theorem of Conditional Probability.
  • Bayes Theorem for Classification.
  • Worked Example and uses for Calculating Bayes Theorem.
  • More uses of Bayes Theorem in Machine Learning.

There are no right or wrong ways of learning AI and ML technologies – the more, the better! These valuable resources can be the starting point for your journey on how to learn Artificial Intelligence and Machine Learning. Do pursuing AI and ML interest you? If you want to step into the world of emerging tech, you can accelerate your career with this Machine Learning And AI Courses by Jigsaw Academy.



Are you ready to build your own career?